Astronomia BRITANNICA, Exhibiting The Doctrine of the Sphere, and Theory of the Planets Decimally by Trigonometry, and by Tables.

Fitted for the Meridian of LONDON, according to the Copernican Systeme As it is illustrated by Bullialdus, and the easie way of Calculation, lately published by Doctor WARD.

By JOHN NEWTON, M: A:

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LONDON, Printed for the Author, by R. and W. Leybourn, and are to be sold by Thomas Pierrepoint, at the Sun in St. Pauls Church­yard, 1657.

To the Right Honourable ROBERT Earl of WARWICK, Baron of LEES, &c.

RIGHT HONOURABLE,

AS it were presumption in me, to think, that I have any thing in my selfe, that is worthy the presenting to your Honour: so it were injustice to keep from you, that which is your own; He that is once an Admiral, hath so great an interest in the Sea, that of necessity he must have some [...]n the Stars also, because Navigation without Astronomy is very lame and defective. The compass I know is the Sea-mans best di­rection [Page] when the weather is foul, but the Sun is found a better when it is faire, yea, serveth to correct the errors committed by the other; unlesse his place there­fore be rightly known, our Sea-men, how otherwise skilfull soever, will be many times troubled to steer their course a­right: This then (without prejudice to o­ther mens endeavors) is that which I aim at, and do believe I have effected, as with more ease, so also with more exactness, then those who have written before me, and that not only in relation to the Sun, but also to the Moon and other Planets, the truth of which Time only can disco­ver, & must be therefore waited for. And now that these endeavors of mine may in the mean while receive some shelter from the envious, through your Honors protection, is the humble suit of him that is

Your Honours to dispose of IOHN NEWTON.

To the Courteous READER.

Courteous Reader,

AS there is no part of Mathematicall learning more excellent, so is there none more difficult then this of Astronomy, it hath for some thou­sands of yeares been much studied, and not without great expence of treasure, brought to that perfection, in which we now enjoy it; nor can we ex­pect, that those mistakes, to which this noble Science is yet too often lyable, should ever be redressed, without the ex­pence of more, and hard it is to perswade the men of this earthly-minded age, to look higher then the earth they tread upon, and wallow in; they will not look so high as Heaven themselves, nor give encouragement unto those that would; but that our Students should neglect the benefit of that knowledg they might enjoy; that they should be in love with those difficulties they might avoid, in a study that is too intricate and difficult at the best, can never be sufficiently admired.

It is therefore our chief and principal aime to shew how [Page] much of trouble may be avoyded in computing the moti­ons of the heavenly bodies; if only the form of our Tables were changed from Sexagenary into Decimall, the excellen­cy of Decimal Arithmeticke will in part appeare, if wee but consider the manner of working, in our Sexagenary Canons of naturall Sines and Tangents, in which (to avoid the vast trouble, if not almost the impossibity of working with a Canon that should consist of vulgar Fractions) the Sine and Tangent of every minute is nothing else but the Decimall of a Unite; and this that famous Mathematician of our age Mr. Henry Brigges did well perceive, when (having perfe­cted that noble invention of Logarithms, first found out by the Right Honourable, John, Lord Neiper, Baron of Merchi­ston in Scotland) he tooke the paines to make a new Canon of Sines and Tangents, dividing the degrees into Decimals, as well as the parts of the Radius answering unto those de­grees; and according to which Canon, Mr. Henry Gille­brand did since prepare a Treatise of Astronomy for the Presse, but his death prevented the publication: To these I may adde Mr. William Oughtred, who is the present wonder of our age, for his extraordinary knowledge in this kind of learning, who in his Clavis Mathematica, doth not only wish that this Decimall form were observed in all Astronomical Ca­nons, but hath also lately professed, that he ever found so much trouble in the Sexagenary way, that he took the pains to turn the Equations in the Rudolphin Tables into Decimals before he used them; besides the trouble of Reduction this advantage our Decimal Tables have above the Sexagenary, that in finding the part proportional, the half of your work is done before you begin, there being a necessity both of Multiplication and Division, in Sexagenary numbers, but here of Multiplication onely, or onely of Division.

And now that this wonderful ease in calculation, com­mended [Page] to us by these famous men, might not still lie buried in oblivion, & that our Artists might be no longer enforced to use those labyrinthical Tables in the Sexagenary form, we have adventured to publish these, which never should have seene the light, if there had been any hope of those which Mr. Gillebrand did long since compose, or that Mr. Moore could have found encouragement to have published his; or that any other could have been perswaded to this Decimal form.

The ease then that is in the form of our Tables, is in truth the reason for which we have undergone this labour, and yet the method of Calculation, which Dr. Ward professor of Astronomy in Oxford hath lately published (in his Book en­tituled Inquisitio in Bullialdi Astronomiae Philolaicae fundamenta) and which we have used in the composure of our Tables, is so brief, so easie, and so exact, as that a better is not to be expected. I am not ignorant, that some (which have a de­sire to make others and themselves work) are not therewith satisfied, they will rather take the pains of seven or eight o­perations, and yet the aequation at last found, is not so legiti­mate as that wch here we find at one; of which there needs no other proof then the Geometry of our Method, our very Enemies being Judges; yet all that we shall promise is the places of the Planets prope rerum, at a cheaper rate; if we do fail of their true Phenomenon, it shall be with less trouble and expence of time. Our Middle-motions, Aphelions, Excen­tricities, and Dimensions of the several Orbs mentioned in the ensuing Treatise, we have borrowed from Bullialdus, the me­thod by which they are computed is the same in all, and therefore as to the Excentricities & Aphelions, we thought it sufficient to instance in the Sun or Earth: and for the pro­portions between the Earths Orb, and the Orbs of the other Planets with their angles of Inclination, we have given an [Page] Example in Saturn only, and refer you to Bullialdus for the rest. And although this method of his be not Geometrically true, yet knowing no better; we have contented our selves with his, untill there be a better found; and to make his Middle-motions to us more useful, we have reduced their E­poches to the Meridian of London, the most famous City of this our Island of Great Britain: For which reason, and for the easiness of the calculation which our own Country-man hath invented, and we here used, the Treatise it selfe doth carry the style of Astronomia Britannica.

And whether this method of finding the first inequality will agree with observation, cannot be known; until a Geo­metrical way of finding the Excentricities & Aphelions of the Planets in an Ellipsis be also propounded to us; and if at last, when all things in this Elliptical Astronomy shall geometrical­ly be demonstrated, the places of the Planets thus found shall not agree with observation, it will be hard to say in what particular the fault doth lie, and therefore we must not then impute it to the first inequality, much lesse now, when the Geometry of that is demonstrated, & other parts are defective, but a new Hypothesis must be thought of; and until this shall be effected, as there are no Tables extant, by which the places of the Planets can be computed with so much ease, so none can be expected, by which their places may be computed with more probability of truth, then by these which wee must now submit to thy censure, and do commend to thy perusal.

IOHN NEWTON.

The Contents of the severall Books or parts of Astronomia Britannica.

The first Book.
The Preface.
Page 1.
THe Suns greatest declination being given, to find his declination in any point of the Eclipticke
9
How to finde the declination of a Planet or fixed Star, with latitude
10
How to finde the Right Ascension of any point of the Eclipticke
13
How to finde the Right Ascension of a Planet or other Star with lati­tude
15
The elevat. of the Pole, & declin. of the Sun given, to find his amplit.
16
The Meridian altitude, and declination of the Sun, with the Poles ele­vation given to find his true place in the Zodiacke
17
Having the Meridian altitude of an unknown Star, and the distance thereof from a known Starre, to find the Right Ascension of the un­known Star
Ibid.
Having the declin. and Right Ascension of a Star given, to finde the longitude and latitude thereof
19
How to finde the Ascensionall difference
20
How to finde the Oblique Ascension or Descention of any point of the Eclipticke
21
The Poles elevation and the Suns declination being given, to finde his altitude at any time assigned
22
Having the Suns greatest declination, with his distance from the next Equinoctional point, to finde the Meridian angle, or intersection of the Meridian with the Eclipticke
26
To finde the angle of the Meridian, with the Horizon
Ibid.
The Poles elevation, with the Suns altitude and declination given, to finde his Azimuth
Ibid.
How to erect a Figure of Heaven
27
To find the angle of the Ecliptick with the horizon, or the altitude of the Nonagesime deg. together with its distance from the mid-heaven
36
To finde the Parallactical angle, or angle of the Ecliptick, with the ver­ticall circle
[...]7
[Page]The elevation of the Pole, and declination of the Sun given, to finde the time when he will be due East and West
39
The elevation of the Pole, with the Suns declination and altitude given, to finde his distance from the Meridian
40
To finde the time of the Suns rising and setting, with the length of the Day and Night
Ibid.
To finde the distance of a Star from the Meridian
41
To finde the elevation of the Pole above any circle of Position
Ibid.
Of the Arke of Direction what it is, and how to finde it
45
How to direct the Mid-heaven, and the Imum Coeli
46
How to direct the Ascendent, or Significator posited in the Signes ascending
Ibid.
How to direct a Significator, posited in the Signes descending
47
How to find the Arch of the Equator, whereby is made the generall Table of Positions
48
How by the generall Table of Positions to make a particular Table for any latitude there exprest
49
Of the doctrine of the Sphere in Tables
51
The second Book.
OF the yeare Civill and Astronomical
57
Of the Figure which the Planets describe in their Motion
66
Of the lines and method to be used for the finding of a Planets true lon­gitude from the Aphelion in this Figure
72
Of the proportion by which the motion of the Planets do increase from the Aphelion to the Perihelion
74
Of the inequality of the Earths annuall motion, and of the Diameter in which the Aphelion and Perihelion are placed
81
Of stating the Earths middle motions by sundry observations
90
To calculate the Suns true place and distance from the Earth
94
Of the Aequation of Civill Dayes
97
Of the Theory and motion of the Moon
98
To calculate the true motion of the Moon by Tables
109
To find the Moons true latitude and place in the Ecliptick
113
Of the motion of the fixed Starres
115
Of the motion of Saturn
116
Of the motion of Jupiter
121
Of the motion of Mars
124
Of the motion of Venus
128
Of the motion of Mercury
133
Of the Semidiameters of the Sun, Moon, and shadow of the Earth
136
[Page]Of the proportion and magnitude of the three great bodies, the Sunne, Moon, and the Earth
142
Of the proportion between the Orbs of the superiour and inferiour Pla­nets, and the Orbe of the Earth
144
To finde the mean Conjunction and Opposition of the Sun & Moon
151
To finde the true Opposition and Conjunction of the Sun and Moon
152
To finde whether there will be an Eclipse or not
154
To finde the quantity of a Lunar Eclipse
Ibid.
To finde the duration of a Lunar Eclipse, or the continuance of the totall darknesse, where the Eclipse is totall
155
To finde the Moons latitude at the beginning & end of the Eclipse
156
To finde the middle of the Eclipse or greatest darknesse
157
Of the calculation of the Suns Eclipse
159
To finde the Parallaxes of longitude and latitude
160
To finde the visible motion of the Moon from the Sun for any time as­signed
162
To find the time of the visible Conjunction of the Sun and Moon
Ibid.
To finde the visible latitude of the Moon, at the time of the visible Conjunction
163
To finde the quantity of a Solar Eclipse
164
To finde the beginning and ending of the Suns Eclipse
Ibid.
To finde the visible latitude of the Moon at the beginning and end of the Suns Eclipse
165
To delineat the Eclipses of the Sun and Moon
166
The use of the Table of Refractions
168
The Index of the Tables.
A View of the more notable Epochae
2
A Table shewing the Dominical Letter in both accompts
4
A Table shewing the Golden number & Epact in both accompts
Ibid.
The Anticipation of the Gregorian Kallender
Ibid.
A Table of moveable Feasts in both accompts
5
A Table of fixed Feasts
6
A Catalogue of Places, their latitudes and distance in longitude from the Meridian of London
8
A Table to convert Sexagenary minutes, seconds, thirds, fourths and fifths into Decimalls, and the contrary
10
A Table to convert the hours, minutes, seconds, thirds, fourths and fifths of a day into Decimalls, and the contrary
14
A Table to convert hours & parts into deg. & parts of the Aequator
20
A perpetual Table for the Equation of Time
21
[Page]The Suns mean motions
22
The Aequations of the Suns Excerntrick
26
The Moons mean motions
29
The Aequations of the Moons Excentrick
34
A Table for the finding of the secōd & third inequalities of the Moon
37
Bullialdus his Table of Evection
40
A compounded Table of the Moons Evection and Variation
43
A Table of the Aequations of Nodes and Moons latitude
53
A Table of the Reductions to the Ecliptick
56
The difference of the true ☌ or ☍ from the middle of the obscuration
57
A Table of the mean Lunations
58
The Horizontall Parallaxes, Semidiameters, and hourly motions of the Sun and Moon
59
The Declination and Meridian Angles
60
Tycho's Table of Refractions
61
Saturn's mean motions
62
Jupiter's mean motions
66
The mean motions of Mars
70
The mean motions of Venus
74
Mercuries mean motions
78
A Table of Declinations
82
A Table of Right Ascensions
89
A Table of Ascensional Differences
100
A Table of Oblique Ascensions
108
A Table of Positions for the latitude of 51 degrees 53 parts
138
A Table shewing the elevation of the Pole upon the severall circles of Position of the 11, 12, 2 and 3 houses for 60 degrees of latitude
151
A generall Table of Positions
152
A Catalogue of the more notable fixed Stars with their longitude, lati­tude, and magnitude for the yeare 1650 compleat.
154

The Preface.

ALL Propositions Astronomical and Astro­logical, have some dependence on the Sphere or Globe, for the better understand­ing therefore of that which follows, it is fit that the Reader be somewhat acquaint­ed with the doctrine thereof; that he know at least what a Globe is, and what the lines, circles and arches usually drawn thereon do represent. Now a Globe or Sphere, is an Analogical representation either of the Heavens or the Earth.

And in this Sphere or Globe there are ten imaginary circles whereof there are six great and foure small. A great circle is such a one as divideth the body of the Globe into two equal Hemispheres. And a small circle is that which divideth the same, into two unequal Hemispheres, wherof the one is more, the other less then half the body of the Globe or Sphere.

The six great circles are these. 1 The Horizon. 2 The Me­ridian. 3 The Equinoctial. 4 The Zodiack. The fifft and sixt are the two colures.

The four lesser circles are, 1 The Tropick of Cancer. 2 The Tropique of Capricorn. 3 The circle Artick. 4 The circle Antarctick. And are all exprest in this annexed Diagram.

  • 1 The Horizon wch is also called the Finitor, is a circle which [Page 2] divideth the visible part of the Heavens from the not visible, that is the lower Hemisphere from the higher, in the figure noted with A B.
  • 2 The Meridian is a circle which passeth by the Poles of the World, and through the Zenith and Nadir, and is mark­ed with A Z B N.
  • 3 The Equinoctial is a Circle which divideth the whole Sphere into two equal parts, and is therefore equally distant from both the Poles, to which when the Sun cometh (which is twice in the Year) the Dayes and Nights are of equal length all the World over, this circle is noted with E F.
  • 4 The Zodiack is a great circle which conteineth the 12 Signes, cutting in the very middle the Equinoctial in two points, which are the beginning of Aries and Libra, whereof the one half. viz. six Signes decline from the Aequator to the North Pole, and are therefore called the Northern Signes, as Aries ♈, Taurus ♉, Gemini ♊, Cancer ♋, Leo ♌; Virgo ♍. The o­ther six decline towards the South Pole and are therfore cal­ed the Southern Signes, as Libra ♎, Scorpio ♏, Sagittarius ♐, Ca­pricornus ♑, Aquarius ♒, Pisces ♓.
  • 5 The one of the Colures which dividing the Sphere into two parts passeth by the Poles of the World and the two E­quinoctial points, called the Equinoctial Colure, and marked with C D.
  • 6 The other Colure which dividing the Sphere also into two equal parts, passeth by the beginning of Cancer and Capri­corn, and the Poles of the World, called the Solstitial Colure, and is the same with the Meridian as the Sphere is here pro­jected.
  • 7 The Tropick of Cancer is one of the lesser circles distant from the Equinoctial towards the North Pole 23 deg. 31 min. 30 seconds, or in Decimal Numbers, 23 deg. 525, to which when the Sun cometh he causeth the longest day, and shortest night to all Northern, the shortest day and longest [Page 3] night to all Southern inhabitants, and is noted with G ♋.
  • 8 The Tropick of Capricorn is a circle distant from the E­quinoctial towards the South Pole: 23 deg. 31 min. 30 seconds, or in Decimal numbers, 23 deg. 525 parts, to which when the Sun cometh, he maketh the longest day and shortest night, to all Southern the shortest day & longest night to all Northern Inhabitants, and is noted, with H ♑. These two circles are called of the Greeks [...] à convertendo, because when the Sun toucheth any of these circles, he is at his greatest distance from the Aequator, and returneth thither again.
    [figure]
  • 9 The Artick circle is distant from the North pole of the world as much as the Tropick of Can­cer is distant from the Equinoctial, and is noted with K L.
  • 10 The Antar­tick circle is di­stant from the South Pole as much as the Tro­pick of Capricorn is distant from the Aequator, and is noted with O M.

Besides these circles exprest upon the Globe, there are o­ther circles not exprest, that are also in familiar use; but these being sufficient for our intended matter, omitting the rest, we will now speak of the several affections of the Sphere or Globe, and so proceed to practice.

According to the diverse habitude of the Aequator to the Ho­rizon (which is either Paralel to it, or else cutteth it, and that [Page 4] either in right or oblique angles) there is a threefold position or Situation of Spheres.

The first is of those that have either Pole for there Zenith or vertical point, with these the Aequator and Horizon are Parallel to each other, or rather indeed do make but one cir­cle between them; and this is called a Parallel Sphere, and they which there inhabit (if any such be) see not the Sun or other Star either rising or setting, or higher or lower, in their diurnal revolution.

[figure]

Besides seeing that the Sun traverseth the whole Zodiack, in a Year, and that half the Zodiack is above the Horizon, and half under it, it comes to pass, that the Sun setteth not with them for the space of six moneths, nor giveth them any light, for the space of other six moneths, and so maketh but one artificial day and night of the whole Year. The second position of the Sphere is of those whose Zenith is in the Aequator, and this is called a right Sphere, in which

[Page 5]

all the Stars are observed to rise and set in an equal space of time, and to continue as long above the Horizon, as they do under it, as by the figure it doth appear, the day and night be­ing alwayes of an equal length.

The third position of the Sphere agreeth to all other pla­ces else, and is called an oblique Sphere, in which the dayes are sometimes longer then the nights, sometimes shorter, and sometimes of equal length: when the Sun is placed in the E­quinoctial point, the dayes and nights are equal, but when he declineth from the Aequator, the dayes are observed to in­crease, and when he declineth towards the opposite Pole the dayes decrease, as it is manifest in the first figure.

And thus having briefly shewed, what a Globe is, the lines thereon described, with the several affections belonging thereunto, what remayneth but that we now proceed to pra­ctice, & shew there use as to the matter in hand; wch is to find [Page 4] [...] [Page 5] [...] [Page 6] the Declinations and Asceusions of the Sun and other Stars whether right or oblique, and divers other things depending on, or belonging to the Doctrine of the Spheare, the which we will shew first by Trigonometrical Calculation, and then by Tables.

Astronomia BRITANNIC …

Astronomia BRITANNICA: The first Book.

CHAP. 1. To find the Suns greatest Declination, and the Poles Elevation.

THe Declination of a Planet, or other Star is his distance from the Aequator, and as he declines from thence either Northward or Southward, so is his declination nominated North or South. And because that all the Planets (the Sun onely excepted) do move sometimes in and sometimes out of the Ecliptick besides there declination North or South from the Aequa­tor, they have also latitude North or South from the Ecliptique, while the Planets keep in the ecliptique, one rule will serve to find their Declinati­on, as well as the Declination, of the Sun, but if they have either North or South latitude, there must another rule be given, in both which rules the greatest Declination of the Sun is supposed to be known; and first there­fore we will shew how, that may be found instrumentally, and then com­pute the Declination of a Planet or other Star, with latitude or without.

For the finding the Suns greatest Declination, you must by a Quadrant or other Instrument, take his greatest and his least Meridian altitude; the difference between which altitudes is the distance of the Tropiques, and half the distance of the Tropiques, is the quantity of the Suns great De­clination, as by the following Figure it doth appear. In which A Z B N represents the Meridian, E F the Eq [...]inoctial, ♋ ♑ the Zodiack, the [Page 8]

[figure]

North pole D the South A B the Horizon Z the Zenith, N the Nadir, ♋ G a parallel of the Suns Diurnall motion at ♋, or the Suns greatest Declination from the Equator towards the North Pole. From whence it is apparent that from A to ♋ is the Suns greatest Meridian altitude from A to H his least, if therefore you deduct A H the least Meridian altitude from A ♋ the greatest, the difference H ♋ is the distance of the Tropiques, and because the angles ♋ center F and ♑ center E are equal, therefore the Suns greatest Declination towards the South Pole is equal to his great­est Declination towards the North, and consequently halfe the distance of the Tropiques, or the arch that is the arch ♋ F is the quantity of the Suns greatest declination. And then if you deduct the Suns greatest declination or the arch A ♋ F from the Suns greatest Meridian altitude or the arch A ♋ the difference wil be A F or the height of the Aequator above the Horizon, the complement whereof to a quadrant is the arch A D equal to C B the height of the Pole.

Example.

The Suns greatest Meridian altitude taken, June 11 at London
61, 99167
The Suns least Meridian altitude, December the 10th.
14, 94167
Their difference is the distance of the Tropiques
47, 05000
Half that difference is the Suns greatest Declination whose difference from the greatest altitude is
23, 52500
The elevation of the Equator and the complement thereof to 90 is the Elevation of the Pole
38, 46667
 
51, 53333

CHAP. 2. The Suns greatest Declination being given, to find his Declination in any point of the Ecliptique.

LEt DFHG represent the Solstitial Colure, D BAG the Equator, F A H the Ecliptique, I the Pole of the Ecliptick, E the pole of the Equator, E C B a meridian line passing from E, through the Sun at C, and falling upon the Equator D A G with right angles at the point B. Therefore in the Rectangle sphaericall Triangle A B C we have known. 1 The Hy­pothenuse A C the Suns distance from the next Aequinoctiall Point, whe­ther Aries or Libra and may be supposed to be in 10 degrees of Cancer, and that being neerer unto Libra then Aries, I take his distance from Li­bra which is two signs and 20 degrees, or 80 degrees.

[figure]

2. We have known the angle B A C the Suns greatest declina­tion, which by the accurate Observation of Tycho is found to be 23 deg. 31 minutes and 30 seconds. And in Decimall numbers 23. 525. Hence to find the present decli­nation the proportion is.

As the Radius is to the sine of the Suns geatest declination. So is the sine of the planets distance from the next Aeqninoctiall point, To the sine of the de­clination required.

And by this proportion, together with the help of the Canon of artifici­all sines and tangents, I find the declination of the Sun at the time pro­posed thus. First, I seek for the sine of Radius or 90 degrees, the measure of the right angle at B, and I find the sine thereof 10, 000000, next I seeke the sine of 80 degrees, and likewise the sine of 23. 5250, these two I adde [Page 10] together and from their aggregate, I substract the Radius and what re­maineth is the sine of the declination sought, as in the following work you may perceive.

As Radius  
To the sine of B A C23. 5259, 6011352
So sine of A C70.9, 9729858
To the sine of B C22. 029109, 5741210

CHAP. 3. How to find the Declination of a planet or fixed Star with Latitude.

What the Declination of a planet is, and how to find the same in any point of the Ecliptique hath been already shewed, we will now shew how to finde the same with latitude either north or south, and for demonstration sake. Let G F I H represent the Solstitial Colure, H A F the Aequator, I A E the Ecliptique, K M N a circle of latitude, G M C a cir­cle of declination, A N the longitude of the star, M C the declination. Then in the Oblique angled spheical▪ Tri­angle M G K we have limited. 1 The side K G the Suns great­est declination. 2 The side K M the complement of lati­tude. 3 The angle M K G the complement of longit. From hence the declination M C may be found at two operations, for first to find K O the pro­portion is,

[figure]

As the Radius to the Cosine of the complement of Longitude, so is the tangent of the Suns greatest declinati­on, To the tangent of the first arch: K O, which being added to or sub­stracted from the complement of Latitude K M, according to the direction ollowing their aggregate or difference will be the arch O M.

[Page 11]If the Declination sought be in the

  • Northerne Signes and
    • North Latitude, substract the arch found from the complement of latitude and what remaineth is the se­cond Arch O M.
    • South Latitude add the arch found to the comple­ment of latitude and their aggregate is the second arch if lesse then a quadrant, but if more the com­plement thereof to a semicircle.
  • Southerne Signes and
    • North Latitude, adde the arch found to the comple­ment of Latitude, and their aggregate is the second arch.
    • South latitude substract the arch found from the com­plement of latitude, and what remaineth is the second arch.

And then the second proportion is,

As the Consine of the first arch found, Is to the cosine of the Suns great­est declination, So is the Cosine of the second arch found, to the Cosine of an arch, whose complement is the declination sought: To make it plain we will in each case adde an example.

In the first Quadrant.

We will suppose a starre to be in 10 deg. of Gemini, with 4 deg. of north latitude.

The longitude of a starre so posited is 70 deg. the complement thereof M K G is 20 deg.

The latitude 4 deg. north, the complement thereof 86 M K. And the Suns greatest declination K G 23 deg. 5250.

Then according to the former analogie, first I say,

As the Radius90.10, 000000
To the Cosine of M K G20.9, 9729858
So is the tangent of K G23. 52509, 6388198
To the tangent of K O22. 259, 6118056
The complement of latitude00 s. 86 d.00
The arch K O2225
Their aggregate10825
Their difference6375

[Page 12]Because the latitude is North I take their difference and say,

As the Cosine of K O:22. [...]59, 9663954
To the Cosine of K G23. 52509, 9623154
So is the Cosine of O M:6 [...]. 759, 6457058
To the Cosine of G M:64. 019, 6416258

The complement thereof 25. 99 is the declination sought.

To find the declination of the same point with 4 degrees of South lati­tude: I take the complement of 108. 25. viz. 71. 75.

And say as the Cosine of K O22. 25.9, 9663954
To the Cosine of K G23. 52509, 9623154
So the Cosine of O M71. 759, 4957715
To the Cosine of G M71. 939, 4916915

whose complement is the declination sought, viz. 18. 7.

The point of the Ecliptique answering hereunto in the 2 quadrant, is the 20 of Cancer, and hath the same declination North and South. In the third and fourth quadrant the 10 of Sagittary, and the 20 of Capri­corn, have the same declination, but with contrary latitude.

In the second Quadrant.

We will suppose a starre in 10 deg. of Leo whose longitude is 130. The latitude 4 deg. north.

The complement of longitude M K G is 50, but because the longitude is more then a quadrant, I take the complement of 50, viz. 40 deg. The complement of latitude M K is 86 as before. And the Suns declination fixed, first then I fay,

As the Radius9010, 0000000
To the Cosine of M K G409, 8842539
So the tangent of K G23. 52509, 6388198
To the tangent of K O.18. 449, 5230737
The complement of latitude 86. 00
The arch K O 18. 44
Their aggregate 104. 44
Their difference 67. 56
For the north latitude I take their difference and say,  
As the Cosine of K O18. 449, 9771084
To the Cosine of K G23. 52509, 9623154
So the Cosine of O M67. 569, 5817400
To the Cosine of G M68. 359, 5669470

whose complement 21. 65 is the declination sought.

[Page 13]For the declination of the same point with South latitude, I take the complement of 104. 44: viz. 75. 56. And say,

As the Cosine of K O18. 449, 9771084
To the Cosine of K G23. 52. 509, 9623154
So the Cosine of O M75. 569, 3968372
To the Cosine of G M76. 059, 3820442

whose complement 13. 95 is the declination with South latitude

The point of the Ecliptique answering hereunto in the first quadrant is the 20 of Taurus, and hath the same declination North latitude North and South.

In the third and fourth Quadrants the points answering thereunto are the 20 of Scorpio and the 10 of Aquarius, and have the same declinati­on but with contrary latitude.

CHAP. 4. How to find the Right Ascension of any point of the Ecliptique.

THe Ascension of the Sun or Starres is the degree of the Aequator that riseth with the same above the Horizno. And the Descension of it is the degree of the Aequator that goeth under the Horizon with the same, both these are either Right or Oblique. The Right Ascension or Descension is the degree of the Aequator that Ascendeth or Descendeth with the Sun or other starre in a Right Spheare, and the Oblique Ascension is the degree of the Aequator, that ascendeth or descendeth with the same in an ob­lique spheare. The former of these is simple, and of one kind onely; be­cause there can be but one position of a Right spheare, but the later is va­rious and manifold according to the diverse inclination of the same. To find the Right Ascension of a planet in the Eclptique, There must be gi­ven as in the first Chapter, the planets longitude or distance from the next Equinoctiall point: and the Suns greatest declination. Then in the Rect­angle sphericall Triangle of the first chapter A B C, we have limi­ted.

  • 1 The angle B A C, the Suns greatest declination 23. 31. 30.
  • 2 The Hypothenuse A C, the Suns distance from the next Equino­ctiall point, whose place we will suppose to be in 10 degrees of Gemini, and consequently his distance from Aries is 70 degrees. Hence to find the base A B, the right Right Ascension the point sought, the proportion is.

As the Radius is to the tangent of the planets distance from the next Ae­quinoctial [Page 14] point: So is the Cosine of the Suns greatest declination▪ to the tangent of the Right Ascension of the point sought, Example.

As the Radius9010, 0000000
To tangent of A C70.10, 4389341
So is the Cosine of B A C23. 52509, 9623154
To the tangent of A B68. 3487410, 4012495

which is the Right Ascension of the Sun or any other planet without lati­tude, when they be in the the 10 degree of Gemini.

Note that if the Right Ascension of the point sought be in the second quadrant (is in Cancer, Leo, Virgo.) you must take the complement of the arch found to a semicircle: if in the third Quadrant (as in Libra, Scor­pio, Sagitarius) you must add a semicircle to the arch found: if in the last quadrant (as in Capricorn, Aquarius, Pisces) you must substract the arch found from a whole circle or 360, and so shall you have the Right Ascension of any point of the Ecliptique, to make it plaine we will in each case add an Example.

In the second Quadrant.

Let the Right Ascension of the point sought be 10 degrees of Virgo, the distance thereof from Libra, which is the next Aequinoctiall point is 20 degrees, according therefore to the former Analogie, I say.

As the Radius90.10. 0000000
To the tangent of A C20.9. 5610658
So is the cosine of B A C23. 52509. 9623154
To the tangent of A B18. 459. 5233813

whose complement to a semicircle 161. 55 is the Right Ascension thereof.

In the third Quadrant.

Let the Right Ascension of the point sought be in 14 degrees of Scorpio, the distance thereof from Libra, the next Aequinoctiall point is 44 de­grees. Therefore I say.

As the Radius90.10. 0000000
To the tangent of A C44. deg.9. 9848371
So is the Cosine of23. 52509. 9623154
To the tangent of A B41529. 9471525

to which if you adde a semicircle or 180 degrees the Right Ascension of of the point sought will be 221. 52.

In the last Quadrant.

Let the Right Ascension of the point sought, be 22 degrees of Aquarius; the distance thereof from Aries, which is the next Aequinoctiall point [...]s 38 degrees. Therefore I say.

As the Raduis90.10. 000000
To the Tangent of A C38.9. 8928098
So is the Cosine of23. 52509. 9623154
To the tangent of A B35. 629. 8551252

which being subtracted from 360 there rests▪ 324. 38 for the Right Ascen­sion of the point sought.

CHAP. 5. How to finde the Right Ascension of a Planet or other Star with Latitude.

THe Declination being found by the 3 Chapter, we have in the ob­lique angled Sphericall Triangle of that Diagram G K M all the sides given with the angle M K G, therefore to finde the angle K G M, say. As the Cosins of the declination, is to the Cosine of the Planets distance from the next Aequinoctiall point. So is the Cosine of its latitude to the Cosine of its Right Ascension.

For Example. The Declination of 10 degrees of Gemini, was found to be 25. 99. with 4 degrees North Latitude. Whose complement is G M. 64. 01 the complement of Longitude is the angle M K G 20, the comple­ment of Latitude is M K 86, hence to finde the Right Ascension, the Analogie is.

As the Sine of G M64. [...]01. co. arith.0. 0463059
To the sine of M K G20.9. 5340516
So is the sine of K M86.9. 9984407
To the sine of K G M.22. 289. 5787982

whose complement 67. 72 is the right Ascension of a Star in 10 de­grees of Gemini, with 4 degrees of North Latitude.

CHAP. 6. The Elevation of the Pole and Declination of the Sun given, to find his Amplitude.

THe Amplitude of the Suns rising or setting is an arch of the Horizon intercepted betwixt the Aequator and the place of the rising and set­ting of the Sun. And it is either Northern or Southward, the Northern Amplitude is when he sets and riseth on this side of the Equator, toward he North Pole: and the Southern when he sets or riseth on the contrary side. Now when the Sun is in the Aequator, he hath no Amplitude at all: but when he is in the Solstitial points, he hath then the greatest Amplitude. That we may find then the Suns amplitude or distance from the East or West points at the time of his rising or setting; let D P L G F represent the Me­ridian, F A I the Horizon, D A L the Equinoctial. P the Pole of the Aequator.

[figure]

Then in the Rectangle Spherical Triangle A B C, let there be given the angle B A C or complement of the Poles elevation, 38. 47 and B C the Suns Declination 23. 15. To find A B the Suns Amplitude, The Ana­logie is.

As the sine of B A C.38. 47. co. ar.0. 2061365
To Radius.90.10. 0000000
So is the sine of B C.23. 15.9. 5945468
To the sine A B39. 19.9. 8006833

CHAP. 7. The Meridian Altitude and Declination of the Sun with the Poles Elevation given to finde his true place in the Zodiac.

IF the Meridian Altitude of the Sun be lesse then the complement of the Poles elevation, subtract the meridian altitude from the height of the Ae­quator, and what remaineth is the Suns Declination towards the South Pole; But if the Meridian altitude of the Sun be more then the height of the Aequator, subtract the height of the Aequator from the Meridian alti­tude and what remaineth is the Suns Declination towards the South Pole.

Then in the Diagram of the second Chapter, in the right angle Sphaeri­call Triangle A B C, we have known, the angle B A C the Suns greatest Declination, and the perpendicular B C the present Declination to finde the Hypothenuse A C, the Suns distance from the next Equinoctiall point, or true place in the Zodiac, for which the Analogie is.

As the sine of B A C.23. 5250 co. ar.0. 3988648
To the sine of B C.23. 159. 5945468
So is the Radius or whole sine.90.10. 0000000
To the sine of A C80. 049. 9934116

That is in 20 degrees of Gemini, and 4 Centesmes, if the Meridian al­titude were taken in Summer: But in 20 degrees 04 Centesmes of Capri­corn, if the Meridian altitude was taken in Winter.

CHAP. 8. Having the Meridian Altitude of an unknown Star and the dist­ance thereof from a known Star, to finde the Right As­cension of the unknown Star.

ABout the end of the year 1577 Tycho observed the distance of the litle Star in the breast of Pegasus from the bright Star of the Vultur to be exactly 45 deg. 31 min. or in decimal numbers 45. 51667. And by the Meridian altitude thereof, he found the Declination to be 22 deg. 26 min. North that is 22. 43333. Which given the Right ascension of the said Starre is to be enquired. For the finding whereof in the oblique angled [Page 18] Sphaericall Triangle (of the annexed Diagram) F O L, there is knowne First, F L the complement of the Declinat. of the bright Star of the Vultur 82. 13333. Secondly F O the complement of the Declination of the Star in the brest of Pegasus, 67. 56667. Thirdly O L the distance of them, 45. 51667, to finde the angle at F or difference of their Right ascen­sion.

[figure]
The side L O.45. 51667. 
The side F L.82. 13333. 
The side F O.67. 56667. 
Sum of the sides.195. 21667. 
The halfe Sum.97. 60833. 
Sine of F L.82. 13333. co. ar.0. 0041064
Sine of F O.67. 56667. co. ar.0. 0341757
Dif. of F L ½ sum.15. 47500.9. 4262148
Dif. of F O ½ sum.30. 04167.9. 6995164
Quadrat of the sine of halfe the angle. 19. 1640133
Halfe is the sine of22. 45453.9. 5820066

[Page 19]Double is the angle L F O. 44. 90906. Equall to the arch D E the diffe­rence of their Right ascensions, which being added to the Right ascension of the bright Star of the Vulture. 292. 58333. The summe 337. 49239 is the Right ascension of the little Star in the breast of Pegasus.

CHAP. 9. Having the Declination and Right ascension of a star given, to finde the longitude and latitude thereof.

IN the Diagram of the 3 Chapter, having the Right ascension of the little Star in the breast of Pegasus A C. 337. 49239. And the decli­nation C M. 22. 43333. with the greatest obliquity of the Ecliptique

B A C. 23. 5250. we are to enquire its Longitude A N. and Lati­tude M N. wherefore in the Triangle A B C. we have the angle B A C. 23. 5250. and the side A C 22. 50761 the complement of the Right ascen­sion: then I say.

As Radius.  
To Tangent of B A C23. 52509▪63 [...]198
So sine of A C.22. 507619. [...]8 [...]787
To Tangent of B C.6. 461259. 2217985
Adde C M.22. 43333 The Declination 
Sum is M B.31. 89458 

when the Declination is South the arch found must be subtracted from it, and their difference shall be M B.

2. To finde the angle A B C.
As the sine of B C9. 46125 co. ar.0. 7841497
To the sine B A C23. 52509. 6011352
So the sine of A C22. 507619. 5829787
To the sine of A B C68. 368439. 9682836

3. To finde the side A B.
As the sine of B A C.23. 52520. co. ar.0. 3988648
To the sine of B C.9. 46125.9. 2158503
So is Radius. 10. 0000000
To the sine of A B.24. 319679. 6147151

4. The angle A B C is equall to the angle M B N, therefore to finde the latitude M N.
[Page 20]As the sine M N B90. 
To the sine of M B31. 89458.9. 722928 [...]
So the sine of M B N.68. 36843.9. 9682836
To the sine of M N.29. 41602.9. 6912118

Lastly, to finde the arch B N.
As Radins.  
To Cotangent of. M B N.68. 36843.9. 5983151
So Tangent of M N.29. 41602.9. 7511554
To the sine of B N.12. 92052.9. 3494705

Which is to be added to A B if the Right ascension be lesse then a semi­circle, but if the Right ascension exceed 180, as in our example, the Com­plement of B N. 357▪07948, is the longitude desired.

CHAP. 10. How to finde the Ascensionall Difference.

THe Ascensional Difference, is nothing else but the difference be­tweene the ascension of any point of the ecliptique in a Right Sphere, and the Ascension of the same point in an oblique Sphaere, as in the annexed Diagram, Let A G E V represent the

[figure]

[Page 21] Meridian, E M T the Horizon, G D M C V the Aequator, D B part of the Zodiac, A the Pole thereof, D the beginning of Aries, V T the com­plement of the Poles elevation, B C the Suns Declination, D C the Right ascension, M C the ascensional Difference.

Then in the Right angled sphaericall Triangle B M C we have limited. 1. The angle C M B the complement of the Pole 38. 46667. Secondly, the side B C 19 deg. the Suns Declination, hence to finde, the ascension­al difference M C the Analogie is.

As the Cotangent of the poles Elevation, is to Radius. So is the tangent of the planets Declination, to the sine of the ascensionall difference.

As the tangent of C M B38. 46667. co. ar.0. 09991 [...]6
Is to Radius 10. 000000
So is tangent of B C22. 02919. 6070441
To the sine of M C30. 616139. 7069577

which is the Ascensionall Difference sought.

CHAP. 11. How to find the Oblique Ascension or Descension of any point in the Ecliptique.

OBlique ascension is when a less arch or portion of the Aequator [...]iseth, then doth of the Zodiack, or else of that Star may be said to rise obliquely with whom a less portion of the Aequator as­cendeth above the Horizon, & so the oblike Descension or setting of a Star, is when a less proportion of the Aequator descendeth with it, then doth in a right Sphere.

In the former Diagram, D C represents the right Ascension, M C the Ascensional Difference, D M the oblique Ascension, D B an arch of the Ecliptique above the Horizon, which being greater then D M, a Star in this position of the Sphere, is said to rise obliquely. The quantity whereof is found, by deducting the Ascensional difference C M from the right as­cension D C, according to the direction following.

If the Declination be

  • North
    • Subt. The Ascensional Difference from the right Ascension, and it giveth the oblique Ascension.
    • Adde The Ascensional Difference to the Right Ascension, and it giveth the oblique Descension.
  • South
    • Adde The Ascensional Difference to the Right Ascension, and it giveth the oblique Ascension.
    • Subt. The Ascensional Difference from the Right Ascensi­on, it giveth the oblique Descension.
Right Ascension of ten degrees of Gemini,
68. 348 [...]
Ascensional Difference
30. 61613
Oblique Ascension of ten degrees of Gemini,
37. 73261
Oblique Descension of ten degrees of Gemini,
99. 08137

CHAP. 12. The Poles Elevation and the Suns Declination being given, to finde his Altitude at any time assigned.

IN this proposition there are three varieties, first, when the Sun is in the Aequator, that is the begining of Aries and Libra, in which case sup­posing in this Diagram the Sun to be at H two houres or 30 degrees distant from the Meridian A, and the poles Elevation R F equall to A C 51. 53333, the angle at A being right, I say.

[figure]

[Page 24]

As the Radius.  
To the Cosine of A H309. 9375 [...]06
So the Cosine of A C51. 533339. 793831 [...]
To the Cosine of C H57. 403519. 7313624

whose complement 32. 59649 is the side L H or altitude sought.

The second varietie is when the Sun is in the Northerne signes Aries, Taurus, Gemini, Cancer, Leo, Virgo. For the solving of the Probleme in this varietie, let A E C represent the Aequinoctiall. F the pole thereof, L E R the Horizon, G the pole thereof. B D a parallel of the Suns decli­nation. F O the Meridian of the Sun. B H the distance of the Sun from the Meridian. H O the Suns declination North, R F the poles elevation, F G the complement.

Admit the Sun at H be distant from the Meridian B 45 degrees, and in ten degrees of Gemini, where his declination O H is 23. 02910. which

[figure]

[Page 24] being taken out of the Quadrant F O 90. there remains F H. 67. 97090. which known in the Triangle F G H, we have given these three parts.

First, the side F G 38. 46667. Secondly, the side F H. 67. 97090. and the included angle F G H. 45 degrees to find G H.

[figure]
As the Radius  
To the Tangent of F G38. 466679. 9000864
So the Cosine of F G H45.9. 8494850
To the Tangent of F K29. 326699. 7495714
Then from F H67. 97090 
Deduct F K29. 32669 
There rests H K38. 64421 
2. As the Cosine of F K29. 32669.co. ar.0. 0595626
To the Cosine of F G38. 466679. 8937451
So Cosine of K H38. 644219. 8926710
To the Cosine of G H44. 541119. 8459787

The complement whereof N H 45. 45889. is the altitude of the Sun above the Horizon.

[Page 25]The third variety is when the Sun is in the southern signes Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces. And in this case supposing the Sun to be in 10 deg. of Sagittarius, and having South de­clination 22. 02910, and also 45 deg. distant from the Meridian as before in the oblique angled triangle F G H of the annexed Diagram we have gi­ven 1. The side F G. 38. 46667. 2. The side F H 112. 02910 and the angle G F H 45 deg. Then as before, I say

[figure]
As Radius  
To the tangent of G F38. 466679, 9000864
So Cosine of G F H45.9, 8494850
To the tangent of F K29. 326699, 7495714
From F H112. 02910 
Deduct F K29. 32669 
Rest K H82. 70241 
[Page 26]As the Cosine of F K29. 32669 co. ar.0, 05956 [...]6
To the Cosine of F G38. 466679, 8937451
So the Cosine of K H82. 703419, 1038818
To the Cosine of G H83. 439749, 0571895

whose compl. H N. 6. 56026 is the Suns altitude required. The like is to be observed of the Moon with the other planets and fixed Starres.

CHAP. 13. Having the Suns greatest Declination, with his distance from the next Equinoctiall point, to find the Meridian angle or intersection of the Meridian with the Ecliptique.

IN the Diagram of the 10 chapter, we have in the triangle D C B. 1. The angle B D C 23. 5250 the Suns greatest Declination. 2 The Hypothenusal D B 70 the distance of the Sun from Aries. 3 The an­gle B C D 90, to find the angle D B C. The Analogie is,

As the Radius  
To the tangent of B D C.23. 5259. 6388198
So the cosine of D B709. 5340516
To the Cotang. of D B C81. 531339. 1728714

or the angle of the Ecliptique with the Meridian.

CHAP. 14. To find the angle of the Meridian with the Horizon.

IN the Diagram of the 5 chapter, we have in the triangle B C M, first, the angle B M C 38. 46667 the elevation of the Equator. 2 B C 22. 02910 the Declination of the point given, to find M B C.

As the Cosine of B C22. 02910 co ar.0. 0329234
Is to Radius 10. 000000
So is Cosine of B M C38. 466679. 8937451
To the Sine of M B C57. 632759. 9266685

CHAP. 15. The Poles elevation, with the Suns Altitude and Declination gi­ven, to find his Azimnth.

IN the oblique angled sphaericall triangle G H F, in the second Dia­gram of the 12 Chapter, we have known H F the complement of the Suns Declination. 2 The side G F the complement of the poles ele­vation. [Page 27] 3 The side H G the complement of the Suns altitude, to find H G F.

[...]. The side F H
67. 97090
2. The side G F
38. 46667
3. The side H G
44. 54111
Summe
150. 97868
Halfe summe
75. 48934
Sine of G F38. 46667 co. ar.0. 2061682
Sine of H G44. 54111 co. ar.0. 1540214
Diff. G F ½ sum37. 022679. 7796909
Diff. H G ½ sum30. 948239. 7111855
Quadrat of the Sine of ½ the angle 19. 8510560
Half is the Sine of57. 396449. 9255280

whose double 104. 79288 is the Suns Azimuth from the North, and the complement thereof 75. 20712 is the Suns Azimuth from the South.

CHAP. 16. How to erect a Figure of Heaven.

AMong the severall wayes for the erecting of a figure, used by the ancient Astronomers, that is held most rationall which divideth the Equinoctiall into twelve parts by circles meeting at the inter­sections of the Meridian and Horizon, which is according to the following Scheame, in which the line W Z E represents the East and West Azimuth W ♈ E is that halfe of the Equinoctiall above the eareh, and W ♎ E is that half of the Equator under the earth. The arch 7 ♈ 1, doth represent that halfe of the ecliptick above the earth.

And 7 ♎ 1 that part under the earth. The utmost circle N E S W re­presents the Horizon, N Z S the meridian, N the north, and S the South end thereof. The Eqninoctiall circle W ♈ E ♎ is divided in to 12 equall parts, by which divisions passe arches, from the North and South inter­sections of the meridian with the Horizon, which cut the Ecliptique at the cuspe of the houses, N 1 S is the cuspe of the Ascendant, N 7 S of the 7 house N 2. 12 S of the second and twelfth, N 3. 11 S of the third and e­leventh, and so of the rest as you see in the Figure.

[Page 28]

[figure]

To find the Mid-heaven or Tenth House.

When you would erect a figure you must have the true place and Right Ascension of the Sun for the time proposed, let the given time in the me­ridian of London where the North pole is elevated above the Horizon 51. 53333 be July the 16. After noon 18 hours, 4564 in the yeare 1587. For which time according to our Tables the Suns place is in Vir­go 4. 07368 which known the Midheaven or 10 house may thus be found.

First, enquire the Right Ascension of the Sun at the time proposed by the 4 Chapter thus

As the Radius  
To the tangent of A C25. 926329. 6867627
So consine of B A C23. 525009. 9623154
To the tangent of B C24. 024279. 6490781

whose complement 155. 97573 is the Right Ascension sought.

To the Right Ascension of the Sun
155. 97573
Adde the Right Ascension of time
276. 84600
Right Ascension of the Mid-heaven
432. 82173
Deduct a whole circle
360.
Then rests for the Right Ascension
072. 82173

Then in the Rectangle Sphericall Triangle ♈ 10 F we have given. 1 ♈ F the Right Ascension of the mid-heaven. 72. 82173 2 The Suns greatest Declination F ♈ 10. 23. 5250 to find ♈ 10 the point culminating.

As the Radius.  
To the Cotangent of F ♈72. 821739. 4901498
So cosine of 10 ♈ F23. 52509. 9623154
To the cotangent of ♈ F O74. 175019. 4524652

To find the Cuspe of the 11 house.

Unto the Right Ascension of the 10 house
72. 82173
Adde 30 degrees
30. 00000
And then the oblique Ascension of the 11 house
102. 82173
To this adde
30.
Oblique Ascension of the 12 house
132. 82173
 
30.
Oblique Ascension of the Ascendant
162. 82173
 
30.
Oblique Ascension of the 2 house
192. 82173
 
30.
Oblique Ascension of the 3 house
222. 82173

The Oblique Ascension of the houses thus found by a continuall additi­on of 30 degrees, we must next find the poles elevation upon their severall circles of position thus, In the rectangle sphericall Triangles E A B and E C D we have limited. 1. Their common angle at E the latitude of the place. 2. E B and E D 38 and 60 with the right angles A and C to find the angles B and D, being the angles that the circles of position make with the Equator.

First, then for the 11 and 3 houses.

As the Radius  
To the Cosine of E D60.9. 69470 [...]0
So tangent of C E D51. 5333310. 0999136
To cotangent of C D E57. 816269. 7988836

whose complement 32. 18374 is the height of the pole above those circles of position.

For the 12 and 2 houses.

As the Radius  
To the Cosine of E B309. 375306
So tangent of A E B51. 5333310. 0999236
To cotangent of A B E42. 5330810. 0374442
whose complement47. 46692 is the height of the pole required. 

Having thus found the severall oblique Ascensions of the severall houses together with the elevation of the pole, above their severall circles of po­sition, in the oblique angled sphericall Triangle ♈ C D we have limited 1. The angle ♈ D C complement to C D E. 2. The angle C♈D the Suns greatest Declination. 3. Their included side ♈ D the oblique Ascension of each house to find ♈ C the point of the Ecliptique. The Analo­gies are.

For the 1 Operation.
  • As the Sine of the halfe summe of the angles.
  • To the Sine of halfe their difference.
  • So the tangent of halfe the side comprehended.
  • To the tangent of halfe the difference of the sides
For the 2 Operation.
  • As the Cosine of the half summe of the angles
  • To the Cosine of their halfe difference.
  • So the Tangent of halfe the side comprehended.
  • To the Tangent of half the Summe of the sides.

The Summe of these two arches, shall give you the point of the Eclip­tique desired.

For the Cuspe of the 11 house.

The oblique Ascension or arch ♈ D is
102. 82173
The halfe thereof is
51. 41086

The complement of C D E 57. 81626 is the angle

♈ D C.122. 18374.   
C ♈ D.23. 52500.Or the Suns greatest Declination
Summe145. 70874Half Summe72. 85437 
Differ.98. 65874½ Differ.49. 32937 
Sine ½ Summe72. 85437 co. ar.0. 0197429
Sine ½ Differ.49. 32937  9. 8799374
Tang. ½ ♈ D51. 41086  10. 0980083
Tang ½ Differ.44. 84740  9. 9976886
For the 2 Operation.
Cosine ½ Summe72. 85437 co. ar.0, 5304705
Cosine ½ Differ.49. [...]29379. 8140541
Tangent ½ ♈ D51. 4108610. 0980083
Tangent ½ Summe70. 1521110. 44 [...]5329
1 Arch adde44. 84740 

Summe 114. 99951 or ♋ 24. 99951 is the point of the Eclip­tique for the 11 house.

For the 12 house.

The Oblique Ascension or arch ♈ D is
132. 82173
The halfe thereof is
66. 41086

The complement of C D E 42. 53308 is the angle

♈ D C137. 46692   
C ♈ D23. 52500   
Summe160. 99192½ Summe80. 49596 
Differ.113. 94192½ Differ.56. 97096 
Sine ½ Summe80. 49596co. ar. 0. 0060025
Sine ½ Differ.56. 97096  9. 9234483
Tang. ½ ♈ D66. 41086  10. 3598529
Tang. ½ Differ.62. 81111  10. 2893037
For the 2 Operation.
Cosine ½ Summe80. 49596 co. ar.0. 7822080
Cosine ½ Differ.56. 970969. 7364475
Tangent ½ ♈ D66. 4108610. 3598529
Tangent ½ Summe82. 4647010. 8785084
1 arch adde62. 81111 

Summe 145. 27581 or ♌ 25. 27581 is the point of the Eclip­tique for the 12 house.

For the Cuspe of the Ascendant.

The Oblique Ascension or ♈ D is
162. 82173
The halfe thereof is
81. 41086

The angle C D E is the same with the height of the Equator 38. 46667 whose complement to a semicircle is the angle.

♈ D C141. 53333  
C ♈ D23. 52500  
Summe165. 05833½ Summe82. 51916
Differ.118. 00833½ Differ.59. 00416

Sine ½ Sum 82. 52916co. ar.0. 0037026
Sine ½ Differ. 59. 00416 9. 9330844
Tangent ½ ♈ D 81. 41086 10. 8209024
Tangent ½ Dif. 80. 09004 10. 7576894
For the 2 Operation.
Cosine ½ Summe82. 52916 co. ar.0. 8859846
Cosine ½ Differ.59. 004169. 7117867
Tang. ½ ♈ D81. 4108610. 8209024
Tang. ½ Summe87. 8160611. 4186737
1 Arch add80. 0900411. 4186737

Summe 167. 90610. Or ♍ 17. 90610 is the point of the Ecliptique for the Ascendant

For the Cuspe of the 2 house.

The Oblique Ascension is 192. 82173 whose complement is the Arch ♈ D 167. 17827.

The half whereof is 83. 58913. The summe and Difference of the an­gles are the same with those for the 12 house.

Therefore I say first,
Sine ½ Summe80. 49596 co. ar.0. 0060025
Sine ½ Differ.56. 970969. 9234483
Tangent ½ ♈ D83. 5891310. 9493879
Tangent ½ Diff.82. 4703610. 8788387
For the 2 Operation.
Cosine ½ Summe80. 49596 co. ar.0. 7822080
Cosine ½ Differ.56. 970960. 7364475
Tangent ½ ♈ D83. 5891310. 9493879
Tangent ½ Summe88. 0505511. 4680434
1 Arch adde82. 47036 

Summe 170. 52091 whose complement 189. 47909 or ♎ 9. 47909, is the Cuspe of the 2 house.

For the Cuspe of the 3 house.

The Oblique Ascension is 222. 82173, whose complement is the arch ♈ D 137. 17827. The half whereof is 68. 58913. The summe and dif­ference of the angles are the same with these for the 11 house.

Therefore I say first,

[Page 33]

Sine ½ Summe72. 85437 co. ar.0. 0297429
Sine ½ Differ.49. 329379. 8799374
Tangent ½ ♈ D68. 5891310. 4065869
Tangent ½ Diff.63. 7103210. 3062672
For the 2 Operation.
Cosine ½ Summe72. 85437 co. ar.0. 5304705
Cosine ½ Differ.49. 329379. 8140541
Tangent ½ ♈ D68. 5891310. 4065869
Tangent ½ Sum79. 9418610. 7511115
1 Arch adde63. 71032 

Summe 143. 65218 whose complem. 216. 34782 or ♏ 6. 34782 is the point of the Ecliptique for the Cuspe of the third house.

The six Orientall houses being thus found, the other 6 are also found, by consequence, being the same degrees and parts of the opposite signes.

And thus we have not onely erected a figure for the time given, but composed a Table, for the generall erecting a figure in this latitude, for by adding together the first and second numbers, in every of these proportions, there is composed 2 numbers for every house, to each of which the Artificiall tangent of halfe the oblique Ascension being added, their aggregates are the tangents of two arches, which added together is the distance of the Cuspe of the house from the first point of Aries. One­ly note that if the oblique Ascension be more then 180 deg. you must take the tangent of halfe the complement to a whole circle; And to find the Cuspe of the house, you must also take the complement of the added arches, as shall be cleared by example.

A New Table of Houses for the Latitude of London.
 11 & 3 hous.Ascendent12 & 2 hous.
1 Oper.9. 89968039. 93678709. 9294508
2 Oper.10. 344524610. 597771310. 5186555

Having found the oblique Ascensions of the houses as before was shew­ed, take out the tangent of half thereof from a Table of Tangents, whose Radius is 10. 0000000, and set them down twice on your paper as you see in the following example, then seek in the top of the Table, the house whose cuspe you would find; and under the same you have two numbers, the first of which being added to one of the tangents in the paper, and [Page 34] the second to the other, will give you the tangents of two arches, whose aggregate is the Cuspe desired.

Example.

The Oblique Ascension of the 11 house was before found to be 102. 82173. And the tangent of the halfe thereof 51. 41086 is 10. 0980083 the first number in the Table under the 11 house is 9. 8996803 their same rejecting Radius 9. 9976886, is the tangent of 44. 84740. The second number in the Table.

Tangent51. 4108610. 0980083
1 Number 9. 8996803
Tangent44. 847409. 9976886

is [...]0. 3445246, which being added to the same tangent, there summe 10. 4425329 is the tangent of 70. 25211 and the aggregate of these two arches.

Tangent51. 4108610. 0980083
2 Number 10. 3445246
Tangent70. 1521110. 4425329
1 Arch44. 84740 
Summe114. 99951 

gives the point of the Ecliptique in Cancer 24. 999

2 Example.

The Oblique Ascension of the 2 house was before found to be 192. 82173 The tangent of halfe the complement 83. 58913 is 10. 9493879

Tangent83. 5891310. 9493879
1 Number 9. 9294508
Tangent82. 4703610. 8788387

Tangent83. 5891310. 9493879
2 Number 10. 5186555
Tangent88. 0505511. 4680434

1 Arch. 82. 47036 Summe 170. 52091 whose complement [...]47909▪ is the Cuspe desired.

The Cuspe of your houses being thus found, draw your figure after this manner, and then place the Signes and Degrees on the Cuspes of their proper houses, beginning with the 10 house.

[Page 35]

A Figure of the 12 Houses of Heaven.
10 house ♊ 14. 17.The opposite houses are in the opposite Signes.4 house ♐ 14. 17.
11 house ♋ 24. 99.The opposite houses are in the opposite Signes.5 house ♑ 24. 99.
12 house ♌ 25. 27.The opposite houses are in the opposite Signes.6 house ♒ 25. 27.
Ascendent ♍ 17. 90.The opposite houses are in the opposite Signes.7 house ♓ 17 90.
2 house ♎ 09. 47.The opposite houses are in the opposite Signes.8 house ♈ 9. 47.
3 house ♏ 06. 34.The opposite houses are in the opposite Signes.9 house ♉ 6. 34.

The 12 signes being placed in the figure we must next enquire for the true places of the Planets, with the Dragons head, the which according to the doctrine of the second Book at the time proposed are as followeth.

Suns place♍ 4. 07.☊ ♏ 1. 40.♃ ♌ 5. 19.♀ ♏ 16. 58.
Moons place♊ 26. 24.♄ ♌ [...] 5. 19.♂ ♑ 8. 87.☿ ♎ 19. 81.

The places of the Planets being thus found, consider under what signe any of them falleth, which being observed, note which of the houses con­tain the signe in which the planet is, observing the number of Degrees, and in due order place the planet in that house.

Right Ascension of the Mid-heaven, 72. 82.

A Scheme of Hea­ven for July 16, Hour 18, parts 4564, AD. 1587. In the Meridian of London, whose Lati­tude is 51. 53.

And when a Planet contains a lesser number of Degrees then the Cuspe of the house, he is to be placed before the house, in the house preceding, but if greater, he is be placed beyond the Cuspe, according to the sequel, and consequence of the signes.

As in the figure, Sol is in 9 degrees and 7 parts of Virgo, and the signe is placed upon the Cuspe of the Ascendent, but because the Cu [...]pe thereof containeth more degrees of that signe then the Sun, I place the Sun in the preceding house, that is in the twelfth.

CHAP. 17. To find the Angle of the Ecliptick with the Horizon, or the Altitude of the Nonagesime deg. together with its distance from the Mid-heaven.

BY the rules delivered in the last Chapter, find the point culmina­ting, whose declination being ended to the altitude of the Equator [...]n the Northerne signes, or subtracted in the Southern, gives you the altitude of the Mid-heaven, suppose 10 degrees of Gemini were [Page 37] in the Mid-heaven, the declination thereof by the 2 Chapter is 22. 02910. which being added to the altitude of the Equator 38. 46667, because the de­clination is North, their sum 60. 49577 is the Altitude of the Mid-heaven, and the meridian angle of the same point by the 13 Chapter is 81. 53133, hence in the triangle 7. 10. S of the Diagram in the last Chapter, we have given 10. S. 60. 49577 the altitude of Mid-heaven. The angle 7. 10. S 81. 53133. the Meridian angle to find the angle 10. 7. S.

As the Radius

To the sine of 7. 10. S.81. 531339. 9952385
So Cosine of 10. S60. 495779, 6923956
To Cosine of 10. 7. S60. 848619. 6876341

And to find 7. 10 or the distance of Mid-heaven from the Nonagesime degree, the Analogie is

As Radius

To the Cosine of 7. 10. S81. 531339. 6677126
So is the cotangent of 10. S60. 495779. 7527167
To the tangent of 7. 1014. 750479. 4204293
Mid-heaven add70. 00000 

Summe 84. 75047 is the Nonagesime degree. And note that arch found is to be added to the Mid-heaven from Capricorn to Cancer, to be subtracted from Cancer to Capricorn.

CHAP. 18. To find the Parallactical angle, or angle of the Ecliptique with the Verticall circle.

THe angle of the Ecliptique with the verticall circle, is an angle made by the oblique cutting of the circle of altitude, with the E­cliptique, which is a right angle, when the said circle passeth through the 90 degree of the Ecliptique, but falling without the same it is oblique; as in the following figure, D denotes the Zenith, D C B the verticall circle, D E H V T the Meridian, T A B H the Ho­rizon, V A E the Ecliptique, C the angle of the intersection of the E­cliptique with the Vertical.

[Page 38]In the 16 Chapter is shewed how to find the point of the Ecliptique Ascending, and the Suns altitude at any time in the 12 Chapter, which being obtained we may speedily find the parallactical angle.

Admit the Sun at C be in ♍ 4. 07368 distant from the Meridian hours 5. 5436 or 83. 1540. Ad ortum. His Declination will be found by the 2 Chapter to be 10. 05037, and his altitude by the 12 Chapter 12. 10189. The point Ascending by the 16 Chapter is ♍ 17. 90610,

[figure]

which known, in the triangle A B C we have. 1. A C 13. 90610. Se­condly, B C 12. 10189, to find the angle A C B. I say then,

As the tangent of A C13, 9061 co. ar.0. 6062707
Is to Radius 10. 0000000
So tangent B C12. 101899. 3312569
To Cosine of A C B30. 000679. 9375276

CHAP. 19. The elevation of the Pole and Declination of the Sun given, to find the time when he will be due East and West.

IN the second variety of the 12 Chapter, the complement of the Suns Declination F H i [...] 67. 97090 and the complement, of the poles eleva­tion F G 38. 46667, hence the angle G F H equal to the Arch of the Aequator A O is to be sought, therefore I say.

[figure]

As Radius

To Cotangent F H67. 970909. 6070621
So tangent F G38. 466679. 9000864
To Cosine of G F H71. 247799. 5071485

whose comple. O F E 18. 75221 being converted into time giveth 1 hour 25147 parts of an hour, and so long it is after 6 in the morning when the Sun will be due East, and before 6 at night when he will be due West.

CHAP. 20 The Elevation of the Pole, with the Suns Declination and Al­titude given, to find his distance from the Meridian.

IN the Oblique angled Spherical triangle G H F in the 2 Diagram of the 12 Chapter, we have known H F the complement of the Suns Declination, G F the complement of the poles elevation, H G the complement of the Suns altitude, to find G F H the angle of the Suns distance from the Meridian.

1 The side H G44. 54111 
2 The side F H67. 97090 
3 The side G F38. 46667 
Summe150. 97868 
[...]alf Summe75. 48934 
[...]ne of F H67. 97090 co. ar.0. 0329234
[...]ne of G F38. 46667 co. ar.0. 2061682
Differ. G F ½ Summe37. 022679. 7796909
Differ. F H ½ Summe07. 518449. 1167578
Quadrat of the sine of half the Angle 19. 1355403
Which bisected, is sine of21. 692959. 5677701

And the double therof is 43. 38590. The Suns distance from the Meridian, And converted into time, gives two houres, 89259 parts.

CHAP. 21. To find the time of the Suns rising and setting, with the length of the Day and Night.

THe Ascensional difference of the Sun being added to the Semi­diurnal arch in a Right Sphere, that is to 90 degrees in the Nor­thern signes, or substracted from it in the Southern, there summe or difference will be the Semidiurnal arch, which doubled is the day Arch, and the Complement to 360 is the night Arch, which bisected is the time of the Suns rising, and the day Arch bisected is the time of his setting.

As when the Sun is in ten degrees of Gemini, his Ascensional difference is found to be
30. 61613
The Quadrant Add
90.
The Semidiurnal Arch
120. 61613
The diurnal arch
241. 23226
Whose Complement
118. 76774

[Page 41]Converted into time gives 7 houres 91078 parts, which bisected gives the time of the Suns rising. 3 hours 95539, parts; or a little before 4 of the clock.

CHAP. 22. To find the distance of a star from the Meridian.

IF a Starre be between the Mid-heaven and the Horoscope deduct the Right Ascension of the Mid-heaven from the Right Ascension of the Starre, what remaineth is the distance from the Meridian. If a starre be between the Mid-heaven and the 7 house, deduct the Right Ascen­sion of the starre from the Right Ascension of the Mid-heaven, and what remaineth is the distance as before.

IF a starre be between the 7 house and the Imum Coeli or fourth house, deduct the Right Ascension of the Imum Coeli from the Right Ascension of the starre, and what remaineth is the distance from the Meridan. If a star be between the Ascendant and the Imum Coeli deduct the Right Ascensi­on of the star from the Right Ascension of the Imum Coeli, and what re­maineth is the distance from the Meridian as before.

For Example. In the preceding figure, the Right Ascension of the Mid-heaven is 072 deg. 82 parts. The Sun is in the 12 house and his

Right Ascension
155. 97
From which deduct the Right Ascension of the M. C.
72. 82
The distance of the Sun from the Meridian is
83. 15

CHAP. 23. To find the Elevation of the Pole above any circle of position.

A Circle of position, is as it were a certaine Horizon (upon which the point or star proposed doth arise) passing by the two intersect­ions of the Horizon with the Meridian, and may be either above or under the Earth, in respect of the place for which the figure is erected.

A star posited in the

  • 1, 2, 3, 4, 5, 6, house is Under the earth
  • 7, 8, 9, 10, 11, 12, house is Above the earth

Thus in the annexed Diagram A H C is a circle of position passing by the Horizontal point of the Significator at H, and the two intersections of the [Page 42] Horizon of the place at A and C, and L M is the elevation of the pole a­bove this Horizon of the star or circle of position.

[figure]

To find which there must be known. 1. The latitude of the place. 2. The Declination of the star or point proposed. 3. The distance thereof from the Meridian. Hence to find the angle of Inclination of the circle of po­sition with the meridian, the proportions are as followeth.

1. As the Radius, To the tangent of the complement of the stars decli­nation: so is the Cosine of the stars distance from the meridian, To the tangent of the first-arch. To which the pole of the place being added, or subtractod from it according to the following direction, their summe or difference is the second arch.

If the distance of the star from the meridian, be more then 90 and the declination South under the earth or north above it, subtract the first arch from the poles elevation, and what remaineth is the second arch.

If the distance of a star from the meridian be lesse then 90, and the de­clination south under the earth, or north above it, adde the poles elevation, to the first arch, and their agg [...]gate if lesse then 90 is the second arch, if more then [...]0 the complement thereof.

If the distance of a star from the meridian, be either more or lesse [Page 43] then 90, and the Declination North under the earth, or South above it. Substract the elevation of the Pole from the first arch, and what remaine [...] [...]s the second arch.

If the distance of a star from the Meridian be a just quadrant, the angle of inclination may be found at one operation, as in the fourth example.

2 As the sine of the first arch found: Is to the cotongent of the Stars distance from the Meridian: So is the sine of the second arch found; To the cotangent of the angle of inclination. Then to find the elevation of the Pole above the circle of position, the analogie is.

3 As the Radius, To the sine of the Pole of the place: So is the sine of the angle of inclination; to the sine of the Pole of the Circle.

1 Example.

Let the distance of a Star from the Meridian, be more then 90, viz. 97 deg. And the Declination of the Star 31 deg. North above the earth: the Pole of the place 45. Then in the oblique Spherical Triangle H M C we have limited. 1 The side M C the Poles elevation 45 degrees. 2 The side H M the complement of the Stars declination 59 degrees. 3 The an­gle H M C, the Stars distance from the Meridian 97, or instead thereof the acue angle I M H 83, the complement of the other to a Semicircle.

Hence to find I M the proportion is.

As the Radius9010. 000000 [...]
To the tangent of H M5910. 2212262
So is the Cosine of I M H839. 085894 [...]
To the tangent of I M11. 479. 3071206

which being substracted from 45 the Poles elevation, there resteth 33. 53 the second arch.

2 As the sine of I M11. 479. 2985361
To the Cotangent of I M H839. 089143 [...]
So is the sine of I C33. 539. 742232 [...]
To the Cotangent of H C M71. 179. 5328404

The angle of inclination.

3 As the Radius9010. 0000000
To the sine of C M459. 8494850
So is the sine of H C M.71. 179. 9761116
To the sine of L M.42. 019. 8255966

The height of the Pole above that Circle of position.

2 Example.

Let the distance of a Star from the meridian be less then a quadrant, [Page 44] viz. 44. 7. The Declination of the Star, 14. 51. North above the Earth, the Pole of the place 45. then as before.

1 I say, As the Radius9010. 0000000
To the tangent of H M.75. 15.10. 5765162
So the Cosine of I M H44. 7.9. 8574210
To the tangent of I M.69. 74.10. 4329372

To which add the Pole, 45. 00. There aggregate is 114. 74. whose Com­plement 65▪ 26. is the second Arch.

2 As the sine of I M.69. 74.9. 9722634
To the cotangent of I M H.44. 7.10. 0141010
So the sine of I C65. 26.9. 9581892
To the Cotangent of H C M4510. 0000267

The angle of Inclination.

3 As the Radius9010. 0000000
To the sine of C M459. 8494850
So is the sine of H C M4519. 8494850
To the sine of L M309. 6989700

The height of the Pole above that Circle of position.

3 Example.

Let the distance of a Star from the Meridian be 22. 82. the declination 13. 53. South above the Earth: And the Pole 49.

1 Then as the Radius9010. 0000000
To the tangent of H M76. 4710. 6186455
So is the Cosine of I M H22. 829. 9646026
To the tangent of I M75. 3710. 5832481

Subtract the Pole 49. 0 [...]. There rests 26. 37. for the 2d arch

2 As the sine of IM75. 379. 9856855
To the Cotangent of I M H22. 8210. 3759530
So is the sine of I C26. 379. 6475454
To the Cotangent of H C M42. 5110. 0378229

The angle of Inclination.

3 As the Radius90.10. 0000000
To the sine of C M49.9. 8777798
So is the sine of H C M42. 519. 8297661
To the sine of L M30. 669. 7075459

The height of the Pole above that Circle of position.

4 Example.

If the distance from the Meridian be a just Quadrant, or 90 degrees [Page 45] then omitting the two first proportions, the angle of Inclination may be found at one operation, by this analogie.

As the tangent of the Complement of declination, is to Radius.

So is the sine of the Pole, to the cotangent of the angle of inclination.

Let then the declination be 23, and the Pole 45. I say,

As the tangent of H M6710. 372148 [...]
Is to Radius or the angle H M C9010. 0000000
So is the sine of M C45.9. 8494850
To the Cotangent of H C M73. 309. 4773369
Then as Radius, to the sine of M C45.9. 8494850
So is the sine of H C M73. 309. 9812850
To the sine of L M42. 639. 8307700

The height of the Pole above that Circle of position.

CHAP. 24. Of the Ark of Direction, what it is, and how to finde it.

AStrologers use to fore-tel the general Fortune of any Native by the consideration of the 12 Houses, but the particular time, in which we may expect, what is promised by the position of the Heavens at the time of the Birth, they measure out by the arke of Direction. That is, by the distance of the Significators from there Promittors reckoned in the Aequator, by Significators usually meaning, the Ascendent, Mid­heaven, Sun, Moon, and part of Fortune: And by Promittors, the seve­ral Aspects of these Significators to the Planets, or the twelve Houses.

For the clearer understanding of what the arke of Direction is, in the Diagram of the last Chapter, Let A D C represent the Meridian D V S E the Aequator, A C the Horizon, M the North-pole, A H C a Circle of position above the Earth, H B and N R two parallels of Declination. H the Significator, D O his right Ascension. H O his Declination. R the Promittor D S his right Ascension, R S his declination. Now when the Promittor at R comes to N, it is in the same Circle of position with the Significator at H, and the Circle of Declination M R S will be changed into the Circle of Declination M N V, and then the arch of the Aequator, D V is the Right Ascension of the Promittor at N, and therefore the arch of the Aequator V S is the arke of Direction sought. And the manner of finding thereof is as various, as the position of the Significator may be in the figure, which is threefold, viz. Either in the Meridian, in the Signes Ascending, or in the Signes Descending.

CHAP. 25. How to direct the Mid-heaven, and the Imum Coeli.

A Star posited in the meridian, that is, either in the mid-heaven or Imum Coeli, must be directed to his Promittors, by the right As­censions of the Significator and Promittor. If a Significator po­sited in the mid-heaven be to be directed. Substact the Right As­cension of the mid-heaven, from the Right Ascension of the Star or Pro­mittor, taken with its latitude if it have any, and what remaineth is the ark of Direction.

For Example. Let the mid-heaven of the preceding figure in the 16 Chapter, be directed to the 12 degree of Capricorn.

The Right Ascension of the 12 degree of Capricorn is
283. 03
From which substract the Right Ascension of the mid-heaven
072. 02
There rests for the Ark of Direction
211. 23

In like manner: If the Imum Coeli or fourth House, or a Star posited upon the Cuspe thereof be to be directed, you must substract the Right As­cension of the Imum Coeli, or fourth House, from the Right Ascension of the Promittor, and what remaineth is the ark of Direction.

CHAP. 26. How to direct the Ascendent, or Significator posited in the Signes Ascending.

THe Horoscope or Ascendent, or a Significator posited in the signes ascending, that is, in the 12, 11, 10, 1, 2, or 3 houses, must be dire­cted to Promittors, by the oblique Ascensions answering to the ele­vation of the Pole above the Circle of position of the Significator. The elevation of the Pole above the ascendent is the same with that of the place for which the figure is erected. The Poles elevation above the Circle of position of any other Significator must be found as hath been shewed in 22 Chapter. Then if you deduct the oblique Ascension of your Signifi­cator, from the oblique Ascension of your Promittor, what remaineth is the arke of direction.

For example. Let the Ascendent of the preceding figure in the 16 Chap­ter be to be directed to the 26 deg of Taurus. The elevation of the Pole of the Circle is the same with that of the place. viz. 51. 5 [...].

And therefore the oblique Ascension of 26 deg. of Taurus,
27. 50
To which add a Circle that substraction may be made
360
And then the Oblique Ascension is
387. 50
The Oblique Ascension of the Ascendent substract
162. 82
There rests for the ark of Direction
224. 68

Another Example.

Let us suppose a Significator to be posited in the signes Ascending but not upon the Cuspe of the Ascendent, in this case though the Arke of Direction must be found out by the Oblique Ascensions as be­fore; yet the elevation of the Pole above the Circle of position must be first found, because it is not given, as in the last Example.

In the Diagram of the 23 Chapter, let the distance of the Significator from the meridian be 44. 07. The declination thereof North above the Earth H O 14. 85. Hence the Pole L M is 30 degrees. Let this Significa­tor be posited in 10 degrees of Taurus, the Right Ascension thereof D O 37. 58. His Ascensional difference under the elevation of 30 degrees F O 8. 80. Let the Promittor be in 25 of Gemini, the Right Ascension thereof D S. 84. 55. And the Ascensional difference when this Promittor comes to N. is represented by the letters F V. 14. 47. Now then if you substract the Ascensional Difference of the Significator F O, 8. 80. from the Ascensio­nal Difference of the Promittor F V. 14. 47. There will remaine O V 5. 67. we call it the Aequation of the Arke of Direction, which be­ing added to the Right Ascension of the Significator D O. 37. 58. There aggregate is the arch D V 43. 25. Then if you deduct the arch D V 43. 25 from the Right Ascension of the Promittor, D S. 84. 55. There difference is V S 41. 30. The Ark of Direction sought.

Or thus, the Oblique Ascension of the Promittor is 70. 08. The Oblique Ascension of the Significator is 28. 78. There difference 41. 30, is the Ark [...] of direction sought, as before.

CHAP. 27. How to direct a Significator posited in the Signes Descending.

THe Descendent or seventh House or Significator there posited, or in any signe descending, that is, in the 4, 5, 6, 7, 8, or 9 Houses, must be directed to his Promittors, by the oblique Descensions answering to the Elevation of the Pole of the Circle of position of the Significator. As suppose the mid-heaven be in 22. 33 of Gemini. And the Right Ascension thereof, 81. 65. Let the Significator be in 10 de­grees of Taur [...]s. The declination thereof 14. 85. North. His distance from the meridian 44. 07. Hence the Elevation of the Pole above that Circle of position is 30, as before.

Let the Promittor be in 25 degrees of Gemini, the declination 23. 40 North: Now the declination of the Significator and Prommittor being the same with the former, and the Pole of the Circle the same, the Ascen­sional [Page 48] Differences as well of the Significator as of the Promittor, must needs be the same with the former Example, and consequently the same Aequation of the ark of Direction: if then you would find this ark of Direction, by the Right Ascensions, Adde this Aequation of the ark of Direction, to the Right Ascension of the opposite point of the Promit­tor: and from their aggregate, subtract the Right Ascension of the opposite point of the Significator, and what remaineth is the ark of Direction.

As the opposite point to this Promittor in the 25 of Gemini, is the 25 of Sagittarius, the Right Ascension whereof is
264. 55
The former Aequation of the ark of Direction
5. 67
Their Aggregate
270. 22
The opposite point to the Significator in the 10 of Tau­rus is the 10 of Scorpio, whose Right Ascension is
217. 56
Which subtracted from the former aggregate leaveth
52. 64

For the ark of Direction sought.

Or if you will by the oblique Ascensions of these opposite points thus:

The oblique Ascension of the 25 of Sagittarius is
279. 01
The oblique Ascension of the 10 of Scorpio, is
226. 38
There Difference is
52. 63

The ark of Direction as before.

Or lastly, by the oblique Descensions, according to the intention of this Chapter, if you subtract the oblique Descension of the Significator, from the oblique Descension of the Promittor, what remaineth will be the ark of Direction.

As in this Example the oblique Descension of the Promittor, under the elevation of 30 degrees is
99. 01
The oblique Descension of the Significator,
46. 38
Which being subtracted from the oblique Descension of the Promittor, there resteth
52. 63

The ark of Direction sought as before.

CHAP. 28. How to find the Arch of the Aequator, whereby is made the general Table of Positions.

FOr finding this arch of the Aequator, there must be given the angle of Inclination of the Circle of position with the Meridian, & the height of the Pole above that Circle, both which may be found by the 9 Chap­ter: [Page 49] but [...] to our present purpose, we are not tied unto such a [...]dious calcu­lation, because the Pole of the Circle may be supposed, and then the angle of Inclination may be found at one Operation, and this arch of the Ae­quator at another.

And first, the Elevation of the Pole above any Circle of position being given together with the latitude of the place or Countrey, the angle of In­clination may be found, by this analogy.

As the sine of the Pole of the place, is in proportion to Radius: So is the sine of the Pole of the Circle, to the sine of the angle of Inclination.

For Example. In the Rectangle Spherical Triangle of the 9th Chapter L M C right angled at L. Let M C the Elevation of the Pole of the place be 45. And the Pole of the circle LM 42, hence to find the angle LCM. I say,

As the sine of M C45.9. 8494850
Is to the Radius90.10. 0000000
So is the sine of L M42.9. 8255108
To the sine of L C M71. 139. 9760258

Then to find the arch of the Aequator, the proportion is: As the Radius to the sine of the Complement of the Pole of the place: So is the tangent of the angle of Inclination, to the tangent of the arch of the Aequator. For Example, In the triangle A D F of the afore-said Diagram, Let there be given the side A D the Comple. of the Pole of the place 45. The angle of Inclinat. DAF 71. 9. Hence to find the arch of the Aequator. DF, I say,

As the Radius9010. 0000000
To the sine of AD459. 8494850
So is the tangent of D A F71. 1310. 4662 [...]85
To the tangent of D F64. 2010. 3157275

Which is the arch of the Aequator sought.

CHAP. 29. How by the general Table of Positions, to make a particular Table for any Latitude there exprest.

IF thou wouldst make a particular table of positions, first, divide your paper or book into as many Columnes as the largness of the page will bear, then in the head of your table write the particular latitude, for which you would have the table, and under this title write in the third Co­lumn of your page. 1 In the fourth, 2, and so forward till you have fild the Columnes of your first page, do so likewise in the 2d. page, and so for­ward till you have written twice over the several Elevations of the Pole a­bove the circle of position from one unto that degree for which your table [Page 50] is intended; then in the first Columne of your left hand page write, North Declination under the earth and South above it, in the second columne thereof write orderly the several degrees of declination, beginning with a cypher or nought, and then 1, 2, 3, and so forwards till you have writ­ten 32, and in the two first columnes of your right hand page write the contrary, that is, in the first thereof write South Declination under the earth and north above it; and in the second the severall degrees of Decli­nation beginning with 32, and so downward 31. 30. 29. until you come to nought: having thus prepared your book according to that Table in this book, enter your general table of positions with one degree of Ele­vation, and in a straight line directy under the latitude of your place, you shall find the arch of the Aequator answering thereunto, then look for the Ascensional differences answering to every degree of Declination, under one degree of the Poles Elevation, the which being substracted from the arch of the Aequator, write the remainder in a direct line under one de­gree of Elevation, in that page which must serve for North Declination under the Earth: but for the South Declination under the Earth adde the Ascensional difference of every degree of Declination to the former arch of the Aequator, and write their aggregate under one degree of Elevation and right against that degree of Declination, whose Ascensional difference was added thereunto, and so shall you have one Column of your table fi­nished, to make it plain we will add an Example.

In the latitude of 51 degrees 33 hundred parts, the arch of the Aequa­tor answering to one degree of the Circle is 0 deg. 79. and the Ascensional difference for one degree of Declination under one degree of Elevation is 0. 1. of which being subtracted from 79, there remaineth 78, which I write against one degree of Declination in that page of the Table serving for North Declination.

Again, to the same arch of the Aequator, I add 0. 01. and their aggre­gate is 80, and this I write against one degree of Declination, and under one degree of Elevation in that page of the Table which serveth for South Declination under the Earth, and thus must you also add or subtract the Ascensional differences of all the other degrees of Declination, according to this Example. And so shall you have a particular Table of positions for your particular latitude. The use of this Table is to finde the Elevation of the Pole above any Circle or position in that particular latitude, for which the Table is framed, as shall be shewed in his proper place.

CHAP. 30. Of the Doctrine of the Sphere in Tables.

ALthough in the former book there is plainly shewed you, how to find the Declination, Right Ascension, Ascensional Difference, Oblique Ascension, Cuspes of the 12 Houses, and the height of Pole above any Circle of position, by Trigonometrical calculati­on: yet considering that, that way is not altogether so expedite and ready for practice, as some may desire, wee will also shew you how to finde the same by those Tables, that are hereunto annexed.

Precept 1.

The Declination of the Sun or other Planet is found by the signe in the head or foot, and the degree on the right side, if the signe be in the foot, or on the left side if it be in the head: for the common angle gives the Decli­nation sought, if you have respect, to your Planets proper latitude, and the proper part proportional.

For Example: Suppose the Moon were in 19 degrees 56 parts of Leo, and her declination were required, having North latitude 3 degrees. Her Declination in that latitude, in 19 degrees of Leo will be found 18. 02

In 20 degrees it is 17. 70
There difference is 0. 32
Now then if one degree give0. 321. 5051499▪
What shall0. 561. 7481880
They give 18 ferè 1. 2533379

Which being subtracted from 18. 02 because the Declination doth de­crease, the Moons Declination will be found to be 17. 84

Precept 2.

The Right Ascension by the Table following is had by the signe in the head and degree in the left side, and in the common angle is the Right Ascension.

Example. The Right Ascension of a Planet in Aries 1 [...] 251, and 2 degrees of South latitude be sought.

The Right Ascension of 13 Degrees
12. 73
The Right Ascension of 12 Degrees
11. 82
Difference
91
If one Degree give911. 9590413
What shall251. 3979400
They give221. 3569813

[Page 52]Which being added to 11. 82, the R. ascension of the point sought will be 12. 04.

But if the R. ascen. of the point sought be in Southern signes, you must add 180 to the arch found in the table, and you have your desire, thus the R. ascens. of 12 deg. 25 parts of Libra, with two degrees of North Latitude by adding 180 to the former arch will be 192. 04.

Precept 3.

The ascensional difference of any part of the Zodiack is found by the degree of declination in the left side, and the degree of the Poles elevation in the head, the common angle gives the ascensional difference [...]ought. Ex­ample. Let a planets Declination be 4. 43. whose ascensional difference is sought under the elevation of 52 deg. The ascensional difference in that Elevation answering to 5 degrees of Declination is 6. 43. to 4 degrees is 5. 13. there difference is 1. 30.

If one degree

Give1. 302. 1139433
What shall4 [...]1. 6334684
They give56 ferè1. 7474117

Which being added to [...]. 13, the ascensional difference of the point sought will be 5. 69.

Precept 4.

The oblique ascension of any part of the Zodiack is found by the signe and degree in the first Column in the left hand, and the Poles Elevation on the head of the Table, the common angle will give you the oblique Ascension sought.

Example. Let the Oblique Ascension of Virgo 09. 23. in the elevati­on of 42 degrees be sought. In that elevation.

The Oblique Ascension of Virgo 10 degrees is
15 [...]. 87
Virgo 6 degree is
155. 80
Their Difference
4. 07
If 4 degrees4. 009. 3979400
Give4. 070. 6095944
What shall3. 230. 50920 [...]5
They give3. 280. 5167369

Which being added to 155. 80. the obli [...] Ascension sought will be 159. 08

Precept 5.

These things premised, the Right Ascension of M. C, and thereby the Mid-heaven it self will easily be found for the houres from Noon (convert­ed into Aequinoctial degrees, by the table for that purpose) being added to [Page 53] the Suns Right Ascension, do make the Right Ascension of the Mid hea­ven, which sought in the Area of the Table of Right Ascensions gives the mid-heaven it self.

Example.
Let the Sun be in 4 deg. 07 parts of Virgo, as in the 16 Chapter, the time from Noon, Houres
18. 4564
The Suns Right Ascension in 4 degrees of Virgo
1 [...]5. 9 [...]
His Right Ascension in 5 deg. of Virgo,
156. 85
Difference
[...]0. 95
If one degree give950. 9777236
What shall071. 8450980
They give061. 8228216

Which being added to 155. 90. The Suns Right Ascension is 155. 96. The Aequinoctial degrees answering to 18 houres, viz. 270 degrees. And the degrees answering to 4564 parts of an houre are 06. 84, and therefore the Right Ascension of time is 276. 84, which being added to the Suns Right Ascension, their aggregate 432. 80. or rejecting 360 degrees, the remainer 72. 80, is the Right Ascension of the Medium Coeli, whereto answers in the Table of R. Ascensions; 74. 75. [...], the point of the Ecliptick for the Mid­heaven it self.

Precept 6.

The Oblique Ascensions of the other Houses are found by a continual addition of 30 degrees to the Right Ascension of the Mid-heaven, as hath been also shewed in the 16 Chapter, and thus the Oblique Ascension of the 11 House is 102. 80. 12 House is 132. 80. Ascendent is 162. 80. 2 House is 192. 80. 3 House is 222. 80.

The Poles of Elevation above the Circle of Position of the Ascendent is always the same with that of the place, for which the figure is erected, the Poles Elevation for the 11, 12, 2 and 3 Houses you may find in the Table for that purpose annexed to the Table of Oblique Ascensions.

Example. By that Table under our Elevation of 51. 53. the Poles Ele­vation above the Circles of position of the 11 and 3 Houses, is 32. 18. And the Poles Elevation above the 12 and 2 Houses is 47. 46.

Now then to find the Cuspe of the 11 House, look the Oblique Ascen­sion thereof, 102. 80. in the Table of Oblique Ascensions answering to 32. 18, of Elevation, and the point of the Ecliptick answering thereunto is Cancer 24. 98.

In like manner, if you look the oblique Ascension of the 12 house, 132. 80 under the elevation of 47. 46. the Cuspe thereof will be Leo, 25, 26.

[Page 54]If you look the oblique Ascension of the Ascendent 162. 80. under the Elevation of 51. 43 the Cuspe thereof will be Virgo 17. 94.

If you look the Oblique Ascension of the second House 192. 80. under the Elevation of 47. 46. the Cuspe will be Libra 9. 44.

Lastly, if you look the Oblique Ascension of the third House, 222. 80 under the Elevation of 32. 18. the Cuspe thereof will be Scorpio, 6. 35. The other 6 Houses, are in the same Degrees and parts of the opposite signes.

Precept 7.

The Poles Elevation above the Horizon of a Star is found by the de­gree of his Declination, in the second Column of the right hand page of your Table, if the Declination thereof be North under the Earth, or South above it; And in the second Column of the left hand page, if the declinati­on be South under the Earth, or North above it, and his distance from the Meridian in a straight line, for in the head of your Table in a direct line (using a double proportional part if need be) you shall have the degree of the Poles Elevation above the Circle of position.

Example.

In the preceding figure of the 16 Chapter, the Sun is in Virgo, 4. 07 and therefore his Declination is 10. 05. North above the Earth; his di­stance from the Meridian by the 22 Chapter, was found to be 83. 15. Now then to find the Poles Elevation, I look in that Table for the Suns declina­tion in the second Column of the left hand page, and his distance from the Meridian in a straight line, and in the last folio of that Table, I finde a­gainst 10 degrees of Declination, the distance of a Star from the Meridi­an neerest to my number to be 83. 37. and over the head thereof 50, which is the degree of the Poles Elevation above that Circle of Position.

Astronomia BRITANNIC …

Astronomia BRITANNICA The second Book.

OR, The Theory of Planets, according to the Copernican Systeme and Demonstration of the Learned BULLIALDUS.

Exhibiting their first Inequalities at one Operation Trigonometrical.

Their other Inequalities, and Eclipses of the SUN and MOON with much Ease.

[bookseller's logo]

LONDON, Printed 1656.

Astronomia BRITANNICA: The second Book.

CHAP. 1. Of the year Civil and Astronomical.

THe Altitudes of the Planets being given to find their places in the Zodiack, hath been already shewed in the Doctrine of the Sphere, & thence their annual or periodical revolutions, toge­ther with their middle motiōs must be sought, but how to state them so exactly as that we may thereby find their true or appa­rent places for any time required, is that which many have endevoured, but none have as yet found out, at least not so, as that their places computed by their rules, shall exactly agree with observation, nor was Astronomy brought to that perfection in which it now stands but by degrees, and al­though there hath been very much done of late towards the perfecting thereof, yet shall it not perhaps come to its full Acme in this our age. That which we intend, is not to shew you from what small beginnings it hath been increased, or by whose labours, it hath from time to time been still corrected and amended, but to shew you how to compute the places of heavenly Bodies, by the plainest, speediest, and exactest ways that are as yet made publike. And in order hereunto we will shew you first the usual way of finding out the time in which the Planets make their Annual or Periodical revolutions, and how from thence to compute their middle Motions, that their annual revolutions may be known, the time of their entrance into one and the same point of the Zodiack, taken in divers years by observation must be given, with a considerable interval of time between these Observations.

And because the Observations taken in any one Meridian (that are as yet published) are not sufficient for our present purpose we must of necessi­ty, [Page 58] use the observations made in diverse places, but the intervall of time between those observations cannot be had, unlesse we can reduce the time of an observation made in one account to the like time in another; Al­though the periodicall revolutions therefore of the planets are the onely proper yeares and first in nature; yet since the civil yeare in every nati­on is somewhat different from them, we will first shew the quantity of that in most nations, and how to reduce the day of the moneth given in one accont, to the correspondent time in another.

The Civil yeare then, though it doth not exactly agree, yet hath it some proportion with the motions of the Sunne or Moone in every nation; Twelve Moones or Moneths is the common measure of the year in Turkey, in every moneth they have 29 or 30 dayes, in the whole yeare 354, and in every third yeare 355 dayes. The Persians and Egyp­tians do also account 12 Months to their yeare, but their months are pro­portioned to the time of the Suns continuance in every of the 12 signes; in their year therefore which is Solar, there are alwayes 365 dayes. And the Julian yeare, which is the account of all Christendome doth dif­fer from the other onely in this, (that by reason of the Suns excesse in mo­tion above 365 dayes, which is about 5 hours 49 minutes) it hath a day intercalated once in 4 yeares, and by reason of this intercalation it is more agreeable with the motion of the Sun then the former, and yet here is a considerable difference between them, which hath occasioned the Church of Rome to make some further amendment of the Solar year, but hath not brought it to that exactness which is desired, nor will (as is to be feared) be over-hastily brought to that exactnes which it might; taking these accounts therefore as they now stand, if we will reconcile that discrepancy that is between them, there must be some beginning appointed to every of these accounts, and that beginning must be referred to some one, as to the common measure of the rest.

The most natural beginning of all accounts, is the time of the Worlds Creation, but they who could not attain the Worlds beginning, have rec­koned from their own, as the Romanes, ab urbe condita, or from some great name or notable event; so the Greeks account from their Olympicks, and the Assyrians from Nabonasser, and all Christians from the birth of Christ, the beginning of which and all other the most notable Epochaes, as others formerly, so we now have also ascertained to their correspondent times in the Julian Period, which Scaliger contrived by the continual mul­tiplication of three circles all in former times of good use, & two of them do [Page 59] yet remain; the Circles yet in use are those of the Sun and Moon, the one to wit the Sun is a Circle of 28 years, in which time the Sunday Letter makes all the varieties that it can have by reason of the Bisextile or Leap­year, and the Circle of the Moon is the revolution of 19 years, in which time, though not precisely, the Lunations do recur; it is called the Golden Number, and was made Christian by the Fathers of the Nicene Council, as being altogether necessaay to the finding out of the Neomenia Pascha­lis, upon which the Feast of Easter, and the rest of the moveable Feasts de­pend. The third Circle which now serves for no other use, then the constitu­ting of the Julian Period, is the Roman Indiction, or a Circle of 15 years, for if you multiply 28 the Cycle of the Sun, by 19 the Cycle of the Moon, the product will be 532, & this by 15, the product will be 7980 the number of years in the Julian Period; whose admirable condition is to distinguish every year within the whole Circle, by a several certain character, the year of the Sun, Moon, and Indiction, being never the same again until the revo­lution of 7980 years be gon about: this Period, the Authour fixed in the Tohu, or eternal Chaos of the World, 764 Julian years before the most re­puted time of Creation; which being, premised, we will now by example shew you how to reduce the years of Forreigners to our Julian years, and the contrary.

1 Example.

I desire to know at what time in the Turkish account, the 5 of June 1649, falls. The work is this

The years compleat are 1648, and are thus turned into Dayes, by the table of Dayes, and Decimals of Dayes in Julian Years.

1000 Julian yeares give dayes
365250
600 years give
219150
40 years give
14610
8 years give
292 [...]
May Compleat
151
Dayes
5
The Summe
602088

[Page 60]Now because the Turkish account began July the 16. Anno Christi 622, convert these yeares into dayes also thus

600 Julian years give
219150
20 years give
7305
1 year gives
365
June Compleat
181
Dayes
15
The Summe subtract
227016
From
602088
There rests
375072
900 Turkish years gives
318930
There rests
56142
150 years gives
53155
There rests
2987
8 years give
2835
There rests
152
Giumadi I. gives
148
There rests
4

Therefore the 5th. of June 1649, in our English accompt, falls in the Turkish accompt, in the year of Mahomet, or their Hegira, 1058, the 4th. day of Giumadi II.

2 Example.

I desire to know upon what day of our Julian year, the 23 day of the moneth Pharmuthi in the 1912 year currant of the Aegyptian accompt from the death of Alexanders fall.

The beginning of this Epoch [...] is from the beginning of the Julian Pe­riod in compleat dayes.

 
1603397
1000 Egyptian years give
365000
900 yeares give
328500
10 years give
3650
1 yeare gives
365
Phamenoth compleat
2 [...]0
Dayes
23
The summe
2301145
6000 Julian yeares
2191500
There rests
109645
300 yeares give
109575
There rests
70
April compleat
59
There rests
11

It therefore fell out in the yeare of the Iulian period 6300 the 11 of March, that is subtracting from that period, 4712 in the yeare of Christ 1588. He that understands this may by like method convert the yeare, of other Epochaes into our Julian yeares and the contrary.

Next to the tables which concern the reduction of years in general, we annexed tables for the perpetual finding of the Sunday letter, Golden number and Epact in both the Old Julian, and New Gregorian accompt, with the fixed and moveable Feasts, and a Catalogue of some famous places with their latitude and distance in longitude from the meridian of Lon­don, whose use is so obvious that it needs but little explanation; yet to take away all difficulty we have added these directions.

The Cycle of Sun, Sunday Letter, Golden Number and the Epact in both accounts are set against the yeare of our Lord, and when those years are out, they may be renewed againe as oft as you please, thus for the yeare 1656 the Cycle of the Sun 1513, the Sunday letters in the English account are F E, in the Gregorian B A the prime or Golden number in both is 4, the Epact in the English accompt is 14 in the Gregorian 4.

And now to find the movable Feast, seek the English Epact, in the first Columne of that Table towards the left hand, and the first F that follows▪ will shew you that the 3d. of February is L X X Sunday, the 17 of Fe­bruary▪ [Page 62] L Sunday, & the 20th of February Ashwednesday, & the first E that follows will shew that Easter day is the 6th. of April, Ascension day the 15th. day of May, Whitsunday the 25 of May, Corpus Christi the fifth of June, Advent Sunday, November the 30th.

But in the Gregorian, the Epact and Sunday Letters must be sought in the first Columne towards the right hand, so shall the Sunday Letters B A shew the Feast of Easter to be on the 9th of their April, and the rest as in that line they are set down.

The fixed Feasts, together with the Week-day Letters, are set against their proper dayes in every moneth of the Julian year, knowing therefore the Sunday Letter, you may easily know upon what day of the Week any Feast or day of the moneth shall be.

The Catalogue of places doth serve to shew the height of the Pole in those places, and the Difference of the Meridians of any place in the Ca­talogue from that of London. The Letter S notes that the distance is West­ward, A that it is Eastward, the figures under the title of Time are Hours and Decimal parts of an houre, the Earth or any Starre comes sooner or later to the Meridian of that place then that of London.

If the time of a Lunar Eclipse then or other appearance be given at London, afternoon 8 hours, 23 parts, and the time when this happens at Uraniburge be inquired, there is found in the Catalogue for Uraniburge 0 hour 83 parts A, if therefore according to the letter A, 83 parts be added to the time given it makes 9 houres 06 parts for the time at Uraniburge. But if the time of another place be to be reduced to the time at London, the diffe­rence is to be applied with the contrary title.

And that these Reductions whether in time or motion may be the bet­ter compared with those bookes that are written in the old Sexagenary forme, we have added tables for the ready converting of Sexagenary parts into Decimall and the contrary, the first of these tables is for the con­verting of the Minutes and Seconds, &c. of a Degree in motion; and the other of the parts of a day in time, an example in each will be a sufficient explanation.

Let it be required to find the Decimall answering to 37′ 25″ 16‴ 5'''' 29''''' in motion.

In the first page of the table I find 37′ 12″ which is the nearest lesse, and 62 answering thereunto, and in the third columne of the second page in the top of the page I find 12″, in which columne I find 25 seconds, and in the sixt and last columne of that page right against 25″, I find this num­ber 36111111, which being annexed to 62.

The Decimall of 37 minutes 25 seconds is
6236111111
And the Decimall of 16 thuds
0000740741
The Decimall of 5 fourths
0000003858
The Decimall of 29 fifths
0000000373
Their summe
6236856083

is the Decimall sought

2. Example

Again, if it be required to find the Decimall of 8 hours, 17 minutes, 8 seconds, 5 thirds, 12 fourths, 9 fifts. In the first columne of the table en­tituled, A Table to convert the hours and minutes of a day into Deci­malls, I find 7 hours 12 minutes, and in the second columne the figure 3, then looking the 12 minutes in the top of the pages, I cast mine eye down­ward in that column till I come to 8 hours 17 minutes, and in the last co­lumne of the page against 8 houres 17 minutes, I find this number 451388889 and therefore,

The Decimall of 8 hours 17 minutes is
3451388889
The Decimall of 8 seconds
925926
The Decimall of 5 thirds
009645
The Decimall of 12 fourths
0387
The Decimal of 9 fifths
0005
Their aggregate
3452324852

Is the decimall sought.

To find the parts of a degree in motion, or of a day in time answering to any Decimal given, is but the contrary worke to the former;

Example.

As if it were required to find the parts of a degree answering to 6236856083, the 2 first figures of this Decimall are 62 which being sought in the first page of the table give me 37′. 12 and 62 being subtract▪ from 6236856083, the remainder will be 36856083 which being sought in the last columne, my nearest number is 36111111, and right a­gainst that number under 12 in the top of the page I find 25, therefore 37′ 25″ are the parts of a degree answering to the Decimall given, but if you would find the thirds, fourths and fifths, from 36856083

Subtract
36111111
The remainder is
749972

Which being sought amongst the Decimals of the thirds, gives me 16 [Page 64] thirds, and this number to be subtracted from it 740741; and the remain­der 004231 being sought amongst the Decimals of the fourths gives me 5 fourths, and this number to be subtracted from it 3858, and the remain­der 373 sought amongst the Decimals of the fifths gives me 29 fifths, and so the parts of a degree answering to the Decimall given are 37 minutes, 25 seconds, 16 thirds, 11 fourths, and 29 fifths. Thus may you also find the parts of a day in time answering to any Decimall given.

The next thing to be done towards the finding of the annuall revolu­tions of the planets is to find their entrance into any point of the Zodiack desired, and that may be done thus. Having the place of the planet taken by observation before and after its entrance into the point desired, sub­tract the observed place next before from the observed place next after, and the remainder shall shew you the apparent motion answerable to the time between those observation, subtract also the former place, from the place in the point desired, and note their difference: for as the former remainder, that is the apparent motion between the observations, is to the time between those observations: so is this difference, to the time between the first observation, and the planets entrance into the point desired: thus we are to deal with those observations that we our selves shall make, but one mans age not being distance enough between the observations from whence the middle motions may be rightly stated, we must take some observations upon trust; and find the middle motions by comparing the observations made in former ages with those of our owne, of the Sun or Earth, take this Example following.

The vernal Equinox observed by Hypparchus in the year from the death of Alexander 178, was Mechir the 26 day, and 95833333, that is at London 86746111. And the vernal Equinox observed at Uraniburge by Tycho 1588 was March the 9th. 86458333, that is at London 82986111. And that the intervall of time between these two vernall Equinoctialls may be known, the 9 of March 1588 must be reduced to the correspon­dent time in Egyptian yeares from the death of Alexander, which accor­ding to the former directions is thus.

The Christian Aera began in the 4713 complete yeare of Julian peri­od, to which 1587 being added, it makes 6 [...]00 from the beginning of the Julian period therefore to the 11 of March 1588, there are dayes as followeth.

6000 Julia [...] yeares give
2191500
300 years give
109575
February
59
Dayes
08
The Summe
2301142

The Aera Alexandri began in the 12 of November in 4390 yeare of the Julian period in which there are dayes,

4000
1461000
300
109575
80
29226
9
3287
October
304
Dayes
11
Which being subtracted
1603397
From
2301142
There rests
697745
1000 Egyptian yeares give
365000
There rests
332745
900 yeares give
328500
There rests
4246
10 years give
3650
There rests
596
1 yeare gives
365
There rests
231
Phamenoth compleate
210
There rests
21

Therefore the 11 of March 2588 in our English account, falls in the 1912 yeare of the Aera Alexandri the [...]1 day of Pharmuthi. In which space of time

There are dayes
697746
And from the death of Alexander to the 26 of Mechir 178, there are
64781
There rests
632965
[Page 66]From days
697746. 829 [...]6111
Subtract
64781. 86746111
There rests
632964. 96240000

And in this time the Earth or Sun hath gone 1733 circles, [...] 623880 degrees. Hence to find the mean motion for a year or 365 days I say▪ If 632964. 9624 d▪ Give 623880 degrees; How many degrees shall 365 dayes give?

And the answer is 359 deg. 7611456036. That is in Sexagenary numbers 359 deg. 45 minutes, 41 seconds, 1 third, 27 fourths. Again, to find the mean motion for a day I say, If 365 dayes gives 359 degrees, 7611456036, what shall one day give?

And the answer is 0. 9856469743. That is in Sexagenary numbers 0 deg, 59 minutes, 8 seconds, 19 thirds, 44 fourths.

And what is here done for the middle motion of the Earth or Sun, may be done for the other planets.

CHAP. 2. Of the figure which the planets describe in their Motion.

HAving shewed in the former Chapter, by what means the Annu­all or Periodicall revolutions of the Planets may be knowne, with their mean or equal motion, for any part of those revoluti­ons, we should now shew you, how by those equal motions to find their true or apparent places. But we can never hope to find the true and exact Phenomenon of the planets, unlesse we first know the figure in which they move; And this must be collected from such affections, as are by the constant observations of all ages found to be proper and natu­rall to them, or may be rationally collected from them.

  • 1 That the planets have one onely motion, in one onely line, and that those motions are equal, constant and perpetual, hath been confirmed by the observation of all ages,
  • 2 And therefore they must needs be regular, their motions must be in a circle or some other line returning into it selfe, or else their motions could not be perpetuall.
  • 3 Their equall motions must have some place assigned (which the pla­nets naturally behold) to be the beginning of this equall motion.
  • 4 And because the apparent place of a planet taken by observation, is generally different from the place reckoned in its middle motion, the in­equality of this middle and apparent motion must be referred to the [Page 67] center of the Zodiacke, [...]s to the point of that inequ [...]lity.
  • 5 And because the center of the Zodiacke and of the world is to out appearance the same, the point of this inequality must be referred to the center of the world.
  • 6 And because of this difference between the middle and apparent mo­tion, the center of the world cannot be the true and exact center of the planets, but the center of that figure which the planets describe in their motion, must be some other point then the center of the Zodiacke.
  • 7 And though the planets to our appearance are observed to be some­times swifter in motion, then at other some, yet the cause of this inequa­lity of motion must not be such as shall alter the natural and equal motion of the planet, it must be such as shall make the planet to be slower in its furthest distance from the center of the world, and swifter at his nearest, without transposing the equal motion into any other then the first place assigned, whether superficies or circle.
  • 8 And further the apparent motions of the planets in their nearest and furthest distances from the center of the world being the same with their middle, the way of the planets must be such, that when they have gone 90 degrees from their farthest distance in their middle motions, their ap­parent motions must be lesse then 90 by the quantity of that whole ine­quality between the middle and apparent motion; And when the planets have gone a quadrant in their apparent motions, their difference between their motions shall be that whole inequality also, and therefore the cen­ter of that figure which the planets describe in their motions must be in the middle between the points of their equal and apparent motions.
  • 9 And because the mean motion from the point of a planets farthest distance from the center of the world, to the first quadrant is greater then the apparent, therefore the apparent motion must be greater then the mean, from the first quadrant to the point of the planets nearest distance, and consequently a greater portion of the line in which the planets move, must be allowed to the apparent from the first quadrant to the point of nearest distance, then from the point of farthest distance to the first qua­drant.
  • 10 And because the equal motion must not change and that the ap­parent motion doth increase from the point of the planets farthest distance from the center of the world, the angles of the middle motion must be reckoned, in the arches of many parallel circles, which shall also increase from the points of farthest to the point of their nearest distance to the cen­ter [Page 68] of the world, and the line of the apparent motion, must containe those circles in one and the same superficies, and therefore that line must be excentricall from those circles of apparent motion, and so placed that all the parts of apparent motion may proportionably answer to all the parts of equal, yet so as that the least circles of equal motion, shall agree with the point of the planets farthest distance, and the greatest circles with the point of the planets nearest distance from the center of the world.

Seeing now that these circles of middle motion must be parallel, succeed­ing one another in a continued series, and are not one within another, and that the apparent motion must in the farthest distance answer to the least circles, & in the nearest distance from the center of the world to the greatest, there is none but a solid Superficies that can be capable of those greater and lesser circles: And that an unequal sided Cone may be so cut, as that the figure upon the plaine of that Section shall truly represent these affecti­ons of the planets, the learned Bullialldus doth Demonstrate, and for a preparation thereunto he sheweth first,

How two equal right lines may be so drawn in an unequal sided Tri­angle, as that the one shall bisect the other.

An unequal sided Cone being cut through the Axis by a plaine perpen­dicular to the plain of the base, shall make an unequal sided Triangle, and let A B C be such a Triangle, whose base B C let be bisected in I, and parallel therunto draw the line P S, which being within the triangle shall be also bisected in the point R, and from a point taken in this line at pleasure, suppose at H, to the Axis of the Cone A I, draw the line H M so, as that the angles H M R and M R H may be equal; then shall H M and H R be equal also, and let the line H M being continued to the sides of the Tri­angle A B and A C be bisected in the point X, and by the point of bi­section at X, draw the line V X T parallel to the base B C, then are the right lines E K and V T equal, and E K is bisected by V T in the point X.

From the points E V K draw the lines V F, K Q, E D parallel to A I, so shall the segments P R and R S, V Z and Z T be equal, because the right line A I bisects the base B C: and the lines E K and V T being con­tinued to F and Q, the lines F K and V Q shall be contained between the parallels F V and K Q, and because the lines E K and D Q are contain­ed between the parallels D E and K Q, and that E X and X K are equal, the triangles E X D and Q K X shall be like and the sides proportionall, that is E X to X D so is X K to X Q. And so is D E to Q K but E X

[Page 69]

and X K are equal by construction, and therefore X D and X K are e­qual, and so are D E & K Q and the perpendiculars Kδ, and Eφ shall be equal also. And because H M is equal to H R, & H R, parallel to Z X, there­fore as H R, to H M, so is Z X to X M, because E D is parallel to Z M, ther­fore X M to X E, so is X Z to X D, but X M & X Z are equal, & there­fore X E and X D are equal, and the double of them E K and D Q are equal also. And because of the parallels V F, K Q, E D and A Z, it is as A Z to Z V so is E D to D V, and also as A Z to Z T so is K Q to Q T, and by composition as the right angle A Z V is to E D V, so is A Z T to K Q T: and because V Z and Z T are equal, and A Z common to both, therefore A Z V is equal to the angle A Z T, and E D V to K Q T, in which because the perpendiculars Kδ and Eφ are equal, T Q and D V are equal, and now if D V and T Q be both added to D T the right line V T shall be equal to D Q, but D Q is equal to E K and therefore also V T and E K are equal, as was to be proved.

And now if this unequal sided Cone be cut through the bisected line E K, the figure made on that plane by such section shall be an Ellipsis one of whose umbilique points shall fall in the Axis of the Cone.

For V T being equal to E K, and E K being bisected in X, the right line X O in the circle V O T shall be the conjugate diameter in the El­lipsis E K, because it is perpendicular to the line E K in the point X, and reacheth to the extremitie of the plain V O T, and it is also a mean pro­portionall [Page 70] between V X and X T, because it cuts the line V T at right an­gles in the point X. And therefore the square of X O is equal to the rect­angle V X T more by the square of Z X but the rectangle V X T more by the square of Z X shall be equal to the square of Z V, and the square of Z V shall be equal to the square of E X, because Z V and E X are equal, and therefore the squares of X O and Z X, shall be equal to the square of E X, but E X is the greatest semidiameter, X O the lesser, and the square of Z X or M X the difference between the squares of E X and X O, and therefore M X shall be the distance of the umbilique point from the center X, and M the umbilique which by construction is placed in the Axis of the Cone A B C, as was to be proved.

And that we may now see how the aforesaid affections of the planets are represented in this figure, let us suppose the Ellipsis following to be exactly made according to these directions. Let X be the centor, M the, umbilique point agreeing with the Axis of the Cone and center of the El­lipsis, whose plane parallel to the plane of the base is represented by the line F M. The conjugate Diameter let be the right line O X N divi­ding the Ellipsis into two equal parts at the center X, Z is the center of the circle V Z T, the plane and Diameter of which circle passe by X the center of the Ellipsis, now because the center is Z and the Diameter V T

[figure]

[Page 71] their V Z and Z T are equal, and the plane passing by the Axis doth in like manner divide all the Diameters of all the other circle [...] E D, F G L Q and P K the which are also parallel to the base of the Cone.

And because the center of the Ellipsis at X is distant from the Axis A I, by the quantity of X Z equal to M X, the plane which bisects the Ellipsis by the conjugate Diameter O X N shall not bisect the circles, but shall cut off V X a greater part towards E, and X T a lesser part to­wards K.

Let the equal motion of the planet therefore be about the Axis of the Cone A I, and through all the circles which are intercepted between E D and P K, and let the centers of those circles be in the Axis of the Cone, and upon those centers let the planets be conceived to make equal angles in equal portions of time, but the terme of apparent motion to which it is referred, let be the other umbilique at H, the place of the Sun (if we suppose him according to our new Astronomy to be the center of the World.). Then is the Aphelion or part remotest from the Sun at E, the Perihelion or nearest part at K.

And now while the planets describing the Ellipsis shall be equally mo­ved about the Axis of the Cone, in their equal or middle motions, they shall have gone a quadrant about the Cone, when yet they shall want of a quadrant in the Ellipsis by the quantity of the right line M X, and shall be in the point Y, which point is in the circle F M G, and in the Ellipsis, and the right line M Y which is drawn from the center of the circle F G, is set at right angles, upon the Diameters both of its owne circle F G and of the Ellipsis E K, and consequently the angle F M Y is a right angle, and therefore the planets shall move 90 deg. of middle motion about the axis of the Cone when they come to Y, but in the Ellipsis they shall not move so much by the arch Y O, or the right line M X. That this is the true and naturall Hypothesis may thus appeare, because

  • 1 The planets thus describe one onely line about the axis of the Cone, in their equal constant and perpetual motions.
  • 2 Their motions thus are regular, though not in a perfect circle, yet in a line returning into it selfe.
  • 3 Their equal motions have their beginning alwayes in one place, [...]at is, in the Axis of the Cone.
  • 4, 5 The apparent motion of the planets is referred to the Sun at H, as to the center of the Zodiac. 6 And the whole inequality between the mid­dle and apprent motion, is between the umbilique points M and H.
  • [Page 72]7 The motion of the Planets are thus made to be flower in the A­phelion, then in the Perihelion, and yet the equal motion is not reckoned any where but in the first place assigned the axis of the Cone.
  • 8 The Planets in their middle motions will thus goe 90 degrees about the axis, being come to Y, when yet they want of a quadrant in the Ellip­sis, the arch Y O, or M X, and so the center of the Ellipsis is in X, the mid­dle of the whole Inequality.
  • 9 There equal motions from the Aphelion at E to the first quadrant are greater then the apparent, but from the first quadrant to the Perihelion at K, the apparent motions are greater then the mean, and therefore a smaller portion of the line which the Planets describe is allowed to the apparent motion from the Aphelion to the first quadrant, to wit, F Y, and a greater part from the first quadrant to the Perihelion, to wit, Y O R.
  • 10 And lastly, because the circles of middle motion, F G, V T, &c. do increase from the Aphelion to the Perihelion, & that the Planets notwith­standing make equal angles in equal portions of time about the axis of the cone, their motions in the Ellipsis do increase also from the Aphelion to the Periheliō, because these greater angles are subtēded by greater lines in grea­ter circles, by lesser lines in lesser circles, & because the lesser circles are pla­ced towards the top of the Cone at A, & Aphelion at E, the greater towards the base and Perihelion at K, the motion in the Ellipsis is slower about the Aphelion and swister towards the Perihelion; And thus the middle motions are not reckoned in one onely circle, but in many parallel cir­cles comprehended between E D and P K, these circles are contained in one plain Superficies, and by these circles the planets describing an Ellip­sis doe continually passe, and yet they are all of them excentricall in re­spect of the figure which the planets describe, as was before required. Thus then there is an admirable Harmony between the motions of the planets in this figure, and their motions in the heavens found by obser­vation; probably therefore we may conclude that the figure which the planets describe in their motions is an Ellipsis.

CHAP. 3. Of the Lines and Method to be used for the finding of a Planets true longitude from the Aphelion in this figure.

HAving resolved upon the figure which the Planets describe in their motions, we come now to shew you what lines must be drawn, and method used for the finding a planets true longitude from the Aphelion in [Page 73] this figure; and in order thereunto, we will shew you first the order of the spheares in which the planets move, and how mechanically to draw this Ellipticall figure of their motions upon a plane. As to the Spheares, 1 We suppose that the Sun is placed in the middle of the world in or a­bout the center of the Spheare of the fixed Starres, and hath no circular motion but centrall onely.

2 That the Earth is one of the planets, and with her annual motion a­bout the Sun describeth her Orbe between the Orbs of Mars and Venus.

3 That the Moon is moved about the Earth, as her center, and so in her annuall motion hath respect both to the Earth, and to the center of the Earths orbe the Sun.

4 That the Orbe of Venus is next under the Orbe of the earth, and the Orbe of Mercury between the Sun & the Orbe of Venus. Next above the Orbe of the earth we suppose the orbe of Mars, the Orbe of Jupiter next above Mars, and the Orbe of Saturn next to the Orbe of the fixed Stars.

According to these supposed principles, we would have immediately shewed the method of calculation, but that the Mechanicall way of draw­ing an Ellpsis, doth if not demostrate, yet at least illustrate that method.

[figure]

[Page 74]An Ellipsis by the helpe of a thread may be mechanically made thus, first draw a right line to that length which you would have the greatest Diameter to be, which let be A P, and from the middle of this line at X, set off with your Compasses the equal distances X M and X H.

Then take a piece of thrid of the same length with the diameter AP, & fasten one end of the thrid in the point M, and the other at H, & with your pen extending the thread thus fastened to A, & from thence towards P, keep­ing the thrid stiffe upon your pen, draw a line from P by B to A, the line so drawne shall be an Ellipsis, in which because the whole thread is equal to the Diameter A P therefore the two lines made by the thread in draw­ing of the Ellipsis must in every point of the Ellipsis be also equal to the fame diameter A P, they that desire a demonstration thereof Geometri­cally may consult with Apollonius Pergaeus, Claudius Mydorgius, o [...] others, in their treatises of Conicall sections; for our present purpose this is sufficient, and from the equality of those two lines, with the Diameter, a brief Method of Calculation, is thus demonstrated by Dr. Warde.

Let the line M E be equal to A P, and draw the lines H B and H E, then in the plaine triangle M H E, having the sides M E equal to the Dia­meter, and M H the distance of the umbilique points, with the angle H M E, the angles M E H and M H E shall be given also, but the angles B E H and B H E are equal, because the sides B H and B E are equal by construction, and therefore if you subtract the angle B E H from the angle M H E, there will remaine the angle at the Sun M H B, which is a planets true longitude from the Aphelion or the equated Anomaly.

And of these three things propounded to be given, the side M E is by construction made equal to the Diameter A P, how the angle H M E and the side M H must be had shall plainely appeare by that which fol­lowes.

CHAP. 4. Of the proportion by which the motion of the Planets doe increase from the Aphelion to the Perihelion.

THough the equal motions of the planets are to be reckoned (as hath been said) in diverse parallel circles about the Axis of the Cone, whose diameters must still increase from the top of the Cone at A, to the base B C, that the motions of the planets in the Ellipsis may encrease also; yet in the calculation we cannot conveni­ently [Page 75] reckon the middle motion in any more circles then one, and there­fore it must be proved, that the angle comprehended between the lines drawn from E to that point in the diameter of the Ellipsis which is made the common Center of the Circles of middle motion, and fr [...] that Center to the planet in the Ellipsis, is alwayes equal to the a [...]gle of middle motion, comprehended between the s [...]midiamet [...] of the pla­nets proper circle of middle motion and the line d [...]wn from the center of that circle to the planet in the Ellipsis, this Bull [...]aldus takes for granted, and Dr. Ward doth thus demonstrate.

[figure]

F M G is a circle of middle motion whose center is in the Axis of the Cone, and in the umbilique point of the Ellipsis M, but a planet being in the Ellipsis at R the proper circle of its middle motion is L β Q and the angle comprehended by the Radius of that circle Lβ, and the line drawn from β the center thereof to R the place of the planet is equal to the angle comprehended between the line E M and the line drawn from M to R in the Ellipsis, for thus there are made two right angled triangles M H R and β H R, in which the side H R is common to both, for it is set at right angles in the Ellipsis and in the circle equant, and the sides M H and β H are equal by what hath beene already said in the 2 Chapter, therefore the angle R M H is equal to the angle R β H, and by consequence R β L and R M E are equal also, but the angle R β L is the angle of the middle mo­tion of a planet from the Aphelion, or the angle of the simple excentricke anomaly, and therefore the angle R M E is the mean anomaly also, whose complement to a semicircle is the angle M E H in the Diagram of the preceding Chapter.

[Page 76]When a Planet therefore descends from E to K, the angles at the axis of the Cone, or at M the umbilique point of the Ellipsis do alwayes increase, and therefore the meane anomalie is increased, for the angles of its circle Equant do answer to more degrees at the axis, and those angles also, are alwayes degrees or parts of greater circles, and therefore the planets in­crease in the swiftnesse of their motion in such proportion as the circles, Diameters, or Radii of those circles equant do increase.

For Demonstration whereof let the line E ψ be made parallel to the axis of the Cone, then shall the parts of the semidiameters of the circles equant comprehended between those parallels E ψ and A I be equal to the semi­diameter of the least circle E O, and the parts intercepted between that parallel E ψ and the side of the triangle A B, shall be the proportionall excesse above the least motion in E O.

[figure]

And the mean acceleration is in that circle equant whose plain parallel to the base of the cone doth pass by the center of the Ellipsis, that is in the cir­cle V D T, for seeing that M X & Z X are equal, as also V D & Z X, V D must needs be the difference between the semidiameter of the least circle E L & the middle circle V T, & the excess of that semidiameter, above the semidiameter of the least circle, must be equal to M X or the excentricity, but the distance of this circle from the Aphelion is 90 degrees, and may be called the Diacentrick circle, and is the Radius of the circle of the e­quated anomalie E X And the difference between the semidiamater of V T, and the parallel circle ω K is also equal to M X, for as E V to E ω so [Page 77] is E X to E K, and again, as E V to E ω so is V D to ω ψ, and because E X is the halfe of E K, therefore V D shall be equal to ω Y or to the halfe of ω ψ, and therefore ω Y is also equal to M X, when a planet therefore is in the circle V T, it is swift in motion, and is in the middle between the swiftest and the slowest motion, and because that middle ac­celeration of the planets, is the acceleration in a quadrant, therefore as E X to V D, so is E M to G π. That is, as Radius to the excentricity, so is the versed sine of the distance from the Aphelion, to the part pro­portionall of the planets acceleration; and therefore also (faith Bullial­dus) it is as the whole sine, to the whole difference, so is the sine of the distance of the middle motion from the Aphelion, to the part of the diffe­rence answering to that distance. From hence and the two following pro­blemes of Vieta, he propounds a method for the finding of the Aphelion and distance of the umbilique points.

Probleme 1.

Three points in the circumference of a circle being given, to find a dia­meter▪ upon which there being perpendiculars let fall from the points given; the segments of the diameter intercepted by these perpendiculars shall be proportional to another proportion given.

In the circle B C D whose center is A, let the points given be B, C, D, and let it be required to find the diameter of that circle upon which per­pendiculars

[figure]

[Page 78] being let fall fall from the points B, C, D, the segments of the Diameter shall be proportional to another proportion given: let the pro­portion of the segments intercepted by the perpendiculars let fall from B and C be required to be as S to R.

Let the line C B be cut in E, so as C B may be to E B, as S to R, and let D E, cut the Diameter F G at right angles in H. Then is F G the Diameter sought, upon which seeing the lines B I, C K, D H doe fall perpendicularly, K I shall be to H I as S to R.

For the right lines C B are parallel, or not parallel, if they be parallel, C B shall be equal to K I, and E B to H I, and then by construction K I shall be H I, that is C B to E B, in the given proportion as S to R. But if they can meet, let the point of their meeting be at L. Then it shall be as L C to L K, so L E to L H, and so is L B to L I. And then dividing and changing the termes, it shall be as K I to H I, so is C B to E B, or so is S to R as was required.

And thus likewise K H and H I, with the arches B C, C D, and B D, being given, we may find the arch B G, and the Diameter F G in the same parts with K H and H I, for the arches C D and D B being given, the subtenses of those arches and angles opposite to them in the triangle B C D shall be given also in the parts of the Diameter F G, and there­fore the sides E B and D B with the angle E B D being given, the angle E D B or D B M shall be given also, which being deducted from the arch B M D shall leave B M or the double of B G.

[figure]

Probleme 2.

Two points in the circumference of a given circle being given, to find the Diameter, upon which perpendiculars being let fall from the points given, the segment of the Diameter intercepted by those perpendiculars shall be equal to a line given.

In the circle B C whose center is A, let the given points be B C, let the given line be Z. Subttend the periphery B C, and let the right line B C be made the Diameter of a circle, in which draw the line C D equal to Z. But by the center let there be drawn E F the Diameter of the cir­cle B L C parallel to D C, and then the perpendicular B D being let fall upon M C, the angle B D C shall be a right angle.

[figure]

And because E F and D C are pa­rallel, B D shall cut E F at right an­gles in the point K, and B K shall be parallel to C I, and therefore D C and K I shall be equal, therefore in the circle B C, the points B and C be­ing given, there is found the Dia­meter E F, upon which the perpen­diculars B K and C I being let fall, the segment K I intercepted by those perpendiculars is equal to C D that is to Z the line given.

Thus likewise the summe of the arches, and the summe of the Sines of these arches being given, we may distinguish the arches and the Sines if the center A be between K and I. Or the difference of the arches and the difference of their sines being given, we may distinguish the arches and the sines, if the point K be betweene the center A and the point I.

When three places therefore in the apparent motion of the Sun orany other planet, with the intervall of time are given, the middle motion of the planet shall be given also, with the difference between the middle and apparent in those intervalls, and the rest from these.

[Page 80]

[figure]

For if the points B C D in the Diagrams of the first probleme be given, to wit, three places in the apparent motion, & the middle motion in the inter­valls of time B C, C D, the difference between the middle and apparent motion shall be given also; let K I the part of the diameter F G, be the dif­ference of the middle from the apparent in the intervall B C, and let H I be the difference in the intervall B D.

Then in the triangle B C D, the arches B C and C D are known, and therefore the angles at D and B are known also, and by consequence the third angle at C, and from thence the subtense C B, now that we may find the angle E D B, the side C B must be cut in the same pro­portion as the line K I is cut in H. That so K I may be to H I as C B to E B. And so we shall have E B in the like parts with B D; and the sides E B, B D, with the angle at B, in the triangle B E D being given, the rest shall be given also, and the angle at D being given, we shall have the arches M B and M D.

And lastly, F G shall be given in the like parts in which K H, and H I are given. For as the summe of the Sines complement B I and C K, to K I, so is the Diameter F G, to the same diameter in the parts of K E and so the first inequality shall be given, and the diameter from whence it begins.

CHAP. 5. Of the inequality of the Earths annual motion, and of the Diameter in which the Aphelion and Perihelion are placed.

THe inequality of the Earths annual motion, if we suppose the motion to be exactly circular, may from the Observations of Copernicus made at Fruenburg in Prussia, 1525, or rather as they were corre­cted by Tycho, 1584 be they found; Between the Autumne and the Vern­al Equinox, according to Tycho there were dayes 178. 43333. 33333. And between the Autumne Equinox, and the middle of Mars there were dayes 45. 15416. 66667.

[figure]

Upon the Center F describe the Suns Orbe A B C, let A be the Vernal Equinox the the Autumne, D the middle of Mars, and let D E intersect A C in the point G, and draw the line A D: Then is the ark of middle motion C D 44 degrees, 5061111111, and therefore the angle C A D, 22. 25305. 55556. and the angle of apparent motion C G D 45 degrees, which being deducted from 180 degrees, give the obtuse angle A G D, 135 degrees.

And therefore the angle C D G
22. 74694. 44444.
And the arch A E
45. 49388. 88889.

Again, the ark C D A, 175 deg. 87500. 00000. from which deducting C D 44. 50611. 11111. the remainder is D A, 1 [...]1. 36888. 88889. The subtense A D 18225828. to which A E being added, the whole is D E, 176. 86277. 77778. and the subtense of D E, 19992506. And because that neither of these Segments do make a Semicircle, we must find the A­phelion in the other part of the circle E B C. Let the line E B represent the Aphelion and Perihelion, G F the excentricity, F H then being drawne perpendicularly shall bisect D E and make right angles in the point H. [Page 82] And in the triangle A G D, the angles being given with the side A D, there is also given G D 9763585, whch being deducted from the halfe of D E there shall remaine G H 232668, and the perpendicular F H may be thus found, D A E wants deg. 3. 13722. 22222 of a semicircle, the halfe whereof is 1. 56861. 11111, whose sine 273740 is the side F H, now then H G and F H being given, we may find the angle F G H 49. 63666. 66667, which with the arch A E 45. 49388. 88889 makes 95. 13055. 55556, therefore the Aphelion is ♋ 5. 13055. 55556, or in sexagenary numbers, in 5 degrees of Cancer 7 min. 50 seconds. And the excentricity F G 359261.

But the method for the finding of the Aphelion and excentricity which we propounded in the last chapter, is more sutable to the Elliptical motion of the planets, and according to that method the earths Aphelion and Ex­centricity, or semidifference of the umbilique points, from the accurate observations of Tycho in the year 1588 may be thus found.

From the middle of Taurus to the middle of Leo there were dayes in the apparent motion, 94. 24662. 03703.

From the middle of Leo to the Autumne Aequinox there were dayes 46. 40277. 77778.

From the middle of Taurus to the Autumne Aequinox there were therefore dayes 140. 64939. 81481.

[figure]

In the annexed Diagram let C represent Taurus 15 deg. D 15 deg. of Leo. Then shall the arch of apparent motion C D be 90 deg. and D B 45, but in the middle motion the arch C D shall be 92. 89277, and D B 45. 73777, and CB 138. 63055.

[Page 83]

First, we will worke with the arches of apparent motion.
Arch.Deg.AnglesDeg.Sides
C D90. 00000C B D45. 00C D70711
D B45.D C B22. 50D B38268
C B135.C D B67. 50C B92388

The halfe differences of the middle from the true.
1 Deg. 1. 44638K H2524 
2 Deg. 0. 36888H O644 
Deg. 1. 81526K O3168 
As K O 3168 co. arith.  6. 4992149
To C B 92388  4. 9656155
So is H O 644  2. 8088858
To E B 18780  4. [...]7 [...]7152

And now in the triangle E D B we have the sides D B 38268, [...] B 18780, and the angle E B D 45 deg. to find the angle E D B.

As the summe of D B and E B57048 co. ar.5. 2437596
To their difference194884. 2897673
So the tangent of ½ D and E67. 5010. 3827756
To the tang. ½ the difference39. 512839. 9163025

The angle E D B 27. 98717 and the double thereof is the arch B M N 55. 97434 from whence taking M N [...]q [...]al to D B 45 there rests B M 10. 97434, and the halfe of that is B G 5. 48717, and the summe of D B and B G 50. 48717, now D represents the 15 deg. of Leo and the complement of D G to a quadrant is the arch D L 39. 51283 from the vernall Equinox to the 15 deg. of Leo is 135 deg. from which deducting D L 39. 51283, there rests for the point of the Aphelion at L 95. 48717, that is in Cancer deg. 5. 48717. And now to find the Semidistance of the umbiliques, As the summe of the Sin [...]s of the complements of B O and C K, is to K O, So is the Radius A G to the same Radius A G. Now if you deduct 15 deg of Taurus from Cancer 5. 48717 the arch C L will be 50. 48717 and B G 5. 48717 being d [...]duct­ed from L G 90, there rests L B, 84. 51283 the sine of L C is K A 77 [...]8 and the sine of A O 99541 and the summe of K A and A O is 176 [...]8 [...] now then,

[Page 82]

As the summe of K A and A O176689 co. ar.4. 7527 [...]94
Is to the ½ difference K O31683. 5007851
So is the Radius A G100000 
To the same Radius A G in the parts of K O17928. 2534945 or degrees 1. 02139 halfe the inequality desired.

But if we take the arches of Middle motion the calculation will be as followeth,

Arch.Deg.AddDed.Sides.
C D92. 89277C B D46. 446 85C D.72473
D B45. 73777D C B22. 868885D B.38862
C B138. 63054C D B C B.93554

Halfe the differences of the middle from the true▪ as before.
1 Deg. 1. 44638K H2524. 14119
2 Deg. 0. 36888H O643. 81259
Deg. 1. 81526K O3167. 95378

As K O3168 co. arith.6. 4992149
Is to C B935544. 9710623
So is H O6442. 8088858
To E B190184. 2791630

And in the triangle E D B the angle at D may be thus found.

The side D B is38862 
The sine E B is19018 
The summe is578805. 2374765
The difference198444. 2976292
Tangent ½ D & E66. 7768110. 3674618
To the tangent ½38. 625869. 9025625

28. 15095 the angle E D B and the double thereof is the arch B M N 56. 30190 & from thence taking M N equal to D B 45. 73777 There rests B M 10. 56413 and the half of that is B G 5. 282065. and the summe of D B and B G 51. 01997. Now D represents the 15 degrees of Leo, and the complement of D G to a quadrant is D L 38. 9800 [...]. from the Vernal Equinox. to the 15 deg. of Leo, is 135 deg. from which deduct­ing D L. 38. 98003, there rests for the point of the Aphelion at L, 96. 01997. that is in Cancer, 6 deg. 01997, from which the difference be­tween the true and mean motion in that interval being deducted 73776, the place of the Aphelion will be in Cancer, 5. 28221.

[Page 83]And to find the Semidistance of the umbiliques deduct 15 deg. of Tau­rus from Cancer 5. 28221, there will remaine for the arch C L 50. 28221, and B G 5. 28206 being deducted from L G 90 there rests for the arch, L B 84. 71779, the sine of C L is K A 76921

The sine of L B is A O 99575

As their summe1764964 co. ar.4. 7532652
Is to K O31683. 5007851
So is the Radius A G 10. 0000000
To the same A G 1795 8. 2540503

This excentricity Bullialdus corrects by the apparent places of the pla­nets in the center of the Ellipsis, and that angle according to the Method of our calculation may be thus found.

From 15 degrees of Taurus, or from
225. deg.
Deduct the Aphelion
095. 28221
There rests the angle M H E
129. 71779
whose complement to 180 deg. is
50. 28221
the summe of M E H and E M H and the halfe thereof
25. 14110
The side H E200000 
The side M H3590 
The summe2035904. 6912436
The Differ.1964105. 2931636
Tang. ½ summe25. 141109. 6714590
Tang. ½ differ.24. 359029. 6558662
The summe49. 50012 E M H 
Difference00. 78208 M E H being doublled is the angle 
M B H1. 56416 
 From E M H49. 50012
 Deduct M E H or E M B00. 78208
 There rests B M H48. 71804

As the sine of M B H1. 56416 co. ar.1. 5638976
Is to the side M H35903. 5550944
So is the sine of B M H48. 718049. 87591264. 9949046
To the side B H98833 
The side X H1795 
The Summe100628 co. ar.4. 9972811
The Differ.970384. 9869418
Tang. ½ sum25. 141109. 67145909. 6556819
Tang. ½ Dif.24. 34989 

Differ. 00. 79121 X B H.

From the 15 deg. of Taurus or from 45
45.
Deduct the angle X B H
00. 79121
There rests the place required
44. 20879
Again, from 0 deg. of Libra or from
180.
Subtract the Aphelion
95. 28221
There rests the angle M H E
84. 71779
And therefore ½ of M E H and E M H
47. 64110
The side H E200000 
The side H M3590 
The Summe203590 co. ar.4. 6912436
The Differ.1964105. 2931636
Tang. ½ summe47. 6411010. 0400951
Tang. ½ Differ.46. 6154210. 0245023
Aggregate
94. 25652 E M H
Difference
1. 02568 M E H which being doubled is
the angle M B H
2. 05136
From E M H
94. 25652
Deduct M E H
1. 02568
There rests B M H
93. 23084
whose complement is A M B
86. 76916
As the sine of M B H2. 05136 co. ar.1. 4461743
Is to the side M H35903. 5550944
So is the Sine of B M H86. 769169. 9993071
To the side B H1001325. 0005758
The side X H1795 

[Page 87]
The summe101927 co. ar.4. 9917108
The differ.983374. 9927169
Tang. ½ summe47. 6411010. 0400951
Tang ½ differ.46. 6167710. 0245228
Differ.1. 02433 The angle X B H. 
And therefore the Earths place
181. 02433
Now then from the Aphelion
95. 28221
Subtract Taurus, that is
44. 20879
There rests the arch C L
51. 07342
And from L G
91. 02433
Deduct B G
5. 28206
There rests the arch L B
85. 74227

77795 is the sine of 51. 07342

99724 is the sine of 85. 74227

Summe 177519
 
As the summe 177519 com. ar.
4. 7505576
Is to K O 3168
3. 5007851
So is A G 100000
5. 0000000
To the same A G 1784
3. 2513427

But according to this method, the Aphelion may be somewhat more ex­actly found, if we take the Arithmetical mean, between the apparent and middle motion, and so;

[Page 88]

Arch.DegAngleDeg.Side
C D91. 44638C B D45. 723 [...]9C D71597
D B45. 36889D C B22. 68444D B38565
C B136. 81527C D B68. 40763C B9 [...]983
Now then to find E B I say,
As K O 3160 co. ar.
6. 4992149
Is to C B 92983
4. 9684035
So is H O 644
2. 8088858
To E B 18902
4. 2765042

Then in the triangle E D B, we have known the side D B 38565, the side E B 18902, and their contained angle E B D 45. 72318, whose complement to a semicircle is 134. 27681. The half summe 67. 13840.

As the summe of D B and EB57467 co. ar.5. 2405815
Is to their differ.196634. 2936497
So is Tang. ½ D and E67. 1384010. 3750715
To the Tang ½ differ.39. 06019 
Differ.28. 07821 the angle E D B 
The angle E D B
28. 07821
E D B doubled is the arch B M N
56. 17926
From which subtract M N or D B
45. 36889
There rests B M
10. 78753
The halfe of B M is the arch B G
5. 39376
And D B being added to B G, D G is
50. 76265
And the complement there of is D L
39. 23735
Which being deducted from ♌ or
435. 00000
There rests the Aphelion at L
95. 76265
And the halfe difference D B
0. 36889
Being deducted there rests
95. 39377
The Aphelion then is in Cancer 5 deg.
39377
And to correct the excentricity from the 15 degree of Taurus or ad­ding a semicircle from
225.
Deduct the Aphelion
95. 39 [...]77
There rests in the Ellipsis M H E
129. 60623
whose complement to 180 is the summe of the opposite angles M E H and EMH
50. 39377

[Page 89]In the Triangle therefore of the last Diagram M E H, we have,

  • 1. The side H E 200000
  • 2. The side H M 3568
  • 3. The angle M H E given
As the summe203568 co. ar.4. 6912904
To the difference1964325. [...]932122
So tang. halfe summe25. 196889. 6724222
To tang. halfe differ.24. 411549. 6569248
Aggregate49. 60842 the angle E M H 
Difference00. 78534 the angle M E H 
Differ. doubled is1. 57068 the angle M B H 
Differ. subtracted48. 82308 is the angle B M H▪ 
As the sine of M B H1. 57068 co. ar.1. 5620900
To the side M H35683. 5524248
So is the sine of B M H48. 825089. 8766104
To the side H B979774. 9911252
The side X H1784 
The summe099761 co. ar.5. 0010393
The differ.961934. 9831434
Tang ½ summe25. 196889. 6724222
Tang. ½ differ.24. 395669. 6566049
Differ.00. 80122 the angle X B H which being subtracted from 15 degrees of Taurus, or from 45 deg. there rests 44. 19878 the Aphelion95. 39377
Place of the earth subtract 44. 39878
There rests the arch C L 51. 19499

Againe from 0 degrees of Libra or from 180.
Deduct the Aphelion 95. 39377
There rests in the Ellipsis M H E 84. 60623
And therefore the ½ summe of the angles E M H and M E H 47. 69688
As the summe203568 co. ar.4. 6912904
To the differ.1964325. 2932122
So tang. ½ summe47. 6968810. 0409444
To tang. ½ differ.46. 6776310. 0254470
Aggregate94. 37451 angle E M H 
Difference01. 01925 angle M E H 
Differ. doubled2. 03850 angle M B H 
Differ. subtract93. 35526 angle B M H 

As the sine of M [...] H2. 0385 co. ar.1. 4489043
To the side M H35683. 5524248
So is the sine of B M H86. 644749. 9992548
To the side H B1001345. 0095839
The side X H1784 
The summe101918 co. ar.4. 9917492
The differ98 [...]504. 9927743
The tang. ½ summe47. 6968810. 0409444
Tang. ½ differ.46. 6790110. 0254679
Difference01. 01787, X B H which being added to ♎ the place will be 181. 01787, from which subtract B G 5. [...]9376 there rests 175 or L B 85. 62411. 

The sine of C L77927 
The sine of L B99707 
As the summe177634 co. ar.4. 7504740
Is to K O31683. 5007851
So is A G100005. 0000000
To A G17833. 2512591

which comes so neer to the Excentricity before found that we may with­out manifest error make use of either.

CHAP. 6. Of Stating the Earths middle motions by sundry observations.

TO find the Earths middle motion for any time under a yeare, the way already prescribed in the first Chapter (as to the use for which it was intended) is exact enough, but to state the true quan­tity of the Earths annual motion, the apparent Equinoctials must be reduced into the mean, which cannot be done unless the Aphelion be first found, having found that therefore by the observations of Tycho, we will now find it by the observations of Albategnius, in the year from the death of Alexander, 1206, and the intervall of time then between the Autumne and the Vernal Equinox was dayes 178. 51250, and the middle motion for that time, is deg. 175. 95083. The true motion is 180.

From which subtract
175. 95083
Their difference is
4. 04917
The half difference is K L
2. 02458
Therefore as A E3568 com. ar.6. 4475752
To A E1000005. 0000000
So is K L35333. 5481436
To K L990194. 9957188

Half the arch H I L is 87. 97541, whose sine 99938 is the side H L, and therefore,

As the side H L99938 co. ar.5. 0002727
Is to Radius, so is K L990194. 9957185
To the angle K H L82. 227189. 9959912

And the angle H L K07. 77282And L F K168. 50353
And the arch H K15. 54564And L F84. 25176
The arch H I L add175. 95083The place of the Aphelion at F 
The arch L I H B191. 49647  

[figure]

[Page 92]This Autumne Equinox was observed September the 19th, from the death of Alexander 1206 yeares, that is in the yeare of our Lord 882. In the beginning therefore of the yeare of Christ 883, the Aphelion was in Gemini 24 d. 25176

And in June 1588, the Aphelion was in Cancer
5. 39377
Their difference is
11. 14201

And betweene both observations there are 706 Egyptian years, now then to find the mean motion of the Aphelion for a yeare I say, If 706 years give 11. 14201, what shall one yeare or 365 dayes give? and the answer is Deg. 0. 0157818838

And againe, if 365 dayes give 0157818838 one day shall give o deg. 0000432380.

In 882 Julian years there are 322150 dayes, by which if you multiply 0000432380 the product will be deg. 13. 9291217, which being de­ducted from the aphelion before found, Gemini 24. 25176, the aphelion in the beginning of the Christian Aera will be in Gemini 10. 3226383, that is, 19 21 29.

But from Hypparchus, that is from 177 yeare from the death of A­lexander to the 1205 yeare compleate in the same account, there are 1028 Egyptian years, and the meane motion of the Aphelion in that time is,

Deg.
16. 2237765464
Gemini
24. 2516600000
Gemini
08. 0278834536

which being deducted from there rests for the aphelion at that time.

And therefore the vernall Equinox observed by Hypparchus in the yeare from the death of Alexander 178 Mechir 26. 95833333, was di­stant from the Aphelion deg. 68. 027883, which being deducted from a Semicircle the angle in the Ellipsis of the next Chapter A M E will be found to be 111. 972117, and this angle is the summe of the angles M E H and M H E, and therefore the equation to be subtracted may be thus found.

[Page 93]

The side M E200000 
The side M H3568Logarithms
The summe203568 co. ar.4. 6912905
The Differ.1964325. 2932122
The tang. ½ summe55. 9860610. 1707846
Tang. ½ differ55. 0318610. 1552873
Differ.00. 95420 angle M E H 

Differ. doubled. 01. 90840 angle M B H or the Equation sought: which may be converted into time thus, if the parts of a degree of equal motion, 98564 give one day; 1. 90840 snall give 1. 93620, and this being added to the true Equinoctial, Mechir 26. 95833 the middle will be Mechir 28. 8945 [...], or deducting 05625; for the difference of me­ridians between Uraniburge and Alexandria, it will be at Uraniburge; Mechir 28. 83828. And the vernall Equinox observed by Tycho at Ura­niburge 1588, was March the 9. 86458, and the Earths aphelion then was in Cancer 5. 39377; and therefore the arch answering to the ex­centricity 3568, viz. deg. 2. 04529 being converted into time as before, will be days 2. 07508, which being added to the former time the middle E­quinoctial wil be March the 11. 93966. And in the Egyptian account from the death of Alexander it was 1912 Pharmuthi 23. 93966, from which if you deduct in the same account 178, Mechir 28. 83828 between both observations there will be found, 1734 Egyptian years, dayes 55. 10138, which being converted into dayes give 632965. 10138. Hence to find the quantity of the Tropicall yeare, I say, if 1733 Zodiacks give dayes 632965. 10138, that one Zodiack shall give dayes 365. 2418357126. And to find the earths middle motion for a yeare, I convert 1733 Zodi­acks into degrees, and they amount to 623880 degrees; then I say, if 632965. 10138 give 623880, that 365 days shal give 359. 76106661098 that is in Sexagenary numbers 359 deg. 45 minutes, 39 seconds, 50 thirds, 24 fourths. And to find the meane motion for a day, I say, if 365 dayes give 359. 76106661098, that one day shall give 9856467579, that is in Sexagenary numbers 0 degrees, 59 minutes, 8 seconds, 19 thirds, 41 fourths, 57 fifths.

[Page 94]And the daily motion of the Aphelion is 0000432380, which being deducted from the diurnall longitude gives the daily motion of the Ano­maly 985603599, these things premised we will now determine the E­pochaes of the middle motions.

The middle Equinoctiall Anno Christi 1588, March 11. 9 [...]966, is from the Aera Nabonassari 2336 Pharmuthi [...]3. 93966. 2335 years being multiplyed by 359. 761067 the product will be 840042. 091445, and the diurnal motion 985647, being multiplied by 232 days, the product will be 228. 670104 and the middle motion answering to the parts of a day, 93966, is 926173, the which being added togethea do amount to 840 [...]71 degrees 687722 parts of a degree, that is, rejecting the whole circles 31 d. 687722, which being deducted from 360, the remainder 328. 312278 or 10 Signes 28 degrees and 312278 parts, is the Radix of the earth or Suns mean longitude in the beginning of the Aera Nabonas­sari. To which if you add deg. 258. 692408 the middle motion for 424 years, the whole circles being rejected, the Radix of the earths middle motion to the beginning of the Aera Alexandri shall be 227. 004686 or 7 sines 17 deg. 004686 parts. And adding to this Epocha, deg. 51. 944398, which is the middle motion for 323 years 131 dayes, the whole circles being rejected, the Radix of the earths middle motion in the beginning of the Christian Aera shall be deg. 278. 949084 or 9 signes, 8 deg. 949084, to which if you add 034223 the equal motion belonging to 034722 the difference between the Meridians of Uraniburge and Lon­don, the Radix of middle motion at London will be 278. 983307

And the Aphelion
70. 322638
And the Mean Anomaly
208. 660669

CHAP. 7. To calculate the Suns true place and distance from the Earth.

HAving composed tables of the Suns middle motions, according to the directions of the last Chapter, his true place in the Zodi­ack, and distance from the earth may thus be found.

1 Write out the Epocha next before the given time and seve­rally under that, set the motions belonging to the years, moneths, and days compleat, and to the houres and scruples current, every one under his like (onely remember that in the Bissextile year, after the end of Febru­ary, [Page 95] the dayes must be increased by an Unite) then adding them alto­gether, the summe shall be the Suns meane motion for the time given.

Example.

Let the time given be May the 12th. houre 11 parts 15 before noon at London in the Bissextile yeare 1656, and the Suns place to be soughts The numbers are thus,

  Suns LongitudeSuns Apogeon
  Deg.partsDeg.parts
The Epocha1640291.2477796.22265
Years comp.15359.37294 23686
April118.27760 519
Dayes12011.82776 52
Houres23 94458  
Scruples15 616  
Suns Mean Longitude421.8768196.46522

2 Subtract the Apogaeum from the Mean Longitude, there rests the mean Anomaly.

Example.

The Suns mean longitude
421. 67681
Apogaeum substract
96. 46522
Rest mean Anomaly
325. 21459
Whose complement to a Circle
34. 78541

is the angle A M E in the Ellipsis.

And the complement of A M E to a semicircle is the angle E M H 145. 21459.

The side M E200000 
The side M H3568 
The summe203568 co. ar.4. 6912905
Differ.1964325. 2932122
Tang. ½ summe of the opposite angles17. 392709. 4958787
 17. 39270 
Tang. ½ Differ16. 817999. 4803814
Differ57471 is the angle M E H. 
Difference doubled1. 14942 is the angle M B H 

3 The mean Anomaly being above 180 deg. the Aequation found must be added to the sunsmeane longitude, so have you the Suns true place.

[Page 96]

[figure]

Example.

The Suns meane longitude
421. 67681
Aequation adde
1 14942
The Suns true place
422. 82623
or 2 Signes 2 degrees 82623 parts of a degree
 
Lastly, to find his distance from the earth, I say,
As the sine of M B H1. 14942 co▪ ar.1. 6977118
Is to the side M H35683. 5524249
So is the sine of B M H34. 785419. 7562590
To the side B H 5. 0063957
or distance required101483 

Thus we have found the Suns place by calculation, we will now shew how to reduce the Suns mean longitude to his true, by the Table of Ae­quations of the Suns excentrick.

The Suns Anomaly in this example is
325. 21459
The Aequation of 325 is
1. 15566
326
1. 12648
Difference is
02918
Now then I say if one deg. co. ar.
5.
Give 2918
3. 4650853
What shall 21459
4. 3316095
The answer is 6 [...]6
2. 7966948
[Page 97]Aequation of 325 deg.
1. 15566
Part proportional subt.
626
Aequation equated
1. 14940
The Snns mean longitude
61. 67681
Aequation adde
1. 14940
Suns true place
62. 82621

And in like manner the Logarithme of the Suns distance from the Earth will be found to be 5. 0063633, which being more necessary then the di­stance it self, in the calculation of the places of the other planets, we have as most convenient placed in the table.

CHAP. 8. Of the Aequation of Civil Dayes.

SOme there are of late, which allow not of any Aequation of Civil Dayes, others will have the inequality proceed from two causes. First, from the unequal motion of the Sun in the Zodiack, and the other from the Zodiacks obliquity; Tycho (whom we shall follow in this particular,) doth make the difference between the Suns true longi­tude and his Right Ascension; to be the absolute Aequation of naturall dayes, the which is also clearly demonstrated, according to the Coper­nican Systeme by Thomas Street in his Ephemeris for the yeare 1655; which being but short is here inserted.

The Aequation of time demonstrated.

Let A be the center of the Sun, and E of the Earth, ♎ E the earths lon­gitude from the Equinoctiall point in the ecliptick, ♎ F the like arch pro­jected in the Equator, ♎ B the Right Ascension of the Earths or Suns true place, G H is a diameter of the Equinoctiall and Meridian of the earths apparent diurnal revolution, A B the semidiameter of the true me­ridian, and equinoctial supposed in the heavens; and G H parallel to A B (though here they appeare as one right line. Then let C D parallel to A F be likewise a diameter of the Equinoctial and Meridian of the meane or equal diurnal revolution.

Hence C E G the angle of the earths libration, equal to B A F the dif­ference of longitude and Right Ascension is the true Equation of time or the difference between the equal and apparent time. And according to this Demonstration is our Table (entituled, A perpetual Table for the E­quation of time) composed. In which you must enter with the signe and de­gree of the Suns place either in the uppermost and left hand columnes de­scending, [Page 98] or in the lowermost and right hand ascending, and in the common angle is the Equation (according to the titles) to be added or subtracted to or from the equal time, that it may be made apparent; But to reduce the apparent to the equal, take the contrary title.

[figure]

CHAP. 9. Of the Theory and Motion of the Moon.

THe Moon according to our Hypothesis is a secondary planet, mo­ving about the earth, as the earth and other planets doe about the Sun, and so not onely the earth, but the whole Systeme of the Moone is also carryed about the Sun in a yeare, And hence according to Hypparchus there ariseth a twofold, but according to Tycho a threefold inequality in the Moons motion. The first is periodicall, and is to be obtained, after the same manner, as was the excentrique Equation of the Sun or Earth; in order whereunto her middle motions should be first stated, the which Bullialdus by the rules delivered in the fourth and fifth Chapters preceding hath for the Meridian of Uraniburge determined to be as followeth.

From the Equinoctiall to the beginning of the Christian Aera, the

Moons middle motion was135d.16′27″
The Meane Anomalie355518
And the Radix of her latitude3662956

These then we will take for granted, until there be a more exact, and true Geometrical way propounded to us,; onely we will convert them into Decimall numbers, and reduce them to the Meridian of London.

[Page 99]From the Equinoctial to the beginning of the Christian Aera, The Moons middle motion in decimal numbers at Uraniburge was 135. 27417

For the Difference of Merid. adde
. 45750
The Moons mean longitude at London
135. 73167
The Meane Anomaly,
At Uraniburge
355. 08833
Differ. Merid. adde
. 45361
Mean Anomaly at London
355. 54194
The Radix of Latitude
At Vraniburge
366. 49889
Differ. Merid. adde
. 45944
Latitude at London
366. 95833 d.
The Diurnal Motion of the Moons
Mean longitude
13. 17639
Anomaly
13. 06500
Latitude
13. 22944
The Annual Motion.
In longitude
129. 38389
Anomaly
88. 71889
Latitude
148. 71278

According to which limitations of the Moones middle motions, we have composed our Tables, by help whereof and the Semi-excentricity of the Moons Orbe, which according to Bullialdus is 4362 the Moons excentrique equation, or place first equated may be found, as before was shewed in the Sun. Save onely that here the Moons Anomaly is given without subtraction.

Example.

Anno 1587, August 17 ho. 19. 41667 in the apparent time, or ho. 19. 28973 in the middle time, the Moon being in the meridian of Vraniburge noble Tycho observed her in 26 deg. 38333 of Gemini with latitude 5 deg. 23333 S. from which middle time if you subtract 83333 for the difference of the meridians of London and Vraniburge, the time in our meridian is, ho. 18. 45640.

And the Suns true place
154. 07347.
The Suns distance from the Earth
100895.
The Log [...]rithme of that distance
5. 0038707

The Moons middle motions for the same time are as here you see them.

[Page 100]

Time given☽ Longitud☽ Anomaly☽ Latitude
Years 1500072. 88194313. 06916017. 17805
80174. 24805158. 80139281. 61167
6069. 4802818 [...]. 37750185. 50583
Iuly27 [...]. 39555249. 77639284. 62194
D [...]yes 16 [...]10. 82222209. 0 [...]972211. 66944
H [...]res 18 [...]9. 882229. 798619. 92222
Paris 4564. 250 [...]1. 24848. 25152
Mean Longitude810. 960771126. 11125990. 76067
Ded [...]ct720.1080.720.
There rests90. 9607746. 11125270. 76067

The Moones meane Anomaly 46. 11125 is the angle A M E in the preceding Ellip [...]is, or the summe of the angles M E H and M H E. Therefore in the triangle M E H we have given, 1. The side M E 200000. 2. The side M H 8724. 3. The angle E M H the complements of the Moones Anomaly, to find M E H, whose double, is the excentrique E­quation M B H. I say then,

As the summe of M E and M H208724 co. ar.4. 6804276
Is to their difference1912765. 2816605
So is the tang. half summe of the opposite angles,23. 055629. 6290228
To the tang halfe diff.21. 307869. 5911109
Differ.1. 74776 is the angle M E H 

Differ▪ doubled 3. 49552 is the angle M B H or the equation sought which being subtracted from the Moons mean longitude, because the Anomaly is lesse then a semicircle you shall have the Moones place first equated.

Example.

The Moones meane longitude
90. 96077
Equation subtract
3. 49552
The Moones place first equated
87. 46525
And to find her distance from the Umbilique point at H.
As the sine of M B H3. 49552 co. ar.1. 2148808
Is to the side M H87243. 9407156
So is the Sine of B M H46. 111259. 8577468
To the side B H1031205. 0133432

[Page 101]But whilest the Moone is thus making her owne periodicall revoluti­on, her whole Systeme is by the motion of the Earth removed from the proper seats thereof, whence there ariseth another revolution which is called Synodicall, the beginning whereof is the line which passeth through the center of the earth to the Sun, and therefore the Moone in that line is void of this second inequality, which is both at the Conjunction and op­position, but being in or about her quarters, where she is farthest removed from the said Zyzigiacal line the angle of her evection is 2 deg. 50′ as is cleerely proved by the observations of Tycho and Bullialdus, whose me­thod we follow, in our calculation of this inequality of the Moon, ma­king 4362 the sine of the greatest evection to be the Diameter K D in the little circle K C D H. The motion of this libration of the Moone must be measured by her double distance from the Sun, because she is void of this inequality at her conjunctions and oppositions as was said before.

Now then let the angle M H B represent the Moones equated Anoma­ly, found by subtracting the former Equation from the simple Anomaly, which is 46. 11125

Aequation subtract
3. 49552
Aequated Anomaly
42. 61573
[figure]
And if from the place of the moon first equated
87. 46525
You subtract the Suns true place
154. 07347
Their distance is
293. 39178
The double distance
226. 78356

is the arch K C D H and drawing the lines F H and H K there shall be made the equicrurall Triangle H F K, whose exteriour angle H F D is known, viz. the excesse of the Sun and Moons double distance above a se micircle 46. 78356. The halfe whereof is the angle D K H 23. [...]9178, e­qual to the angle A H G, which being subtracted from the Equated A­nomaly A H B 42. 61573. The angle G H B or the Synodical Anomaly will be 19. 2239 [...], whose complement to a semicircle is the angle B H K 160. 77605. The side H B 103120 as before, and the side H K may be found in this manner. The arch H V K is the complement of the double distance of the Sun and Moon to a whole circle 13 [...]. 21644 the subtense of this arch is H K, H V the halfe arch is 66. 60822, and H X is the right sine thereof.

Now then, As the Radius,  
Is to the Diameter K D4 [...]62.3. 6396857
So is the sine of H V or H X66. 608229. 9627533
To the Subtense H K40033. 6024390

Therefore in the Triangle B H K we have known,
1. The angle B H K160. 77605. 
2. The side H B103120 To find the angle H B K. 
3. The side H K4003 To find the angle H B K. 
As the summe107123 co. ar.4. 9701173
To the differ.991174. 9961481
So tang. ½ the opposite ang.9. 611979. 2287638
To the tang. ½ differ.8. 905029. 1950292

Their difference 0. 70695 is the angle of the evection, H B K to be added if the Synodicall Anomaly be more then 180, and to be sub­tracted from the place of the Moone first equated when lesse, as here it is in our example, and therefore to be subtracted from the Moons place 87 46525, and then her place secondly equated will be 86. 7 [...]830.

And according to this Analogie may be made a table of the Moons e­vection, when she is in quadrature or 90 degrees distant from the Sun; for then the equated and Synodicall Anomalies are both the same, and therefore in the Triangle E M H we have give the angle E H M, or the e­quated [Page 103] Anomaly which suppose 25 degrees, the side M H 8724 and the side H E [...]00000, to find the angle at E.

[figure]
As the sum of H E and M H208724 co. ar.4. 6804276
Is to their difference1912765. 2816605
So is the tang. half summe 10. 6542447
To tang. half differ.76. 4043510. 6163328
Their differ.1. 09565 is the angle M E H 
Whose double is2. 19130 is the angle M B H 
Then as the sine of M B H2. 1913 co. ar.1. 4175273
To the sine of B M H27. 19139. 6598808
So is the side M H. 87243. 9407156
To the side B H10. 41615. 0181235
or the Moons distance from the umbilique.  

Hence in the first Diagram of this Chapter, in the Triangle B H K we have given A H B the equated Anomaly, 25 degrees, the Moons di­stance H B 104161, with the side H K, or rather D K, the Diameter of the little circle 4362, to find the angle H B K.

[Page 104]

As the summe of H B and H K108523 co. ar.4. 9644782
To their difference997994. 9991262
So is tang. halfe summe12. 509. 3447552
To tang. halfe differ.11. 523149. 3093596

whose difference . 97686 is the evection sought and by Bullial­dus . 97805 which is so little differing from what we have found, that I have taken his Table and converted it into Deci­mall numbers.

And for the finding the part proportial between the quadrature and the Zyzygia, Bullialdus whom we follow, hath annexed scruples of pro­portion in this manner.

As Radius to 60 minutes or one degree; so is the fine of halfe the de­grees of the equated Anomaly to the scruples of proportion required.

But this proportion in the Sexagenary Canon will not give the scruples either so easily or so exactly as the Decimal Canon will, because the seconds must still be found in that Canon by the part proportional, which in the beginning of the Canon cannot be true, but working by a Decimal Canon the natural sines of halfe the degrees, are the Decimall parts required, as the naturall sine of 4 degrees; 069756, are the Decimall parts for 8 degrees of equated anomaly, and so of the rest.

Having done with the first and second inequalities of the Moon, we come to the third which Tycho calls the variation, Bullialdus the Reflecti­on for as the Moons Systeme is carryed about by the earth, the place of her Apogaeon is changed, or doth reflect contrary to the succession of the Signes, by reason of which reflection the angle of her Evection is some­times more sometimes lesse then it will be found by the former directions, but the quantity of this variation according to Tycho doth never exceed 40′ 30″ or in Decimal numbers 67500, to be added to or subtracted from the place of the Moone secondly equated, and the proportion by which he finds it is thus,

As the Radius

To the sine of the complement of the double distance of the Sun and Moon if lesse then a Semicircle: To the excesse if more:

So is the sine of the greatest variation, or Reflection.

To the variation required, which is to be added to the Moons place, secondly, equated if the double distance be lesse then 180 deg. to be sub­tracted, when it is more.

[Page 105]

Therefore in our Example,
As the Radius  
To the sine of H F D46. 783569. 8625917
So is the sine of675008. 0711591
To the variation491897. 9337508
The Moones place secondly equated
86. 75830
Variation subtract
49189
The Moones place in her Orbe
86. 26641

Lastly, to find the Moones latitude and place in the Ecliptique, take the middle motion of her latitude for the time propounded, the which rejecting the whole circles is 270. 76067 and in which according to Tycho there is a twofold variation, The first is occasioned by the various intersection of the Moones orbe with the Zodiack, and the o­ther by the reciprocal progression and retrogradation of the Nodes. In the New and Full Moones the limits of her greatest latitude, are 4. 97500, but in her quarters 5. 29167, as Tycho hath experimented by many dili­gent and accurate observations, whose method of calculation is as fol­loweth.

From the meane motion of the Moones latitude
270. 76067
Subtract the Moones absolute Equation
4. 694 6
The Equated latitude of the Moon
266. 06631

Then to find the Equation of the Nodes, let the line A D or the angle A T D 5. 13333 represent the meane inclination of the Moones Orbe with the Ecliptique, let the least inclination be represented by A B 4. 97500, and the greatest by A C 5. 29166. And from the distance of the Sun and Moon before found,

 
293. 39178
Subtract the evection and variation
[...]1. [...]9884
True distance of the Sun and Moon
292. 19 [...]94
The double thereof is
224. 385 [...]8

which being numbred from B by C to F in the Triangle F D A we have known A D 5. 13333 the meane inclination of the Moones Orbe. 2. D F 15833 the halfe difference of the least and greatest inclination. 3. With the angle F D A 135. 61412, the complement of the double di­stance of the Sun and Moon to a whole circle: whence to find the angle F A D the Aequation of the Nodes, by the Doctrine of spherical Triangles say,

[Page 106]

[figure]
First, As the Radius  
To the cosine of F D C44. 385889. 8540905
So is the tang. of D F158337. 4413175
To the tang of D C113217. 2954080
Adde the arch A D5. 13333 
Summe is A C5. 24654 
2 As sine D C11321 c [...]. ar.2. 7046002
To the sine A C5. 246548. 9611430
So cotang. F D C44. 3858810. 0093107
To cotang. F A D1. 2106211. 6750539
From the Moones latitude equated 266. 06787
Equation Nodes subtract 1. 21062
True motion of the Moones latitude. 264. 85725
whose complement to a whole circle 95. 14275

[Page 107]And to find A F or the angle of [...] A T [...], the [...] of the Sun and Moone being more than 180 degrees, and lesse th [...] [...] ▪ I deduct the Moones double distance 224 d. 3858 [...] being numbred [...] the little circle, from B by C to F, from the Arch B C F G 270, there re­maines F G 45. 61412, and then the A [...]alogie is,

As the Radius D C 10. 0000000
To the sine of F G or D F45. 614129. 8540305
So is the sine of the arch, D C. 158337. 4413159
To the sine of the arch D E. 113197. 2953464

The aggregate is B E . 27152 which being added to the least angle of inclination A T B, or the arch A B 4. 97500 the present inclina­tion is A F or the angle A T F 5. 24652.

Hence to find the Moones true latitude, I say,
As Radius 10. 0000000
To the sine of A T F5. 246528. 9611413
So is the sine of A T84. 857259. 9982481
To the sine of A F5. 225338. 9593894
or the angle A S F.  

And by these Analogies may be made the Table of the Moons latitude wc [...] we have borrowed of Tycho, converting it onely into Decimall numbers.) For supposing the Moon to be in her Syzygial points, the angle of Incli­nation is alwayes A T B 4. 975, and then her latitude for every degree of her true motion of latitude may be found by the last Analogie; As Radius

Example.

To the sine of A T B4. 9758. 9381242
So is the sine of A T45.9. 8494850
To the sine of A B3. 515648. 7876092

And her latitude when she is in Quadratu [...]e or 90 degrees distant from the Sun may be found by the same analogie, if you make the angle of In­clination A T C 5. 29166.

Example.

As Radius  
To the sine of A T C5. 291668. 9648517
So is the sine of A T45.9. 8494850
To the sine of A F3. 739108. 8143367

Subtract A B 3. 51564 there rests the Excesse to be placed in the Table 0. 22346.

The proportipnal part of which excesse to be added to the Moones la­itude [Page 108] must be found by scruples of proportion, and the Scruples themselves for every degree of the Moones distance from the Sunne may thus be had.

[figure]
As Radius▪  
To the Co [...]ine of the Moones double distance D H409. 8842539
So is the sine of D B0. 158337. 4413575
To the sine of D H0. 121427. 3256114
Their differ▪ is B H0. 03691 
Then as the Diameter B C316665. 4994068
Is to the Diameter B C100. 0005. 0000000
So is B H0. 036913. 5671440
To B H0, 116564. 0665508

Or more readily thus D H 76604 is the sine of 50 or the Cosine of 40 the Moones double distance from the Sun, which being deducted from Radius, the remainder is the versed sine B H 23396 the halfe 11698, are the scruples of proportion answering to 20 deg. of the Moones single di­stance from the Sun,

From the Moones place in her Orbe
86. 26641
Subtract the Moones true latitude
264. 85725
The Moones Node ascending
181. 40916
Lastly, for her Reduction▪
[Page 109]As Radius  
To the Cosine of A T F5. 247759. 9981757
So tang. of A T84. 8572511. 0458587
To tang. of T F84. 8368911. 0440344
Difference 02036 is the Reduction sought
From the place in her Orbe
86. 26641
Subtract her Reduction
. 02036
The Moones place in the Ecliptique
86. 24605

CHAP. 10. To calculate the true Motion of the Moon by Tables.

HAving gathered the meane motions of the Moones Longitude, Anomaly, and argument of Latitude, as in the last Chapter, by the Anomaly find the Moones Eccentrick equation, and by that her Eccentrick place.

2 Apply her eccentrick Equation acoording to the title both to the meane Anomaly, and to the motion or argument of Latitude; So have you the equated Anomaly and motion of Latitude, first equated.

Example.

Anno 1587, August 17 ho. 18. 45640 the Moons meane Longi­tude was before found to be 90. 96077

Her meane Anomaly 46. 11125
Her motion of Latitude 270. 76067
Her Eccentrick equation to47 deg.3. 54892
 46 deg.3. 48880
Differ. 0. 06012
Now then as 1 deg. 5. 0000000
Is to060123. 7790190
So is111254. 0463000
To006682. 8253190
To the Equation of 46 deg. 3. 48880
Adde the part proportionall 668
The Moones eccentrick Equation 3. 49548

which being subtracted from her meane Longitude, Anomaly and Lati­tude.

Her place first equated is
87. 46529
Her equated Anomaly
42. 61577
Her Latitude first Equated
267. 26519

[Page]3. By her meane Anomaly you must also find the Logarithme o [...]he [...] distance from her umbilique.

The Logarithme to46 Deg. is5. 0133649
 47 Deg. is5. 0131474
 Differ.2175
As if one Degree 5. 0000000
Is to21753. 3374592
So is111254. 0463000
To2412. 837592
Which being deducted from 5. 0133649
The Moones Logarithme is 5. 0133408

4▪ Subtract the true place of the Sun, from the Moones eccentrick place, so have you the distance of the luminaries, with the double where­of seeke in the Table the eccentricity of the Moones evection, and the quantity of her variation or reflection, using the part proportional if need require.

5 If the double distance of the luminaries with which you enter the Table be lesse then a semicircle, adde halfe the complement thereof unto the equated Anomaly, or if it be more than a semicircle, deduct halfe the excesse above a semicircle from the equated Anomaly, then the summe or difference if lesse then a Semicircle, is the summe of the oppo­site angles, or if it be more, take the complement, to a whole circle.

Example.

 ☉ Longitude☉ Apogaon
Years 1500290. 2007694. 01167
80. 598261. 26342
6359. 55205. 09473
Iuly208. 95710917
Dayes 1615. 7703569
Houres 18. 73923 
Parts 4564. 01874 
Suns Longitude875. 8364995. 37968
Apogaeon subtract095. 37968 
Mean Anomaly060. 45681 

The Suns eccentrick to61 deg.1. 77254
The Suns eccentrick to60 deg.1. 75464
Difference 1790
As one degree 5. 0000000
Is to17903. 2528530
So is456814. 6597 [...]56
To8172. 9125886
The equation to 60 deg. 1. 75464
Adde th [...] part proportional 817
The absolute Equation subtract 1. 76281
From the Suns meane Longitude 155. 83649
The Suns true place subtract 154. 07368
From the Moones eccentrick place 87. 46529
The distance of the Sun and Moon 293. 39161
The double distance 226. 78322
The Logarithme of the Eccentrick to226 deg.3. 6037118
The Logarithme of the Eccentrick to227 deg.3. 60208 [...]4
Difference 16284
As one degree 5.
Is to162844. 2117610
So is783224. 8938837
To127534. 1056447
which being subtracted from 3. 6037118
The Logarithme of the Eccentricity is 3. 6024365

Thus we have found the Logarithms of the two lateral distances, name­ly of the distance of the Moon from her Umbilique▪ 5. 0133408 and of the Eccentricity of her Evectioon 3. 6024365. And because the double di­stance of the Sun and Moone is more then a semicircle 226. 78322

Deduct 180 there rests
46. 78322
The halfe whereof
23 39161
Deduct from the equated Anomaly
42. 61577
There resteth the Synodical Anomaly
[...]9. 22416

or summe of the opposite angles. Hence to find the Evection,

Say, As the greater Logarithme co▪ ar.
4. 9866502
Is to the lesser
3. 6024365
So is Radius
[...]0. 000 [...]0
To the tang. of 2 deg. 22494
8. [...]890 [...]

Adde 45

2 Operation.
As Radius 10. 0000000
To the Cotang.47. 224949. 9662367
So tang. half sum9. 612089. 2287955
To the tang. half dif.8. 905559. 1950324

Evection 0. 70653. Subtract because the Synodical anomaly is lesse then 180.

Then for the variation, I enter the Table with the Moones double distance 22678322; and using the part proportional I find it to be 0. 49186 subtract.

The Evection to be subtracted is
0. 70653
The Variation to be subtracted is
. 49186
Their summe
1. 19839
Subtract from the Moons Eccentrick place
87. 46529
There rests the Moones place in her Orbe
86. 26690
Otherwise thus.

Enter the Table entit [...]led Bullialdus his Table of Evections, with the Synodical Anomaly 19. 224 [...]6, and using the part proportional you shall find it to be 75942, subtract, then take from thence with the Moones double distance 226. 78322 the scruples of proportion also, the which observing the part proportional are; 91781, by which the Evection found is thus to be corrected. As 1 degree is to 75942: so is 91781 to the Evection sought 69701 subtract, and this subtracted according to the title from the Moones Eccentrick place 87. 46529 There rests her place secondly equated 86. 75828 Then for the variation enter this or the former table with the Moons dou­ble distance 226. 78322, and using the part proportional you shall find it to be 49186 as before, with the title Subtract; and therefore the Moons place in her Orbe 86. 26742, but little differing from the former.

And from these two Tables of Evection & Variation, we have composed a third Table, entituled a compounded Table of the Moones second and third inequalities, for the yet more speedy finding of these equations, whose construction is thus.

First, enter the Table of the Moones Evection with her Synodicall Anomaly to find the Evection, and with her double distance from the Sun to find the Scruples of proportion.

The Moones double distance may be supposed, and the Synodicall ano­maly easily made from it: as suppose the Moones distance from the Sun to [Page 113] be 3 degrees thereof to a quadrant 87 being added to the equated Ano­maly which you may also suppose to be what you please, will give the synodical Anomaly, thus if the equated Anomaly be 25, adde 87 thereto, and then the synodical Anomaly will be 112 and the angle of evection answering thereto 2. 38861 subtract: and the scruples of proportion an­swering to 6 degrees 52335. Hence to finde the true evection. I say,

As 1 degree1. 000000. 0000000
Is to the evection in the table2. 388610. 3781452
So are the Scruples of prop.0. 523351. 7187912
To the evection sought, Sub.0. 125000. 0969374
The variation to 6 deg. adde0. 07055 

And because the evection and variation are of different titles there­fore there difference 05445 is the compounded equation sought, which I place against 25 degrees of equated Anomaly in the columne of 3 deg. of the Moons distance from the Sun, with the title subtract, because the title of the biggest number was subtract.

And therefore the second and the third inequalities of the Moone are to be found in this table by entering it with the Moones distance from the Sun in the head or foot of the table, and with the equated Anomaly in the sides, for so the common angle using the part proportional, if need require, will give the Equation sought to be applyed to the Moons place accord­ing to the title.

Example.

Suppose the distance of the Sun and Moone were 293. 39161, that is, de­ducting a Semicircle 113. 39161, and her equated Anomaly 42. 61577 because the Moones distance from the Sun is found in the bottome of the table, I number the equated Anomaly in the first columne towards the right hand ascending, and in the common angle (by making proportion for the intercepted degrees) I finde the Equation to be 1. 188 S. that is the title subtract, and therefore this Equation being subtracted from the Moones Eccentrick place, what remaineth shall be the Moones place in her orbe.

CHAP. 11. To finde the Moones true Latitude and place in the Ecliptick.

TO the motion of Latitude first Equated, according to the title ap­ply the agregate of the Moones second and third Equations, so have you the motion of Latitude secondly equated.

[Page 114]2. To the distance of the Sun and Moon before found apply the agre­gate of the Moons 2 d. and [...] d. Equations according to the title, so have you the true distance of the Sun and Moone.

Example.

Motion of Latitude first equated
267. 26519
Second and third equations sub.
1. 19839
Motion of Latitude secondly equated
266. 06680
Distance of the Sun and Moone as before
293. 39161
Second and third Equation sub.
1. 19839
True distance of the Sun and Moone
292. 19322

3. With the true distance of the Sun and Moon enter the table of the Equation of the Nodes, and take thence the Equation of the Nodes, which according to the title, apply to the motion of Latitude secondly E­quated, and you have the true and absolute motion of Latitude. At the same entrance take out also the scruples of proportion and reserve them.

Example.

With the true distance of the Sun and Moone
292. 19322
I finde the Equation of the Nodes, subt.
1. 21103
From the Latitude secondly Equated
266. 06680
So the true motion of Latitude
264. 85577
And the scruples of proportion
85729

4. With the true motion of Latitude enter the table of Latitude, and thence take the Latitude and the excesse, then say, as one degree to the ex­cesse in the table: so are the scruples of proportion before reserved, to the excess sought, which being added to the Latitude found by the table, the summe shall be the true Latitude of the Moone, which is North when the true motion of Latitude is lesse then 6 [...]ignes, and South when it is more.

Example.

The true motion of Latitude 264. 85577
Gives The Latitude 4. 95490
Gives The Excess 31519
As one degree1. 00000 
To the excess in the table315191. 4985724
So the scrupls of propor.857291. 9331277
To the excess desired270201. 4317001
Which being added to the Latitude 4. 95490
It gives the true Latitude▪ South 5. 22510

[Page 115]5. If the true motion of Latitude be subtracted from the Moones true place in her orbe, there resteth the Node Ascendant.

As The Moones true place
86. 26690
As The Motion of Latitude subt.
264. 85577
The Node ascendant
181. 41113

6. With the true motion of Latitude enter the table of Reduction, and take out the Reduction, which according to the title apply to the Moones place in her orbe, you have her true place in the Ecliptick.

Example.

The true motion of Latitude
264. 85577
Gives the reduction to be subt.
02067
From the Moones place in her Orbe
86. 26690
The Moons place in the Ecliptick
86. 24623

CHAP. 12. Of the motion of the fixed Starres.

THe motions of the fixed Stars are by the observations of all ages found to be equall, and the quantity of that equal motion, Noble Tycho by comparing his owne observations with those of the an­cients hath determined to be exact 51 seconds, Bullialdus 50″ 55‴ ferè, and the place of the first Star in Aries in the yeare of our Lord 1600 compleat to be 27 deg. 37 min. which being converted into Deci­malls the Radix of the middle motions of the fixed Stars at that time will be 27. 61667 and the yearely motion. 01414, that is the decimall of 50 seconds 55 thirds.

Hence to finde their places at any time assigned, we have exhibited a table of the longitudes and latitudes of some of the most notable fixed Stars for the yeare 1650 compleat, which by the motions of the fixed stars in the tables of the Suns meane motions, may thus be done for any other time. Take the difference betweene the time given and 1650 compleat, and the motion agreeing to that difference, this motion subtract from the place in the table when the time given is before 1650, or else adde it, and you have the place desired. The Latitudes and Magnitudes are still the same.

Example.

The time given 1683 September.

Difference from 1650 compl.
33 yeare 8 Moneths
Motion Correspondent
. 476 [...]8
Place of Oculus ♉ 1650 compl.
♊ 4. 91667
Place required
♊ 5. 39305
Latitude South
5. 51667

CHAP. 13. Of the Motion of Saturne.

OUr Tables of Saturns meane motions as of the other Planets, are he same with those of Bullialdus, being onely reduced to the Meridian of London, and converted into Decimall numbers whose eccentrick being so easie to be found, and the investigation of his true place, with the places of Jupiter, Mars, Venus and Mercury, being out of curiosity, rather then use▪ we shall content our selves with the Trigonometricall calculation onely, first, of Saturne for the time before given 1587. August 17: h: 18: 4564: and then of the rest.

An. Christ.Longit. ♄Aphel. ♄Node ♄
1500064. 98279262. 82583109. 79361
80258. 765282. 5 [...]6940. 57611
673. 39056. 190780. 04306
Iuly▪7. 10111. 01833. 00444
D 16. 53183. 00139. 00030
H 18. 02500  
P 4564. 00063  

Meane Mot. 404. 801 20265. 57327110. 41752

Aphel. Subt. 265. 57327 Rests Anomaly 139. 22793

The halfe of Saturns first inequality, or his eccentricity supposing the Semidiameter of Saturns orbe to be 100. 000. is 5774. and the Semidia­meter of the Earths orbe 10480. As they are computed by Bullialdus, but the Semidiameter of the Earths orbe being before supposed to be 100. 000 the Semidiameter of Saturns orbe will be 954198, for as 10480 is to 100. 000. So is 100. 000. to 954198. and Saturns eccentricity in the same parts will be 55145. for as 100. 000 is to 954198. So is 5774 to 55145. whose double 110200 is the side M H in the figure following; in the triangle therefore M E H, we have knowne, 1. The Angle H M E 40. 77207, the complement of Saturns Anomaly to a semicircle [...]9. 22793 or the halfe sum of the angles M E H and M H E viz. halfe the anomaly 69. 61396.

2. The side M E 1908396 To finde the Angle M E H.

3. The side M H 110290 To finde the Angle M E H.

[Page 117]

[figure]
As there sum2 [...]18686 co. ar.3. 694931 [...]
Is to their differ.17981066. 2548153
So is tang. halfe sum69. 6139610. 4299016
To tang. halfe diff.67. [...]537510. 3796482
Difference2. 26021 is the angle M E H. 

Difference doubled 4. 52042 is the angle M B H, or the Equa­tion sought, to be subtracted from Saturns meane Longitude, the Anoma­ly being lesse then a semicircle.

Saturns meane Longitude
44. 80120
Equation Subt.
4. 52042
Saturns eccentrick place
40. 28078

2. To finde his distance from the Sun.

As the sine M B H4. 52042 co. ar.1. 1034042
Is to the side M H.1102905. 0425361
So sine E M H40. 772079. 8149473
To the side B H9138765. 9608876

[...]. From the eccentrick place of Saturne subduct the Node, there rest­eth the argument of Latitude: by help whereof and the angle of his great­est inclination, which according to Bullialdus is 2 d. 50, or 4362, we may easily finde his Reduction, but the side E B 4362 in the parts of 100. 000, must be reduced into the parts of Saturns semidiameter 954198, to finde the curtation. As 100. 000 is to 954198, so is 4 [...]62 to 41622. Saturns eccentrick place

Example.
 
40. 28078
Node substract
110. 41752
Argument of Latitude
289. 86326
Whose complement is K L
70. 13674

[Page 118]

As Radius  
To cosine of XKL2. 509. 999586
So is tang. of KL70. 1367410. 4421682
To tang. of70. 1292910. 4417546
Whose difference. 01745 is the Reduction sought: 

And to be subtracted from the ecceutrick place, if he move from either Node towards the limits of his greatest latitude, but if he depart from the limits and approach towards the Nodes the reduction is to be added, for so the sum or difference will be the place in the Ecliptique. As in our example, Saturne is past the limits of his greatest latitude, and is approaching to­wards his Node, and therefore the reduction is to be added.

Saturns eccentrick place
40. 28078
Reduction adde
. 01745
The eccentrick reduced
40. 29823

The inclination of his orbite from the eccliptique represented in the se­cond figure following by the line XL, may thus be found.

As the Radius KE 90.  
To the greatest in clination EB416224. 6193229
So is the sine of KL70. 136749. 9733616
To the side XL [...]91454▪5926845

which is the inclination agreeing to the common Radius 954 198, where­as the distance of Saturne from the sun is to be put for the Radius, and then XL will be but 37491.

As DL954198 co. ar.4. 0203616
To AL9138765. 9608876
So is XL391454. 5926845
To XL374914. 5739336

The distance of Saturne in his orbite from the Sun being given with the inclination of his orbite from the eccliptique, the distance corrected by curtation may thus be found.

As AL913876 co. ar.4. 0391124
Is to Radius9010. 0000000
So is LX374914. 5739 [...]36
To the tang. of LA [...]2. 351218. 6130460
As Radius  
To AL9138765. 9608876
So cosine of LAX2. 351219. 9996343
To AX9131075. 9605219

[Page 119]

To finde Saturns second inequality.

Subtract the suns place from the Eccentrick reduced, or this from it, so that lesse then 180 degrees may remain, this remainer is the Anomaly of the orbe, the complement whereof is the angle NAS, or the halfe, is the halfe sum of the opposite angles.

Example▪
Saturns Eccentrick reduced 40. 29823
The Suns true place 154. 07347
The Anomaly of the orbe 113. 77524
The angle NAS 66. 22476
The halfe Anomaly 56. 88762
As the greater side AN913107 co, ar.4. 0394781
Is to the less AS1008955. 0038707
So Radius, to the tang.6. 305419. 0433488
Adde45. 
[Page 120]As Radius  
To cotang. of the summe51. 305419. 9036304
So is tang. halfe summe56. 8876210. 1856192
To tang. halfe differ.50. 8461310. 0892496
Summe107. 73375 Angle ASN. 
Differ.6. 04149 Angle ANS. 

Because Saturne eccentrick reduced was subtracted from the Suns true place, therefore the angle of his Elongation ASN 107. 73375 must be subtracted also, and then Saturns place will be 125. 19972.

To finde Saturns distance from the Earth.

As the sine of AXS6. 04149 co. ar.0. 9777838
To the side AS1008955. 0038707
So the sine of XAS66. 224769. 9614845
To the side SX8772815. 9431390

[figure]

[Page 121]

To find the latitude of ♄ from the earth.  
As SX.877291 Co. ar.4. 0568610
Is to Radius 10. 0000000
So is XL,374914. 5739336
To the tang. of XSL,2. 44711.8. 6307946

which is the quantity of ♄ Southern Latitude, because the argument of La­titude was more then 6 signes, when it is less then 6 signs, the Latitude is North.

CHAP. 14. Of the Motion of Jupiter.

THe investigation of the place of this and the other Planets, is well nigh the same with that of ♄, they differ more in the Di­mensions of their Orbs, then in the manner of their calculation. Yet that there may be no mistake, we will not onely give you the Dimensions of their several orbs, but makes examples of their calculation to the former time given.

The meane motions of Jupiter.

Anno Christi.Longitude ♃Aphelion ♃Node ♃
Years 1500004. 50000185. 54833097. 93889
80269. 044441. 98000. 54722
6182. 13667. 14833. 04111
Iuly17. 62333. 01444. 00389
Dayes 161. 33000. 00104. 00030
Houres 18. 06222  
Parts 4564. 00154  
Mean motion.474. 69820187. 6841498. 53141
Aphelion subt.187. 68414Rests Anomaly287. 01406

The halfe of Jupiter first inequality, or his eccentricity, supposing his Semidiameter to be 100. 000 by the computation of Bullialdus is 4856, and the Semidiameter of the Earths Orbe 19138▪ and therefore to find ♃ Semidiameter, when the Semidiameter of the Earths Orb is 100. 000 the proportion is, As 19138. Is to 100. 000 so is 100. 000 to 522520, the Semidiameter required, which being doubled is the Diameter of the El­lipsis, [Page 122] or the side M E 1045040. And to find the eccentricity in the same parts, say, as 100. 000. is to 522520, so is 4856, to 2537 [...]. the excentri­city, and the double thereof. 50746 is M H the distance of the foces.

The complement of the Anomaly 72. 98594 is the angle A M E, and the halfe compl: 36. 49297, is the halfe sum of the opposite angles M E H and M H E.

The side M E1045040 
The side M H50746 
Sum1095786 co. ar.3. 9602744
Differ9942945. 9975147
Tang. ½ sum36. 492979. 8690974
Tang. ½ differ33. 871629. 8268865
Differ.2. 62135 Angle M E H 

Double differ. 5. 24270 Angle M B H or the Equatiō sought, and to be added to Jupiters mean longitude, the Anomaly being above a Semi-circle.

Jupiters mean longitude
114. 69820
Equation add
5. 24270
Jupiters eccentrick place
119. 94090
The Node subt.
98. 53141
Argument of Latitude.
21. 40949

By help whereof, and the angle of his greatest inclination 1. 36333, or E B 2379, we may find the reduction: but to find the parts of inclination in proportion to the given Radius 522520. say, As 100. 000. is to 2379, so is 522520 to 13619. the parts required.

To finde the Reduction.

As Radius  
So Cosine of X K L.1. 363339. 9998770
To tang. of K L.21. 409499. 5933823
To tang. of X K.21. 403539. 5932593
Differ.. 00596 Reduction. 

Because the argument of Latitude is lesse then 90. the Reduction must be subtracted from the eccentrick place.

Jupiters eccentrick place
119. 94090
Reduction subt.
. 00596
Eccentrick reduced
119. 93494

To find the Inclination.

As Radius  
To the greatest inclin: E B136194. 1341452
So is the sine of K L21. 409499. 5623296
To the side X L49713. 6964748

which are the parts of inclination agreeing to the cōmon Radius 522520, but the distance of ♃ from the ☉ is to be put for the Radius, the which distance may thus be found.

As the sine of M B H5. 24270. Co. ar.1. 0391741
Is to the side M H507464. 7054018
So is the fine of E M H72. 985949. 9805636
To the side B H5310555. 7251395
As the common Rad: D L522520 Co. ar.4. 2818971
To Jupiter dist: B H or A L5310555. 7251 [...]95
So is X L49713. 69647 [...]8
To X L50523. 7035114

To finde ♃ distance corrected by Curtation.

As A L531055 Co. ar.4. 2748605
Is to Radius 10. 0000000
So is L X50523. 7035114
To the sine of L A X545157. 9783719
As the Radius  
To A L5310555. 7251395
So is the Cosine of L A X 9. 9999831
To A X5310345. 7251226

To finde the second inequality of Jupiter.

We must have given, 1. The angle N A S, which is to be found by subducting the ☉ place from ♃ eccentrick or reduced, or this from it, so that lesse then 6 Signes may remain, this remainer is the Anomaly of the Orbe, and the Complement thereof is the Angle N A S, or the halfe is the halfe sum of the opposite angles.

Example.
Jupiters eccentrick reduced
119. 9 [...]494
☉ True place
154. 07347
The Anomaly of the Orbe
34. 13893
The angle N A S
14. 86107
The halfe Anomaly is
17. 0694 [...]

These given with the sides N A and A S, I say.

[Page 124]

As the greater side A N531034 co. ar.4. 2748774
Is to the Radius 10. 0000000
So is the lesser side A S1008955. 0038707
To the tang. of10. 757839. 2787481
Adde45 
As Radius to Co-tang.55. 757839. 8329403
So tang: of ½ summe17. 069469. 4872186
To tang. of ½ differ.11. 805229. 3201589
Summe28. 87468 Angle A S N 
Differ.5. 26424 Angle A N S 

Because ♃ eccentrick reduced was subtracted from the ☉ place, therefore the angle of his Elongation A S N 28. 87468 must be subtracted also, and so ♃ place 125. 19839.

To finde the distance of Jupiter from the Earth.

As the sine of A N S5. 26424 co. ar.1. 0373985
To the side A S1008955. 0038707
So the sine of N A S34. 138939. 7491287
To the side S N6031115. 7803979

To finde the latitude of ♃ from the Earth.

As the side S N603111 co. ar.4. 2196021
To the side X L50523. 7035114
So is the Radius9010. 0000000
To tang. of X S L0. 479987. 9231135
Which is the quantity of ♃ Northern latitude.  

CHAP. 15. Of the Motion of Mars.

THere being no other variety in calculating the place of this Pla­net, then what hath been already shewed, in the motions of Sa­turn and Jupiter, we will proceed in the same method, and ga­ther first the middle motions for the former time given, and then shew the Dimensions of his several Orbs, as we shall have occasion for them.

[Page 125]

An. Christ.Longit. ♂Aphel. ♂Node ♂
Yeares 1500245. 61611146. 8091645. 40250
80193. 327781. 751391. 07194
668. 23750. 13139. 08028
Iuly111. 10306. 01250. 00778
D 168. 38500. 00096. 00057
H 18. 39306  
P 4564. 00996  
Mean Mot.627. 07247148. 70540046. 56307
Aphel. Subt.14. 70540Rest Anom. [...]19. 36707
Supposing the Semidiameter of ♂ his Orbe
100. 000
His eccentricity according to Bullialdus is
9239
Semidiameter of the Earths Orbe
656 [...]8
The sine of his angle of Inclination
3230
And the Arch answering thereto
1. 85111
And therefore suppose the R. of the Earths Orbe
100. 000
The eccentricity of Mars will be
14075
The Semidiameter of his Orbe
152350
The parts of his greatest Inclination
4921

The Anomaly 119. 36707 is the angle A M E in the Ellipsis of the 13 Chapter, and therefore the halfe of it is the halfe sum of the angles M E H and M H E 59. 68353

2. The side M E304700 
3. The side M H28150 
Summe332850 co. ar.4. 4777515
Differ.2765505. 4417726
Tang: ½ sum59. 6835310. 2330382
Tang: ½ diff:54. 8629010. 1525633
Difference4. 82063 Angle M E H 

Difference doubled 9. 64126 Angle M B H or the Aequa­tion sought, and to be subtracted from the planets mean Longitude, be­cause the Anomaly is lesse then 180. viz. 119. 36707.

Meane longitude of Mars
267. 07247
Aequation subtracted
9. 64126
Mars his Eccentrick place
257. 43121

To finde his distance from the Sun.

As the sine of M B H9. 64126 co. ar.0. 7760404
To the side M H281504. 4494783
So is the sine of M B H60. 632939. 9402403
To the side B H1464735. 1657590
From the eccentrick place sub: Node. 119. 36707
Argument of Latitude 128. 06614
Whose complement is K L 51. 93586

To finde the Reduction.

As the sine of 90  
To Cosine the great inclin: X K L1. 851119. 9997732
So tang: of K L51. 9349410. 1061739
To tang: of X K51. 9203910. 1059471
Differ.. 01455 Reduction. 

Because the argument of Latitude is more then 90, the Reduction must be added to the Eccentrick place.

The eccentrick place of Mars
257. 43121
Reduction adde
. 01455
Eccentrick reduced
257. 44576

To finde the present inclination.

As Radius  
To the greatest inclin: E B99213. 6920533
So the sine of K L51. 934949. 8960878
To the X L38733. 5881411

Which are the parts of inclination agreeing to the common Radius, 152350. But the distance of Mars from the ☉ is to be put for the Radi­us, and then the parts of inclination will be 3724.

For as common Radius D L152350 co. ar.4. 8171576
To ♂ distance B H or A L1464735. 1657590
So is X L38733. 5881411
To X L37243. 5710577

To finde the distance of ♂ corrected by Curtation.

As A L146473 co. ar.4. 8342410
To Radius 10. 0000000
So is X L37243. 5710577
To the sine of L A X1. 457038. 4052987
[Page 127]As Radius  
To A L1464735. 1657590
So Cosine of L A X1. 457039. 9998596
To A X1464265. 1656186

To finde the second inequality of Mars.

We must have given, 1 The angle N A S, which is to be found by subducting the ☉ place from the eccentrick of ♂ reduced, or this from it, so that lesse then 6 signes may remain, this remainer is the Anomaly of the Orbe, and the complement thereof is the angle N A S, or the halfe, is the halfe sum of the opposite angles.

Example.
The eccentrick of ♂ reduced
257. 44576
The ☉ true place
154. 07347
Anomaly of the Orbe
103. 37229
Complement is N A S
76. 62771
Halfe Anomaly
51. 68614
These given with the sides N A & S A, I say,
As the greatest side N A146426 co. ar.4. 8343814
Is to Radius 10. 0000000
So is the lesser side S A1008955. 0038707
To the tang. of34. 568879. 8382521
Adde45 
As Radius  
To co-tang.79. 568879. 2650444
So tang. [...]/ [...] sum51. 6861410. 1022929
To tang. ½ diff.13. 115369. 3673373
Summe64. 80150 angle A S N 
Differ.38. 57078 angle A N S 

Because the Suns place was subtracted from the eccentrick of ♂ redu­ced, therefore the angle of elongation A S N 64. 80150 must be added to the ☉ place 154. 07347 and then the place of ♂ will be 218. 87497.

To finde the distance of ♂ from the Earth.

As the sine of A N S38. 57078 co. ar.0. 2051769
To the side A S1008955. 0038707
So sine of N A S76. 627719. 9880626
To the S N1574385. 1971102

To finde the latitude of Mars from the Earth.

As the side S X157438 co. ar.4. 8028898
To the side X L37243. 5710577
So is Radius 10. 0000000
To tangent of X S L0. 135607. 3739475
Which is the quantity of ♂ his Northern latitude.  

CHAP. 16. Of the Motion of Venus.

HAving done with the three superiour Planets, Saturn, Iupiter and Mars, we come to the two inferiour, Venus and Mer­cury, the investigation of whose places is much after the same manner with the former, the difference is in the second inequali­ty, occasioned by their motion under the earth, the Orbs of the other Pla­nets being above it; that this difference may be the better discerned, we have added an example in each for the time before given.

The meane motions of Venus.

An. Christ.Longit. ♀Aphel. ♀Node ♀
Yeares 1500333. 11667303. 97639073. 28944
8015. 484721. 12694. 67028
6270. 36028. 08444. 05028
Iuly339. 65833. 00806. 00500
D 1625. 63472. 00062. 00039
H 181. 20194  
P 4564. 03048  
Meane Mot.265. 48714305. 19645074. 01537
Aphel. Subt.305. 19645Rest Anom.320. 29069

The Semidiameter of the orbe of Venus, in such parts of which the Earths orbe is 100. 000, by the computation of Bullialdus is 72398, her Eccentricity 575. The parts of her greatest inclination 4270. And the an­gle it selfe 3. 38111. In the triangle therefore of the following Diagram M E H, we have three things given.

[Page 129]1. The halfe sum of the angles M E H and M H E 19. 85465, viz. the halfe complement of the meane Anomaly to a circle.

2. The side M E144796 
3. The side M H.1150 
Summe145946 co. ar.4. 8358079
Difference1436465. 1572934
Tang. halfe sum.19. 854659. 5576273
Tangent halfe difference19. 565609. 55072 [...]6
Difference. 28905 Angle M E H. 
Differ. doubled. 57810 Angle M B H. 

or the Equation to be added to the mean longitude, because the Anomaly is more then a semicircle.

[figure]
The meane Longitude of Venus
265. 48714
Equation adde
. 57810
The eccentrick place of Venus
266. 06524
Node subtract
74. 01537
Argument of latitude K L
192. 04987

To finde the distance of Venus from the Sun.

As the sine of M B H0. 57810 co. ar.1. 9961373
To the side M H11503. 0606978
So the sine of H M B39. 709319. 8054279
To the side B H728224. 8622630

To finde the Reduction.

As the Radius  
To the Cosine of the great inclina. X K L3. 381119. 999 [...]433▪
So tangent of K L12. 049879. 329 [...]295
To tangent of X K12. 029509. 3285728
Difference. 02037Reduction.

Because the Argument of Latitude is more then 180, the Reduction must be subtracted from the eccentrick place.

The eccentrick place of Venus
266. 06524
Reduction subtract
. 02037
Eccentrick reduced
266. 04487

To finde the present inclination.

As Radius  
To the greatest inclinat. E B.42703. 6304 [...]78
So sine of K L12. 049879. 3196533
To the inclinat. X L8912. 9500811

Which are the parts of inclination agreeing to the common Radius 72398, but the distance of Venus from the Sun, 72822 being put for Radi­us, the inclination will be 896.

As the common Radius D L72398 co. ar.5. 1402735
To Venus distance B H or A L728224. 8622630
So is X L8912. 9508115
To X L8962. 9526176

To finde the distance corrected by Curtation.

As A L7 [...]822 co. ar.5. 1377370
To Radius, so is X L8962. 9526176
To the sine of L A X0. 705508. 0903546
As Radius  
To A L728224. 8622630
So Cosine of L A X070559. 9999671
To A X728164. 8622301

To finde the second inequality of Venus.

We must have given, 1. The angle N A S which is to be found by sub­ducting the Suns place from the eccentrick of Venus reduced, or this from it so that less then 6 signes may remain, this remainer is the Anomaly of the orbe and the complement is the angle N A S, or the halfe is the halfe sum of the opposite angle.

[Page 131]

[figure]
Example.
The eccentrick of Venus reduced
266. 04487
The Suns true place
154. 07347
Anomaly of the orbe
111. 97140
Complement is N A S
68. 02860
Halfe Anomaly
55. 98570

These given with the sides N A and S A the Analogies are.

As the greater side S A100895 co. ar.4. 9961293
Is to Radius 10. 0000000
So is the lesser side N A728164. 8622300
To the tangent of35. 818159. 8583593
Adde45. 
As Radius  
To cotangent80. 818159. 2085475
So tang. halfe sum55. 9857010. 1707787
To tang. halfe diff.13. 469269. 3793262
Summe69. 45496 Angle A N S 
Difference42. 51644 Angle A S N 

[Page 132]In the superiour Planets, Saturne, Iupiter, and Mars, the summe of these angles is the elongation, but in the inferiour Venus and Mercury there difference is the Elongation sought, and in our Example is to be ad­ded to the Suns place, because the Suns place was subtracted from the Eccen­trick of Venus reduced.

[figure]
Suns true place
154. 07347
Elongation A S N add
42. 51644
True place of Venus
196. 58991

To finde the distance of Venus from the Earth.

As the sine of A N S69. 45496 co. ar.0. 0285403
To the side A S1008955. 0038707
So sine of N A S68. 028609. 9672296
To the side S N999174. 9996406

To finde the latitude of Venus from the Earth.

As the side S X9991. 7 co. ar.5. 0003594
Is to Radius 10. 0000000
So is X L8962. 9526176
To the tangent of X S L0. 514177. 9529770
which is the South latitude of Venus.  

CHAP. 17. Of the Motion of Mercury.

THe forme of calculating the place of this Planet is the same with Venus, the Dimensions of whose orbs we shall give you, as the learned Bullialdus hath computed them, but first we will set down the middle motions thereof to the former time.

The middle motions of Mercury.

An. Christ.Longit. ☿Aphel. ☿Node ☿
1500352. 53750248. 73556039. 85639
8059. 534722. 316112. 12417
6326. 41889. 17361. 15917
Iuly147. 58583. 01694. 01528
D 1 [...]65. 47806. 00126. 00117
H 183. 06917  
P 4564. 07781  
Meane Mot.234. 70198251. 2434842. 15618
Aphel. Snbt.251. 24348Rest Anom.343. 45850

The proportion between the Earths orb, and the orbe of Mercury is as 100. 000 to 38585 Semicentricity in the same parts is, 8105. The parts or greatest inclination 4635. And the angle it selfe 6. 90. In the trian­gle therefore M E H, of the first Diagram of the former Chapter we have known. 1. The halfe sum of the opposite angles M E H and M H E, 8. 27075 the halfe of 16. 54150 which is the complement of the meane A­nomaly, 343. 4585 to a circle.

2. The side M E77170 
3. The side M H16210 
Summe93380 co. ar.5. 0297462
Differ.609604. 7850449
So tang. halfe sum.8. 270759. 1628126
To tang. halfe differ.5. 425328. 9776037
Difference2. 84543 Angle M E H 
Difference doubled5. 69086 Angle M B H or the E­quation to be added to the meane longitude, because the Anomaly is more then a semicircle. 
Example.
The meane Longitude of Mercury
234. 70198
Equation adde
5. 69086
Eccentrick place
240. 39284
Node subtract
42. 15618
Argument of Latitude K L
198. 23666

To finde the distance of Mercury from the Sun.

As the sine of MBH5. 69086 co. ar.1. 0036592
To the side MH162104. 20978 [...]0
So sine of EMH16. 541509. 4544022
To the side BH465414. 6678444

To finde the Reduction.

As Radius, to cosine of XKL6. 909. 9968431
So tangent of KL18. 236669. 5178453
To tangent of XK11. 113229. 5146884
Reduction12344 

And because the argument of Latitude is more then 180, it must be sub­tracted from the eccentrick place 240. 39284

And then the eccentrick reduced will be. 240. 26940

To finde the present inclination.

As Radius  
To the greatest inclination EB46353. 6660497
So sine of KL.18. 236669. 4954646
To the inclinat. XL14503. 1615143

Which are the parts of inclination agreeing to the common Radius 38585. But the distance of Mercury from the Sun being put for Radius, the inclination will be. 1749

For as Radius DL38585 co. ar.5. 41358 [...]5
To Mercury dist. BH or AL465414. 6678444
So is XL14503. 1615143
To XL17493. 2429402

To finde the distance corrected by Curtation.

As AL46541 co. ar.5. 3321556
To Radius 10. 0000000
So is XL17493. 2429402
To the sine of LAX2. 154378. 5750958
As Radius 10. 0000000
To AL465414. 6678444
So cosine of LAX2. 154379. 9996929
To AX465094. 6675373

To finde the second inequality of Mercury.

We must have given, 1. The Angle NAS which is to be found by sub­ductiug the Suns place, from the eccentrick place of Mercury reduced, or this from it, so that less then 6 signes may remain, this remainer is the [Page 135] Anomaly of the orbe, and the complement thereof is the Angle NAS, or the halfe, is the halfe sum of the opposite angles.

Example.
The eccentrick of Mercury reduced
220. 26940
The Suns true place
154. 07347
Anomaly of the orbe
96. 19593
Complement is NAS
83. 80407
Halfe Anomaly
48. 09796

These given with the sides NA and SA. the Analogies are

As the greater side SA100895 co. ar.4. 9961293
Is to Radius 10. 0000000
So is the lesser side NA465094. 6675373
To the tangent of24. 747999. 6636666
Adde45. 
As Radius  
To the cotang. of69. 747999. 5669785
So tang. halfe summe48. 0979610. 0470559
To tang. halfe difference22. 351609. 6140344
Summe70. 44956 Angle ANS 
Difference25. 74636 Angle ASN 

Because the Suns place was subtracted from the eccentrick of Mercury reduced, therefore the angle of Elongation ASN must be added to the

Suns place.
154. 07347
Elongation ASN adde
25. 74636
True place of Mercury
179. 81983

To finde the distance of Mercury from the Earth.

As the sine of ANS70. 44956 co. ar.0. 0257891
To the side AS1008955. 0038707
So the sine of NAS83. 804079. 9974556
To the side SN1064425. 0271154

To finde the Latitude of Mercury from the Earth.

As the side SX106442 co. ar.4. 9728846
Is to Radius 10. 0000000
So is XL17493. 2429402
To the tang. of XSL0. 941698. 2158248
Which is the south Latitude of Mercury.  

CHAP. 18. Of the Semidiameters of the Sun, Moon, and shadow of the Earth.

THe angle of the Suns apparent Semidiameter, in his nearest di­stance to the Earth, Bullialdus hath by observation found to be 16′ 45″, or in Decimall numbers 27917. And by an Eclipse of the Moon, December 1638, he found her Semidiameter to be 16′ 54″ or 28167, and the Semidiameter of the Earth; shadow 44′ 9″, or 7 583, at which time (being the time of incidence) her distance from the Earth by his computation was 97908 parts of the Semiaxis of the Elipsis 100. 000. By this and another observation in the same Eclipse, he shew­eth how to finde her apparent semidiameter, in all the other intervalls. The inferiour limbe of the Moon and the first Starre in the foot of the for­mer Twin, (whose place then according to Tycho was Gemini 28. 25′ 17″, or Gemini 28. 42138 with South Latitude, 0 d. 58′ or 0. 96667.) being in the same Azimuth, was 8′ or 13333 higher then the Star and the Alti­tude of the heart of Hydra then taken by him at Paris was 30 deg. 37′, or 30 d. 61667. From whence the hour was found, 30 h. 40′, or 13 h. 66667 and the houre being given the altitude of the Starre is also given, deg. 56. 42′ 15″, or deg. 56. 70416. The apparent altitude of the center of the Moone was deg. 57 7′ 9″, or deg. 57 11916, but by her latitude and place it should have beene deg. 57 40′ 4″, or deg. 57 66778 and there­fore her parallax of altitude 32′ 55″, or 54861. The situation of the Moone and Azimuth in which her interiour limbe and the Stars were, being given, her aparent Longitude was almost in Gemini, deg. 28 38′ 30″, or Gemini deg. 28 64167, her parallax of longitude 18 min. or 30000 and therefore the center of the Moon in her true motion in Gemini 28 d. 57 min. fere. or in Gemini 28 d. 95000, her parallax of Latitude is 19 min. or 31667. to which 21′ or 35007, the difference of the observed latitude of the Moon and Stars, being added the true difference is 50 min. or 83333 min. and thence the Moons Latitude 8 min. or 13333 S.

Now then to finde the distance of the Moon from the Earth, in this E­clipse, the Earths semidiameter being one degree, Let FEC represent the true Horizon, BDE, the vertical at Paris E the center of the earth, D the City of Paris: the Moons true altitude, AEF, deg. 5766778, the observed altitude ADG, deg. 5711916. The parallacticall angle DAE, deg. 0. 34861. Therefore in the Triangle ADE we have given all the angles, and the finde DE one Semidiameter of the Earth, to finde AE, for which the anolagy is.

[Page 137]

[figure]
As the sine of DAE 0 d.54861 co. ar.2. 0188745
To the side DE 1 0. 0000000
So is the sine of ADB 32 d.880849. 7347147
To the side AE56. 701. 7535892

This foundation being laid, he proceedeth to the rest: and to shew how we may possibly fall into some absurditie, he supposeth the Moons distance from the Earth in this Ecclipse to be but 55 semidiameters, or the side BC in the following figure, the apparent angle of the semidiameter of the Earths shadow CHI, 0. 73583 AEF represents the Sun, his semidiame­ter AE, the angle of his apparent Semidiameter when he is Perig. AGE 16. 45, or in decimalls 27916 BHG represents the Earth. BG the Semi­diameter thereof, hence to finde HI in the triangle HIC the proportion is.

As the sine of HIC89. 26417 co. ar.0. 0000358
To the side HC541. 7323937
So is the Radius HCI9010. 0000000
To the Hypothenusal HI54. 0041. 7324295

2. In the triangle HBI we have given the sides BH. 1. and HI 54. 004 with the angle BHI 179. 26417, hence to finde the Angle BHI, the Analogie is.

[Page 138]

As the greater side H I54. 004 co. ar.8. 2675705
Is to the less H B1.0. 0000000
So is Radius 10. 0000000
To the tangent of1. 060828. 2675705
Adde45. 
As Radius 10. 0000000
To the Cotang. of46. 060829. 9839145
So Tang. halfe summe367917. 8075980
To tang. halfe differ.354547. 7915125
Angle B I H01337. And the angle C B I72246

3. In the triangle C B I, we have given the angles and the side B C 55 to find C I. Therefore say,

As Radius

To the tangent of C B I722468. 1007064
So is B C551. 7403627
To C I0. 6935 = to B K1. 8410691

and therefore K G 3065, and the angle K I G 0. 31857.

For, [...] I K55 co. ar.8. 2596373
To Radius 10. 0000000
So is K G0. 30651. 4864305
To the tangent of K I G0. 318577. 7450678

and the angle B D G is equal thereunto, but so the angle of the Suns ap­par [...]n [...] Semidiameter A G E 27916 by observation, is lesse then the angle A D E, which is absurd, and therefore some part assumed is false. The Semidiameters of the Sun and Moon must not be changed, constant experience agreeing with these observations.

In this Eclipse therefore Bullialdus doth take for the distance of the Moone from the earth, B C 57. 85 Semidiameters of the earth, and the Semidiameter of the earths shadow, C B I 75111. Hence to find C I, the analogie is.

As Radius

To the side B C57. 851. 7623034
So the tang. of B C0. 751118. 1176019
To C. I.0. 758411. 8799053

Let B K be equal to C. I. So is K G 24159. The [...]

[Page 139]

As I K57. 85 co. ar.8. 2376066
To Radius 10. 0000000
So is K G241591. 3830789
To the tang. of K I G.23928 or B D G7. 6207755

equal to E D A, and the Suns apparent Semidiameter being given A G E, 27916, the angle G A B, or the difference between the angles A G E, and E D A shall be given also, viz. 03988. the Suns Horizontal parallax when he is Perigaeon. And the Moones Perigaeon distance from the earth, in Syzigiis, 56. 50 Semidiameters of the earth.

For, as97908 co. ar.5. 0091819
To57. 851. 7623034
So is956384. 9806304
To B C56. 501. 7521157

Hence to find the Moones Horizontal parallax when she is perigaeon, the analogie is, in the preceding Diagram.

As E G or B C56. 50 co, ar.8. 2478843
Is to Radius: So is D E1.0. 0000000
To the sine of E G D1. 013998. 2478843

The Horizontal parallax of the Sun when he is perigaeon or the angle

B A G was found to be
. 03988
The Moones Horizontal parallax is
1. 01399
Their aggregate
2. 05387
Semidiameter of the Sun subtract
. 27916
There rests the angle C B I
. 77471

or the apparent semidiameter of the earths shadow in loco transitus Lun [...], Perig.

In the triangle therefore B C I, we having the angles and the side B C given, C I shall be also given.

For, As the sine of90 deg. 
Is the side B C56. 501. 7521157
So tang. of C B I774728. 1310339
To the side C I7640 = B K1. 8831496
And therefore K G [...]360 

And in the triangle A G B having the angles and B G given the side A B is also given, for

As the tang. of B A G03988 co. ar.3. 1585620
Is to B G 1. So is Radius 10. 0000000
To A B1440. 663. 1585520

[Page 140] which is the distance of the Earth from the Sun, when he is Perihelion. And because the Suns eccentricity is 1784, his Apogaean distance is 101784, hence to find his distance, in Semidiameters of the earth, say,

As his Perigaean distance98216 co. ar.5. 0078178
Is to his distance1440. 663. 1585620
So is his Apog. distance1017845. 0076794
To his Apog. dist.1493. 033. 1740692
Then as B S1493. 03. or E G6. 8259308
To Radius, so is E D.110. 0000000
To the sine of E G D0. 38556. 8259308

The Suns Horizontal parallax when he is Apogaeon.

As Radius, to A B:1440. 663. 1585620
So is tang. of A B E279167. 6877120
To A E701890. 8462740
Then as B S1493. 03 co. ar.6. 8259308
To Radius, so is S T70189▪ ☉ Semid.0. 8462740
To the tang. of S B T269367. 6722048

The apparent Semidiameter of the Sun when he is Apogaeon.

The Sun being Perigaean, we have given B G 1. K B. 75841. KG. 24159 and B C. 56. 50, the distance of the Moon from the Earth when she is Pe­rigaean; from whence the longitude of the earths shadow may thus be found.

As K G2360 co. ar.10. 6270880
To K I56. 501. 7521157
So is C I76401. 8831496
To C D182. 932. 2623533

Add B C 56. 50 then is B D 239. 43. the longitude of the earths sha­dow.

Let B S be the Apogaean distance of the Sun,
1493. 03
The angle of the Suns apparent Semidiameter S G T
26936
The Perigaean Semidiameter or the angle A G E
27916
Their difference is the angle Z G E
00980

Let TG be produced to N, then shall the angle I G N be equal to the an­gle Z G E, but the Sun being Perigaean, the angle B D G was found to be o. degrees 239 [...]8. whose complement is the angle B G D 89. 76072 therefore when the Sun is Apogaean, it shall be 89▪77052, therefore B X G 0. 22948, equal to K N G. [Page 141] Hence to find K G the analogie is.

As Radius9010. 0000000
To K I56. 501. 7521157
So tang. of K I G0. 229487. 6006035
To K G226321. 3547192
And K B77368. Then to find C B N. Say. 
As B C56. 50 co. ar.8. 247 [...]843
To Radius9010. 0000000
So C I or rather C N.773681. 8885613
To the tang. of C B N7844 [...]8. 1364456

The Sun being Apogaean; and the angle C B I, the Sun being Paerigaean, was before found to be 77471, and therefore the difference of the earths shadow between the Suns Apogaean and Perigaean is, 00971. Then,

As K G22632 co. ar.10. 6452808
To K I56. 501. 7521157
So is C N773681. 8885613
To C X19 [...]. 182. 2859578
Add B C56. 50. Then is B X249. 68.

The semidiameter of the Moon, when she is Perigaean, is greater then the semidiameter of the Sun, being Apogaean, and therefore Bullialdus doth make it 17. or 28333, and because the eccentricity of the Moon is given 4362, her Apogaean distance in Syzygiis 104362, the Moon being Perigaean her distance from the earth is, 95638, and in semidiameters of the earth 56. 50 and therefore her Apogaean distance in semidiameters of the earth, by the analogy following,

As95638 co. ar.5. 0193696
To56. 501. 7521157
So is1043625. 0185423
To61. 661. 7900276
As her Apogaean dist.61. 66 Co. ar.8. 2099724
To the Moons Perig. semid.283331. 4522925
So is the Moon Perig. dist.56. 501. 7521157
To the Apog. semid.259641. 4143806

We have the semidiameter of the Cone C I 76400, and her Perigaean distance 56. 50, and D C 182. 93, but when the Moon is Apogaean, D C will be no more then 177. 77. found by abating K I or K N 61. 66. from B D 239. 43. Hence to find C I or C N in the same parts say.

[Page 142]

As D C182. 93 co. ar.7. 7376467
To C I76401. 8831496
So is C D177. 772. 2498584
To C I74241. 8706547
Then as B C61. 66 co. ar.8. 2099724
Is to Radius9010. 0000000
So is C I74241. 8706547
To the tang. of C B I. 689818. 0806271

Here then we have determined 
 Apogaeon26936
The Suns Semidiameter  
 Perigaeon27916
 Apogaeon1493. 03
His distance from the earth  
 Perigaeon1440. 66
 Apogaeon ☉249. 68
The Axis of the earths shadow  
 Perigaeon ☉239. 43

The Semidiameter of the shadow, when the Sun is Apogaeon. In loco [...]ransitus Lunae, Apog 78442 Perig. 77471.

 Apogaeon25964
The Semidiater of the Moone in Syzygiis  
 Perigaeon28333
 Apog.61. 66
The distance of the Moon from the earth in Syzygiis  
 Perig.56. 50
 Perig.23928.
Semiangle of the Cone  
 Apog.22948.

CHAP. 19. Of the Proportion and Magnitude of the three great b [...]dies, the Sun, Moon and the Earth.

THat it is a hard matter exactly to determine the true Magnitude of the coelestial bodies, is not I beleeve denied by any, it will be therefore sufficient if we shall determine them so, as that there be no sensible errour in them; and to such exactnesse, we may traine by the rules and proportions following.

[Page 143] As the Semidiameter of the Earths shadow C B I. Is to the Semidia­meter of the shadow in parts of the Earths Semidiameter C I = B K: So is the apparent Semidiameter of the Moon. To the Semidiameter of the Moone in parts of the Ear [...]hs Semidiameter, that is

As C B I77471 co. ar.10. 1108609
To C I76401. 8831496
So is the Moones semid.283331. 4522925
To the Moones semid.279451. 4463030

And Sphears being in triplicated proportion of their diameters, the pro­portion of the earth to the Moone will be as 1. 00000. 00000. 00000. the Cube of the earths Semidiameter to 02182. 28939. 33625. the Cube of the Moones semid. 27945. and therefore dividing the earths Semidiame­ter by the Moons, the quotient will be 45. 823, and so many times is the body of the Moon contained in the Earth.

The proportion between the Semidiameter of the Earth and the Semidi­ameter of the Sun, may be found by this analogy,

As Radius90 
To A B1440. 663. 1585614
So is tang. A B E279167. 687706 [...]
To A E7. 01890. 8462683
But if to A B1440. 66 
You adde B D239. 43 
Their summe is A D1680. 09 
And then, As Radius90 
To the side A D1680. 093. 2255415
So is tang. of A D E or K I G239287. 6207755
To A E7. 01970. 8463170

And now if you take the lesser semidiameter of the Sun, the Cube there­of will be [...]45. 781, but taking the Semidiameter of the Sun to be but 7 semidiameters of the earth, the Sun will be 343 times bigger then the Earth.

The proportion of the Semidiameter of the earth and the Moone is as 1 to 27945, of the Sun and the Earth as 7 to 1, and therefore of the Sun and the Moon as 7 to 27945. The Cube of 7 is 343, the Cube of 27945 is 02182, &c, by which dividing the Cube of the Suns semidiameter the quotient will be 15717. 47 and so many times is the Moone contained in the Sun.

CHAP. 20. Of the proportion between the Orbs of the superiour and inferiour Planets, and the Orb of the Earth.

WHat proportion the Orbs of these Planets have to the earths Orb, we have set down in those Chapters, in which we have shewed the manner of computing their places, and by what meanes the truth of those proportions may appeare, we shall set downe in this, and because we have used those proportions which Bullialdus hath with great diligence computed; we shall exhibit here an Example in Saturne according to which method the proportions between the orbe of the earth and the orbes of the other planets are also to be found.

And Saturns proportion to the earths orbe, as Bullialdus hath determi­ned it, and which we have used, Chap. 13. is as 100. 000 to 10480.

The observation from whence this proportion is gathered was made Anno Christi 1587. January the 9th. Hour 9th. 75 parts, at which time Saturn was observed to be in Aries 26, 13333. with South latitude, deg. 2. 46667. The Suns true place then was in ♉ deg. 29, 41778. and his di­stance from the earth, 98374. Saturns true place from the Sun by calcula­tion was in ♉ deg. 2, 31416. whose difference from his observed place, deg. 6, 18083. is the parallax of the orbe or the angle A N S, and the an­gle N A S, 87. [...]0362, is found by deducting Saturns place from the place of the Sun, which with his distance from the Sun or side A N 95596 be­ing given, the side A S will be found to be 10310.

Now as the Suns distance from the earth,
98374
Is to the distance,
10310
So is the Semidiameter of ♄ orbe,
100. 000
To the Semidiameter of the earths orbe,
10480

By a second Observation made Anno Christi 1590, February 8, about 8 of the clock in the evening; Saturn was in Gemini, deg. 7. 53333. with South latitude, deg. 1. 50. The true place of the Sun at the same time was in Pisces, deg. 0. 02805. and his distance from the earth, 98953. And Saturns place from the Sun by calculation was in Gemini, deg. 13. 82167. from which deducting his place taken by observation, their difference, 6. 28834 is the parallax of his orbe, represented by the angle A I S. And subtract­ing [Page 145] Saturns place 73. 82167 from the Suns place 330. 02805 their diffe­rences 256. 20638 reject a semicircle is the angle, I A S 76. 20638 and Saturns distance from the Sun represented by A I 94338 and hence the side A S 10423.

And now as the Suns distance from the earth
9893
Is to the distance A G
10423.
So is the Semidiameter of Saturns orbe
100. 000
To the Semidiameter of the earths orbe
10533
[figure]

By a third observation made in the same year of Christ 1590 Septemb. 7 at midnight, Saturns place was in Gemini deg. 28. 1 with South lati­tude deg. 1. 18333. The Suns true place at the same time was in Virgo deg 24. 49833. And his distance from the earth 100300. Saturnes place from the Suns by calculation, was in Gemini deg. 21. 76722, which be­ing deducted from his place taken by observation, their difference is the parallax of his o [...]e, or the angle A K L 6. 33278, and deducting Sa­turns place from the place of the Sun the angle A L K is 9 [...]. 73111, and therefore the side A L 10415.

Now as the Suns distance from the earth
100300
Is to the distance A L
10415
So is the Semidiameter of Saturns Orbe
100000
To the Semidiameter of the earths orbe
10383

But Bullialdus whom we follow doth retaine the first of these 10480 as being the meane, and most agreeable to Tycho's observation; And from these three observations the inclination of Saturns orbe may thus be found.

The Triangles L D. N. I D O, and D G M of the following Diagram, have their sides and angles equal with the triangles, N A S. I A S and L A K in the Diagram preceding, being drawne from the same observa­tions; in every of which we are to compute ♄ distance from the earth; for which in the triangle L D N by the first of these observations we have given the angle L N D 86. 71556. The angle L D N 87. 10362 and ♄ distance from the Sun L D 95596 to find L N.

As the sine of L N D86. 71556 co. ar.0. 0007130
Is to the side D L955964. 9804397
So the sine of L D N87. 103629. 9994447
To the side L N956304. 9805974

Then in the right angled triangle L K N right angled at K, we have given the angle of South latitude L N K 2. 46667, and the side L N 95630, to find L K.

As Radius 10. 0000000
Is to L N956304. 9805974
So is the sine of L N K2. 466678. 6338534
To the side L K41163. 6144508

Hence to find the angle of Latitude at the Sun say,

As the side L D95596 co. ar.5. 0195603
Is to Radius 10. 0000000
So is the side L K [...]1163. 6144508
To the Sine of L D K2. 467568. 6340111

By the second observation in the triangle I D O we have given the an­gle I O D 97. 50528 whose complement is 82. 49472 the angle I D O 76. 20638, and ♄ distance from the Sun I D, to find his distance from the earth I O.

[Page 147]

As the sine of I O D82. 49472 co. ar. [...]. 00373 [...]
Is to the side I D943384. 974686 [...]
So is the sine of I D O76. 206389. 9872910
To the side I O924094. 9657145

Then in the right angled Triangle H I O right angled at H, we have given the angle of Saturns South latitude H O I 1. 50, and the side I O to find H I.

As Radius 10. 0000000
To the side I O924094. 9657145
So is the sine of H O I1. 508. 4179190
To the side H I24193. 3836335

Hence to find the angle of Latitude at the Sun
As the side I D94338 co. ar.5. 0253134
Is to Radius 10. 0000000
So is the side H I24193. 3836335
To the sine of I D H1. 469328. 4089469

[figure]

By the third observation in the triangle GMD we have given the angle [Page 148] M D G 87. 26889 the angle M G D 86. 39833 the side G D 94239 to find M G.

As the sine of G M D86. 39833 co. ar.0. 0008588
To the sine of M D G87. 268899. 9995064
So is the side G D942394. 9742306
To the side M G943184. 9745958

Then in the right angled triangle G M F right angled at F we have gi­ven the angle of Saturns South latitude G M F 1. 18333, and the side G M to find G F.

As Radius 10. 0000000
Is to the side M G943184. 9745958
So is the sine of G M F1. 183338. 3149535
To the side G F19483. 2895493

Hence to find the angle of latitude at the Sun,

As the side D G94239 co. ar.5. 0257694
Is to Radius 10. 0000000
So is the side G F19483. 2895493
To the sine of G D F1. 184348. 3153187

These things premised the places of the Nodes and the angle of incli­nation of the planes may thus be found.

In the following Diagram let the place of the first observation be at A, and the angle of latitude at the Sun D G 2. 46756. The second at B, and the latitude G E 1. 4693 [...]. The third at C, and the latitude G F 1. 18434.

The Arches of apparent motion from the

First observation to the second A B
41. 50751
Second to the the third B C
7. 94555
First to the third A C
49. 45306

The halfe of these arches are the measure

of the angle B A C3. 97277whose sines are the sides A B35435
of the angle B C A20. 75375whose sines are the sides B C6929
  whose sines are the sides A C41828

The angles of Latitude at the Sun found are

L D K2. 46756whose sines are the sides G D4306
I D K1. 46932whose sines are the sides G E2617
G D F1. 18434whose sines are the sides G F2064
The difference between G E and G F is F E
553
The difference between G D and G F is F D
2242
The difference between G E and G D is E D
1689
[figure]

Hence to find the side A L in the triangle A B L use this analogie

As F D2242 co ar.6. 6493644
Is to C A418284. 621467 [...]
So is E D16893. 2276296
To A L315114. 4984611

Then to find the angle A B L
We have given the side A B35435and B A L3. 97277
We have given the side A L31511and B A L3. 97277

whose complement is 176. 02723, and the halfe thereof 88. 01361 is the halfe summe of the opposite angles.

As the summe of A B and A L66946 co. ar.5. 1742754
Is to their difference39243. 3937289
So the tang. halfe summe88. 0136111. 4598852
To the tang. halfe differ.59. 3866810. 22889 [...]
The summe147. 40029 is the angle A L B 
The difference28. 62693 is the angle A B L 

whose double 57. 25386 is the arch A M, [...]o which if you [Page 150] adde the arch A B 41. 50751 their summe is the Arch B A M 98. 76137, whose complement to 180 gives the arch B H and M I 81. 23863, and the halfe thereof is the arch B H 40. 61931. Now then the point B is in 73. 82167

To which if you adde B H
40. 61931
The Node ascending is
114. 44098
And deducting B C from B H40. 61931whose natural sines are G E65098
Their difference is C H32. 67376whose natural sines are G F53980
The summe of H B and B A is H A82. 12682whose natural sines are G D99057

To find the angle of Inclination by the first observation, say

As G D99057 co. ar.5. 0041149
To G D43063. 6340740
So is G K Radius 10. 0000000
To G K the sine of deg.2. 489088. 6381889

To find the angle of Inclination by the second observation, say

As G E65098 co. ar.5. 1864324
To G E26173. 4178037
So G K Radius 10. 0000000
To G K the sine of D.2. 303978. 6042361

To find the angle of Inclination by the third observation, say

As G F53980 co. ar.5. 2677672
To G F20643. 3147096
So is G K100. 000 or Radius10. 0000000
To G K the sine of deg.2. 191288. 5824768

But by reason of this varietie, we may well suspect the truth of one or other, of the observations given; and therefore Bullialdus hath a [...]igned another place for the point of the Node ascending; viz. deg. 110. 42333 and the angle of Inclination somewhat more then that found by the first observation. viz. deg. 1. 50 that so he might make these observations to agree as neere as might be.

And now if you suppose the Node ascending to be
110. 42333
And from thence deduct the place of the 2d. observation
73. 82167

Their difference shall be the arch H B 36. 60166 and the sine thereof is G E 59624. Againe deducting B C 7. 94555 from B H, their difference will give C H 28. 65611, and the sine thereof G F 47954.

[Page 151]And by adding A B 41. 50751 to H B their summe shall be H A 78. 10917 and the sine thereof G D 97854.

For the latitude agreeing to the first observation

As G K100. 0005. 0000000
Is to G K deg.2. 508. 6396795
So is G D9. 78544. 9905785
To G D or the latitude2. 446328. 6302580

whereas it should have been 2. 46667.

For the latitude agreeing to the second observation

As G K100. 0005. 0000000
Is to K G deg.2. 508. 6396795
So is G E596244. 7754210
To G E or the latitude1. 490298. 4151005

whereas it should have been 1. 56667.

For the latitude agreeing to the third observation

As G K100. 0005. 0000000
Is to G K or the angle of inclin.2. 508. 6396795
So is G F479544. 6808248
To G F or the sine of latit.1. 198568. 3205043

whereas it should have been but 1. 19

CHAP. 21. To find the mean Conjunction and Opposition of the Sun and Moon.

FOr this purpose the Table which Shakerley transcribed from Bulli­aldus, we have here exhibited in Decimall numbers, the use whereof, as he hath explaind the same is this: Set down first the Epoch [...] next preceding the yeare given, then the yeares and moneths compleate having a care of the yeare Bisse [...]tile, and to every one set downe the time answering in the Table; then adde them altogether, and the summe subtract from the next greater in the Canonian, under the title [...], if you [...]ee [...] a Conjunction, or ☌, if an opposition, the remainer shew­eth the time required compleat from the beginning of the moneth cur­rent.

Example.

I would know the time of the meane opposition of the Sun and Moon in March, 1652. The worke is this.

 
Hou. Parts
The Epocha 1640
701. 96639
Yeares compleat 11
20. 14722
February compleat Bissextile
022. 53539
The summe subtract
744. 64500
From the Opposition next greater
1063. 10139
Rests the meane opposition
318. 45639

that is 13 dayes 6 houres and 45639 parts.

CHAP. 22. To find the true Opposition or Conjunction of the Sun and Moon.

FOr the time of the meane Conjunction or Opposition given, find the true place of the Sun, and the eccentrick place of the Moon, and compare them; if they either be precisely the same or precisely op­posite, the time of the true Conjunction or Opposition agrees with the meane; but if they differ take the difference, by subtracting the lesse from the greater, and that call the distance of the Sun and Moon.

2 Out of the Table of Semidiameters, and hourly motions; with the meane Anomalies of the Sun and Moon, take out their hourly motions, and subtract the hourly motion of the Sun, from the hourly motion of the Moon, by the remainer (which is the hourly motion of the Moon from the Sun) divide the distance of the Sun and Moone before kept, the quoti­ent gives the time, which must be added to the mean time of Conjunction or Opposition, if the excesse be in the Suns place, or subtracted, if in the Moones place.

3 At this time thus corrected, find againe the true place of the Sun and [...]centrick place of the Moon, together with their distance, and re­peat your former work, till you find them absolutely to concurre, and the time thus found shall be the true time of Conjunction or Opposition. As in the Example,

 D.Hou. parts
At the time of the meane ☍ March136. 45639
The true place of the Sun is 4. 85039
The Eccentrick place of the Moone 180. 38631
The Distance of the Sun from ☍ Moon 4. 46408
Mean Anomaly of the Sun 266. 40860
His hourly motion . 04112
[Page 153]Meane Anomaly of the Moone 30. 26681
Her hourly motion . 51827
Hourly motion of the Moone from the Sun . 47715
By which dividing the distance 4. 46408
The quotient gives Hours 9. 3558 to be added.  
So the time first corrected March1315. 81279
The true place of the Sun is 5. 23520
The eccentrick place of the Moone 1 [...]5. 15798
The distance of the Sun from ☍ of the Moon . 07722
Which divided by the hourly motion of the Moon from the Sun . 48114
Gives in time to be added . 16049
So the time secondly corrected1315. 97328
The true place of the Sun is 5. 24180
The eccentrick place of the Moon 185. [...]4010
The distance of the Sun from ☍ the Moon . 00170
Which divided by the hourly motion of the Moon from the Sun . 48121
Gives in time to be added . 00353
So the true time1315. 97681
The true place of the Sun is 5. 24194
The eccentrick place of the Moon 185. 24190

4 For this time find out the true motion of the Moons Latitude, and thereby the Reduction, which divide by the hourly motion of the Moon from the Sun, and the quotient contrary to the title of Reduction, apply to the last corrected; so have you the true time. In our Example.

The true motion of Latitude 174. 04881
The Reduction Adde . 02398
The quotient Subt. . 04983
So the true opposition1315. 92698

5 Lastly, apply the equation of time to this equal time to make it ap­parent.

The true time of the ☍1315. 92698
The equation of time Subt. . 02884
The apparent time of the ☍▪1315. 89814

CHAP. 23. To find whether there will be an Eclipse or not.

THere are two wayes to know this, of which the one is more easie, the other more certain, The first is this; At the true con­junction, if the true motion of latitude be within 17 degrees backward or forward of 6 or 12 signes, or at the opposition within 12 de­grees, there is a possibility of an Ecclipse, otherwise not.

In our Example the Moons true motion of latitude is 174 deg. 04881, which being not fully 6 degrees distant from 6 signes, shewes the neces­sity of an Eclipse.

The other way is this. If at the visible conjunction the visible latitude of the Moon be lesse then the aggregate of the Semidiameters of the Sun and Moon, there must be an eclipse or else not. 2. If at the true opposi­tion the true latitude of the Moon, be lesse then the summe of the Semidi­ameters of the Moon and the earths shadow, there must be an Eclipse o­therwise not.

This latter way is most certain, onely subject to this inconvenience, that a great part of the calculation is performed before we come to the [...], or power to judge of the possibility.

CHAP. 24. To find the Quantity of a Lunar Ecclipse.

BY the true motion of the Moons Latitude, find her true latitude, according to the former directions: this in our example is 0. 51496 North Descendant.

2 Find out the Semidiameter of the Moon by her meane ano­maly out of the Table, as also h [...] Horizontall parallax; and with the meane anomaly of the Sun, take out the Semiangle of the Cone of the shadow; and this subtract from the Moons Horizontall parallax, there rests the Semid. of shaddow.

3 Adde together the Semidiameter of the shadow, and Semidiameter of the Moon, and from the summe subtract the Latitude of the Moon, the remainder is the scruples of the Moons diameter ecclipsed.

Example.

Horizontall parallax of the Moon
. 94409
Semiangle of the Cone Subt.
. 23455
Semidiameter of the shaddow
. 70954
Semidia meter of the Moon
. 26431
Summe of the Semidiameters
. 97385
Latitud [...] of the Moon, Subt.
. 51496
Scruples deficient
. 45889

4 Convert these Scruples into digits or parts, whereof the Moones body containes 12, thus,

As the Moones diameter 52862 co. ar.
5. 276857
Is to the Scruples deficient 45889
4. 661708
So is 12 digits
1. 079181
To the digits ecclipsed 10. 417
1. 017746

Yet note that Lunar Eclipses are of three sorts.

  • 1 Partiall, when the Scruples deficient are lesse then the diameter.
  • 2 Totall without continuance when they are equall.
  • 3 Totall with continuance when the scruples deficient are greater then the diameter, and in these the digits eclipsed are more then 12, which are so to be understood, as that they shew how far the ecclipse is over the body of the Moon.

CHAP. 25. To find the duration of a Lunar Ecclipse, or the continuance of the totall darknesse, where the Ecclipse is totall.

FInd the scruples of Incidence thus: Take the Logarithmes of the summe and difference, of the Moones latitude and the summ of the Semidiameters of the Moon, and the shadow, halfe the summe of the two Logarithmes shall be the Logarithme of the Scruples of incidence required.

Example.

Summe of the Semidiameters97385 
Latitude of the Moone51496 
Their summe1. 488815. 172836
Their difference. 458894. 661308
Summe of the Logarithmes 9. 834544
Scruples of incidence 82656 4. 917272

2 Divide the Scruples of incidence by the hourly motion of the Moon from the Sun, the quotient gives the time of incidence or halfe durati­on of the Eclipse. This subtracted from the true time of the opposition▪ gives the beginning of the Eclipse; or added to it gives the ending.

Example.

The Scruples of incidence 82656
4. 917272
Divided by the hourly motion of the Moon from the Sun 48121
4. 682326
Time of incidence, hours 1. 7177
0. 234946
The true time of the opposition
13 d. 15. 89814
Time of incidence subt.
1. 71770
The beginning of the Eclipse
14. 18044
Time of incidence added, gives the end
17. 61584
The whole duration
3. 43540

3 If the Eclipse be total and you desire to know the continuance of total darkenesse, take the difference of the Semidiameters instead of the sum, and thereby worke as you are directed in the first example of this Chap­ter, and you have the halfe tarrience in the shadow, whose double is the thing sought.

CHAP. 26. To find the Moons Latitude at the beginning and end of the Eclipse.

MUltiply the Suns hourly motion, by the time of incidence, the pro­duct being added to the scruples of incidence, gives you the motion of the Moone agreeing to the time of incidence.

2 From the true motion of latitude at the true opposition subtract, this motion of the Moon; there rests the true motion of latitude [Page 157] at the beginning of the Eclipse; or if you adde it you have the motion of latitude at the ending, with which out of the Table of latitude you may find out the latitude, answering to the beginning and end, as in our Example.

The time of incidence
1. 7177
The Suns hourly motion
. 0411
Their product is
. 07059
The scruples of incidence
. 82656
The summe
. 89715
Motion of Latitude at true ☍
1 [...]4. 04882
Motion of Latitude at beginning
173. 15166
Latitude at beginning North Desc.
. 59223
Motion of Latitude at ending
174. 94596
Latitude at ending North Desc.
. 43746

CHAP 27. To find the middle of the Eclipse or greatest darkenesse.

THe time of the true Conjunction or Opposition the most recei­ved, is when the Sun and Moon are in one line perpendicular to the Ecliptique, to find this with the Moons true Latitude at the true opposition, enter the little Table of the difference of the true Conjunction or opposition from the greatest obscuration, and you shall find the difference with the title, which divide by the hourly motion of the Moon from the Sun, and the quotient according to the title, apply to the time of the true opposition; so have you the time of the greatest darkenesse, or middle obscuration.

Example.

The Moons Latitude, North Descend. . 51496
The difference adde . 04489
Which divide by the hourly motion of the Moon . 48121
Gives the difference in time to be added . 09328
To the true opposition March 13. 15 . 89814
So the middle of the Eclipse13.15h. 99142

The Calculation of the forementioned Ecclipse according to the preceding directions.

 d.ho.
Meane opposition March136. 45639
Interval Adde 9. 35580
True opposition13.15. 97681
True place of Sun 5. 24194
Eccentrick place of the Moone 185. 24190
Meane Anomaly of the Sun 266. 79954
Meane Anomaly of the Moone 35. 44378
True motion of Latitude 174. 04881
True Latitude North descend. . 51496
Reduction Adde . 02398
Hourly motion of the Sun . 04111
Hourly motion of the Moon 0. 52232
Hourly motion of the Moon from the Sun . 48121
Reduction in time Subt. . 04983
True opposition corrected1315. 92698
Equation of time Subt. . 02884
T [...]uest opposition13.15. 89814
Horizontall Parallax of the Moone . 94409
Semiangle of the Cone . 23455
Semidiameter of the shadow . 70954
Semidiameter of the Moone . 26431
Sum of the Semidiameters . 97385
Scruples deficient . 45880
Digits eclipsed 10. 4197
Scruples of incidence . 82656
Time of incidence 1. 71770
Beginning of the Eclipse1314. 18044
End of the Eclipse1317. 61584
The whole duration 3. 43540
Latitude of the Moone at the beginning North D. . 59223
Latitude of the Moone at the ending North D. . 43746
Difference from the middle, Added . 09328
The middle of the Eclipse13. 15. 99142

CHAP. 28. Of the Calculation of the Suns Eclipse.

THis Eclipse is not properly, the Eclipse of the Sun, but of the earth in regard it is not the Sun, but the earth which looseth light the Sun being only apparently darke, the earth in truth, we will how ever use the name, that others have given it, and shew you the manner of the Calculation.

Find the meane conjnction, and from thence the true, which correct by the Reduction and Equation of time in all things as in the Moon.

Example of a Solar Eclipse, which happened March 28. 1652.

 D 
Mean Conjunction March280. 82333
Suns place 19. 36150
Eccentrick place of the Moon 20. 89832
Distance of the Moon from the Sun 1. 53682
Meane Anomaly of the Sun 280. 96132
His hourly motion . 04090
Meane Anomaly of the Moon 223. 17513
Her hourly motion . 60109
Hourly motion of the Moon from the Sun . 56019
which dividing the distance 1. 53682
Gives in the quotient subt. 2. 74336
So the time first corrected [...]722. 07997
True place of the Sun 19. 24962
The Eccentrick place of the Moon 19. 29533
The distance of the Sun from the Moon . 04571
which divided by the hourly motion of the Moon from the Sun . 56137
Gives in time subtract . 08143
So the time secondly corrected2721. 99854
True place of the Sun 19. 24631
Eccentrick place of the Moon 19. 24766
Distance of the Sun from the Moone . 00135
which divided by the hourly motion of the Moon from the Sun▪ . 56140
Gives in time subtract . 00240
So the true time of Conjunction2721. 99614
[Page 160]The true pl [...]ce of the Sun 19. 24621
Eccentrick place of the Moon 19. 24625
True motion of Latitude 8. 80745
The Reduction Subtract 0. 03536
The quotient . 06298
So the true Conjunction. 2722. 05912
Equation of time subtract . 09970
The apparent time of the ☌. 2721. 95942

CHAP. 29. To find the Parallaxes of Longitude and Latitude.

BY the rules delivered in the former part, find at the true Conjucti­on the Midheaven, with its altitude and the Meridian angle.

Example.

The Suns place
♈ 19. 246
The Suns Right Ascension
17. 749
Time in Degrees
329. 391
Right Ascension of Midheaven
347. 140
Midheaven
♓ 16. 022
Meridian angle
67, 078
Declination of Midheaven
5. 533
Altitude of the Equator at London
38. 467
Altitude of Midheaven
32. 834

2 The angle of the Ecliptique and Horizon, or altitude of the Nona­gesime degree, and his distance from the Midheaven is thus found, by the 17 Chapter of the first part.

As the Radius

To the sine of the Meridian angle67. 079. 9642509
So is Cosine of the Altitude of M C32. 839. 9244255
To the Cosine of the Angle, &c.39. 309. 8886764

Then as Radius

To the Cosine of the Meridian angle67. 079. 5906259
So is cotang. of the altitude of the M. C.32. 8310. 1903074
To the tang. of the distance of the M. C. from the Nonagesime degree16. 029. 7809333
This M C falling betweene Capricorn and Cancer this distance is to be added to the Midheaven ♓ 16. 02
And the Nonagesime degree will be in ♈ 17. 14

[Page 161]3 Find the Node Ascendent and Subtract it from the Nonagesime de­gree, with the remainder enter the Table of the Moones latitude, which if North adde to the angle of the Ecliptique and Horizon; if South sub­tract it from it, so have you the altitude of the Nonagesime degree of the Moones orbe.

Example.

The Node Ascendent Subt.
10. 439
The Nonagesime degree
17. 140
There rests
6. 701
Which gives the Moones Latitude Adde
. 570
The angle of the Ecliptick and Horizon
39. 300
Altitude of the Nonagesime degree of the Moones orbe
39. 870

4 Take the distance of the S [...]n from the Nonagesime degree, which in our Example of the true Conj [...]ction is [...] d. 10.

5 Out of the table of Horizontall parallaxes, take the Horizontall Pa­rallax of the Sun and Moon, the difference of them is the Horizantall pa­rallax of the Moon from the Sun.

Example.

The Horizontall parallax of the Sun is
. 03912
The Horizontall parallax of the Moon
. 99396
Horizontall parallax of the Moon from the Sun
. 95484

6 Adde the Logarithme of the Horizontall parallax of the Moon from the Sun, the sine of the Altitude of the Moones orbe, and the sine of the distance of the Sun from the Nonagesime, their summe subtracting twice Radius, is the Logarithme of the parallax of longitude.

Example.

Horizontall parallax of the Moon from the Sun954841. 9799306
Altitude of Nonagesime in the Moones orbe, sine39. 879. 8068904
Distance of the Sun from the Nonagesime, sine2. 108. 5639994
Parallax of longitude 02243 2. 3508204

Here note that whensoever the Suns place is lesse then the Nonage­sime degree, the Parallax of Longitude, makes the luminaries appeare more west than the truth, and in the occidentall Quadrant, when more then in the orientall.

7 Adde the Logarithme of the Horizontall parallax of the Moon from the Sun to the Cosine of the Nonagesime in the Moones orb; the summe rejecting Radius is the Logarithme of the parallax of Latitude.

Example.

Horizontall parrallax of the Moon from the Sun954841. 979930 [...]
Altitude of Nonag. in the Moones orb, Cos [...]ne39. 879. 8850789
Parallax of latitude0. 732841. 8650095

CHAP. 30. To find the visible motion of the Moon from the Sun for any time assigned.

AT the beginning and end of the time proposed find the parallax of the Moone from the Sun in Longitude, and then observe these rules.

  • 1 If during all the time proposed, the luminaries be in the ori­entall quadrant, and the parallax of longitude increase or be greater at the end of the time given then at the beginning, adde the differences of the two parallaxes of longitude unto the true motion of the Moone from the Sun agreeing to the time given, or if it decrease, subtract it and you have what you desire.
  • 2 If during all the time the luminaries be in the occidentall quadrant, and the parallax of longitude increase, subtract the said difference from the true motion, if it decrease, adde it, and you have the visible motion.
  • 3 If at the beginning of the time the luminaries be in the orientall quadrant, and at the ending in the occidentall, subtract the said diffe­rence from the true motion, and you have the visible motion during that time.

Example.

Let it be proposed to find the visi [...]le motion of the Moon from the Sun, for one halfe hour before the true Conjunction.

In our Example, the true halfe hourly motion is
. 28070
Parallax of Longitude at the beginning
. 07628
Parallax of Longitude at the end
. 02243
Their difference is Subtract
. 05385
from the true halfe hourly motion Rests
. 22658

the visible halfe hourly motion before the Conjunction.

CHAP. 31. To finde the time of the visible Conjunction of the Sun and Moon.

USe this Analogie, As the apparent motion in any time assigned (found by the former Chapter) is to the time assigned; so is the parallax of longitude at the true Conjunction to the difference in time between the true and visible Conjunction.

[Page 163]This difference in the orientall quadrant must be subtracted from the time of the true Conjunction, in the occidentall quadrant added thereto; so have you the visible Conjunction.

Example.

As the visible halfe hourly motion 22685 co. ar.
0. 644262
Is to the time assigned 50′
1. 698970
So parallax longitude 02243
2. 350829
To the difference betwixt the true and visible Conjunction 04943
2. 694061
The true Conjunction
27 21. 95942
Difference subtract
. 04943
The visible Conjunction
27 21. 90999

At this time finde out the true distance of the Moon from the Sun, as also the parallax of longitude, if they agree it is a signe that the visible Conjunction is truly found, otherwise repeat the former worke till there be a concurrance.

Example

At the visible Conjunction, March
27 21. 90999
The true distance of the Moone from the Sun
. 0 [...]847
The Parallax of Longitude
. 02775
Their difference
. 00072

which being so small sheweth that the visible Conjunction is precisely enough found.

CHAP. 32. To finde the visible Latitude of the Moon, at the time of the visible Conjunction.

IN these Northerne regions which we inhabit, the parallax of latitude allwayes makes the Moon to appeare more South then indeed she is to find the visible latitude therefore observe these rules.

1 At the time of the visible conjunction find out the true latitude of the Moon thus. If the Eclipse happen in the orientall quadrant, adde the parallax of longitude to the motion of the Sun, agreeing to the diffe­rence between the true and visible Conjunction, and the summe subtract from the true motion of latitude at the time of the true Conjunction; or if the Eclipse happen in the occidentall quadrant adde the said summ [...] thereto, and you have the true motion of latitude at the visible Con­junction, by which as formerly taught, finde out the true Latitude of the Moone.

Example.

Motion of the Sun agreeing to 04943
. 00202
Parallax of Longitude at visible ☌
. 02775
The Summ Sub [...].
. 02977
Motion of Latitude at true ☌
8. 80745
Motion of Latitude at visible ☌
8. 77768
True Latitude at visible ☌ North
. 75808

At the same time find the parallax of latitude, and compare it with the true latitude. If the latitude be South, adde them together, the summe is the South visible latitude of the Moone, but if North, subtract the lesse from the greater; there remaines the visible latitude of the Moon, which shall be North when the latitude is greater then the parallax, o­therwise South.

Example.

The true latitude of the Moon, North
0. 75808
Parallax of Latitude
0. 73633
The visible latitude North
. 02175

CHAP. 33. To find the quantity of a Solar Eclipse.

THis differs very little from that in the 24 Chapter, for finding the quantity of a lunar Eclipse, for it with their meane Anomalie [...] you enter the Table, and thence take out the Semidiameter of the Sun and Moone, and adde them together; and from the summe subduct the visible latitude of the Moone, at the visible Conjunction, there rests the Scruples of the Suns body deficient, which as in the Moon, so here in the Sun convert into digits.

Example.

Semidiameter of the Sun
. 27386
Semidiameter of the Moon
. 27815
Summe of the [...]emidiameters
. 55201
Visible latitude Subtracted
. 02175
Scruples deficient
. 53026
So the digits eclipsed
11. 61500

CHAP. 34. To find the beginning and ending of the Suns Eclipse.

BY the visible latitude of the Moon, and the summe of the Semidia­meters of the Sun and Moon, find the Scruples of incidence, as in the Moones Eclipse Chap. 25.

[Page 165]2 For one hour before the visible Conjunction, find by the 30 Chapter, the visible hourly motion of the Moon from the Sun, by which divide the Scruples of incidence, the quotient is the time of incidence, which subtracted from the time of the visible Conjunction, leaves the beginning of the Eclipse

3 For one hour after the visible Conjunction, finde the visible hourly motion of the Moon from the Sun, by which divide the Scruples of inci­dence, the quotient is the time of Repletion: which added to the time of the visible Conjunction, gives the end of the Eclipse.

Example.

Summe of the Semidiameters
. 55201
Visible latitude
. 02175
Scruples of Incidence
. 55158
At 1 ho. before the visible ☌ March 27
20. 90999
Parallax of longitude Orient.
. 13209
True hourly motion of the Moon from the Sun
. 56140
Visible hourly motion
. 45174
Time of incidence
1. 22150
Beginning of the Eclipse March 27
20. 68849
At 1 ho. after the visible ☌ 27
22. 90999
Parallax of longitude Occid.
. 10119
Visible hourly motion of the Moone from the Sun
48796
Time of repletion 1
h. . 1303 [...]
End of the Eclipse 27
23. 04029
The whole duration
2. 35180

CHAP. 35. To find the Visible latitude of the, Moon at the beginning and end of the Suns Eclipse.

FOr the beginning, adde to the minutes of Incidence the motion of the Sun agreeing to the time of Incidence, and the summe sub­tract from the true motion of latitude at the time of the visible Sy­nod, so have you the true motion of latitude at the beginning, by which find the true latitude, and by these according to the second rule of the 32 Chapter, may be had the visible latitude.

Example.

The Scruples of incidence
. 5515 [...]
Motion of the Sun answering to the time
. 05016
The summe subt.
. 60174
Motion of latitude at visible ☌
8. 77768
Motion of latitude at beginning
8. 17594
True latitude North
. 70648
Parallax of latitude
. 82004
Visible latitude South
. 11353

2 For the end, adde to the minutes of incidence the motion of the Sun agreeing to the time of repletion and the sum adde to the true motion of latitude at the time of the visible Conjunction; so have you the true moti­on of latitude at the end; by which proceed as before, to find the visible Latitude.

Example.

Scruples of Incidence
. 55158
Motion of the Sun agreeing to the time of repl.
. 04642
The Summe Adde
. 59800
Motion of Latitude at the visible ☌
8. 77768
Motion of Latitude at the ending
9. 37568
True Latitude North
. 80925
Parallax of Latitude
. 65218
Visible Latitude North
. 15707

CHAP. 36. To Delineate the Eclipses▪ of the Sun and Moon.

FOr the Moon draw the lines AC and BD to intersect one ano­ther at right angles in E, which point of intersection is the place of the Ecliptique where the Eclipse happens: upon which as a Cen­ter draw the Peripherie ABCD, of the quantity of the summe of the Semidiameters of the Moon and the earths shadow (which may be done by helpe of a Scale or Sector of equal divisions) also to the quan­tity of the Semidiameter of the earths shadow, draw upon the same cen­ter another Peripherie.

Then because the Moones Eclipse begins on the east part of her body, you must upon the west side of your plane, note downe the latitude of the [Page 167] Moon in the arch BCD, which here▪ represents the west part▪ and may be thus done, From E upon the line BD prick out the latitude at the be­ginning; towards B, if the Latitude be North, towards D if South, and it terminat [...]s at G, from which draw a parallel to AC, and in the arch BC it marks out F. Also for the end of the Eclipse proceed in like man­ner on the other side, and you have the latitude terminated at I, and the parallel falling at H. Then draw a line between F and H and where it in­tersects BD marke it with K. Lastly, upon the centers F, K and H, draw three equal circles, having for Radius the Semidiameter of the Moone, and the worke is done.

Typus Eclipseos Lunae praedictae.

[figure]

Example of the forementioned Eclipse of the Moon March 15. 1652

Summe of the Semidiameters EB
. 97385
Semidiameter of shadow EM
. 70954
Initial latitude of the Moon EG, North
. 59223
Final latitude of the Moon EI North
. 43746
Semidiameter of the Moon MB
. 26431

2 For the Eclipse of the Sun, it differs nothing at all from this of the Moon, but onely that instead of the Semidiameter of the shadow of the earth you use the Semidiameter of the Sun; and the visible latitude for the true.

Example of the forementioned Sol [...] Eclipse March 28. [...]652.

Summe of the Semidiameters EB
. 5520 [...]
Semidiameter of the Sun EM
. 27386
Initiall visible latitude EG South
. 11353
Finall visible latitude EI North
. 15707
Semidiameter of the Moon MB
. 27815

Typus Eclipseos Solis pr [...]dict [...].

[figure]

CHAP. 37. The use of the Table of Refractions.

ALthough the Table of Refractions, belongs not to the calaulati­on of these Tables, yet will it not be amisse to shew its use in comparing of observation with calculation. Know then that Refraction, causeth the stars to appeare higher then really they are. Therefore with an observed altitude enter this Table and take out the Refraction, which subtract from the observed altitude, and you have the true altitude, or having the true altitude, the apparent is found by ad­ding the Refraction thereto.

FINIS.

This Scheame hath particular relation to page 103, and is there printed in most Copies, but in some Copies there is another Scheame placed instead thereof, the Reader is therefore desired (where it is wanting) to insert it.

Errata.

Page 7. line the last, for the North read C the North.

Page 8. line 10 read or the arch H ♋.

Page 21. line 20 for else of that, read else that.

Page 29. line 39 for ED 38 read ED 30.

Page 37. line 23 for paraallctical read parallactical.

Page 76. line 14 for plane parallel read plane is parallel.

In the Tables.

Page 26 against degree 11 for 0, 38836 read 0, 38336.

Page 27 against degree 90 for 5, 0201387 read 5, 0001387.

Page 27 against degree 117 for 4, 9961795 read 4, 9965795.

Page 34 against degree 56 for 3, 04 &c. read 4, 04 &c.

Page 35 against degree 87 for 5, 0010809 read 5, 0018089.

Page 35 against degree 119 for 4, 163 &c. read 4, 463 &c.

Page 36 against degree 132 for 3, 874 &c. read 824 &c.

Page 36 against degree 139 for 3, 38920 read 3, 38902.

Page 36 against degree 126 for 4, 9895915 read 4, 9895925.

Page 36 against degree 179 for 0, 69126 read 0, 09126.

Page 86 In the Title, for A Table of Declinations, read A Table of Right Ascensions.

Let this leafe be folded in at page 168, which is between the second and third Books.

[...]

This Diagram having particular relation to the 18 Chapter of the second Book, will be in use for di­verse leaves together, I thought it therefore con­venient, to place it so that when the Book is opened in any part, the Dirgram might be in▪ sight, and have therefore ordered it to be folded in.

[...]
Astronomia BRITANNIC …

Astronomia BRITANNICA The third Part: Exhibiting Tables, for the converting of Sexagenary Numbers into Decimal and the contrary, for Astrononomical Chronologie with the Ecclesiastical Compu­tation, and the Calculation of the places of the Planets, Eclipses of the Luminaries and Doctrine of the Sphere.

[bookseller's logo]

LONDON.

Printed by R. and W. Leybourne Anno Domini 1656.

A view of the more notable Epochae.

EpochaeYeares of the Julian PeriodMoneths
The Iulian Period1Ianuar. 1
Creation of the World765Ianuar. 1
Aera of the Olympiades3938Iuly 8
The building of Rome3961April 21
Epochae of Nabonassor3667Febru. 26
The beginning of Meton's Circle4281Iune 26
The beginning of the Periods of Calippus4384Iune 28
The Death of Alexander the great4390Nove. 12
Aera of the Chaldees4403Octob. 15
The Aera of Dyonisius4429Marc. 25

The beginning of the Christian Aera falls in the 4713 Yeare of the Julian period com­pleat.Yeares of ChristMoneth.
The Diocletian Aera284Augu. 29
The Turkish Aera or Negyra622Iuly 16
The Persian Aera from Jesdagird632Iune 16
The Aera of the Persian Sultan1079Marc. 14

Dayes in yeares of the
Julian accomptEgypt. and Persian accompt
10003652501000365000
2000730500200073000 
300010957503000109500 
400014610004000146000 
5000182625050001825000
6000219150060002190000
700025567507000255500 
8000292200080002920000
9000328725090003285000
100003652500100003650000

Dayes in Moneths of the
Julian Com.B ssEgyptianPersian accompt.
Januar. 311Th [...]th 30Pharvadin 30
Februar. 5 [...]60Paophi 60Aripehest 60
March 9091Athyr 90Chortat 90
April 120121Chaeac 120Tyrma 120
May 151152Tybi 150Mertat 150
June 181182Mechir 180Sachriur 180
July 212213Phamenoth 210Mecherma 210
August 243244Pharmuthi 240Apanma 245
Septem. 273274Pachon 270Wahak 245
Octob. 304305Payni 300Ad [...]rma 275
Novem 334335Ephephi 330Dima 305
Decem. 365366Mesori 360Pechmam 335
  Epagomena 365Asphander 365

Dayes in Turkish or Arabical Years.
1 354 
2 709 
3 . 1063 
4 . 1417 
5 . 1772 
6 . 2126 
7 . 2480 
8 . 2835 
9 . 3189 
10 . 3543 
11 . 3898 
12 . 4252 
13 . 4607 
14 . 4961 
15 . 5315 
16 . 5670 
17 . 6024 
18 . 6378 
19 . 6733 
20 . 7087 
21 . 7442 
22 . 7796 
23 . 8150 
24 . 8505 
25 . 88 [...]9 
26 . 9213 
27 9568 
28 9922 
29 10276 
300106310
600212620
900318930
1200425240
1500531550
1800637860
210074417 
2400850480
2700956790
30001063100

Dayes in Turkish Moneths.
Muharram30Sahahen236
Sephar59Ramadhan266
Rabie I89Schevall295
Rabie II118Dulkadati325
Giumadi I148Dulhajati354
Giumadi II177Dsilhit [...]sche, Tur [...].354
Regeb207In anno abundanti355

A Table shewing the Dominical Letter in both accompts.
Years of our LordCycle of the SunJulian accomGreg. accom
16441G FC B
16452EA
16463DG
16474CF
16485B AE D
16496GC
16507FB
16518EA
16529D CG F
165310BE
165411AD
165512GC
165613F EB A
165714DG
165815CF
165916BE
166017A GD C
166118FB
166219EA
166320DG
166421C BF [...]
166522AD
166623GC
166724FB
166825E DA G
166926CF
167027BE
167128AD

A Table shewing the Epact in both ac­compts.
Years of our LordGold Num.Epac. Juliā.Epact Greg.
16531111
165422212
16553323
16564144
165752515
16586626
16597177
166082818
16619929
1662102010
166311121
166412122
1665132313
166614424
166715155
1668162616
166917727
167018188
1671192919

The Anticipation of the Gregori­an Kalender.
A5Oct.101582
 111700
A24Fe.121800
 131900
 142100
 152200
 162 [...]0
 d.A. D.
 172500
 182600
 192700
 202900
 213000
 223100

A Table of moveable Feasts in both accompts.
EpDLLxxLAsh.East.Asce.Pen.Corp.AdventSun.  
25DJan 18Feb. 1Feb. 4MarchAp. 30May 1 [...]May29Nove.D [...]2
24E192523May 1112230 E21
23F203624212231DecemF20
22G214725413242 G19
21A225826414253 A18
20B2369275152627Nove.B17
19C24710286162728 C16
18D25811297172829 D15
17E26912308182930 E14
16F27101331919301DecemF13
15G281114Ap. 11020312 G12
34A29121521121June 13 A11
13B30131631222227Nove.B10
12C31141741323328 C9
11DFeb. 1151851424429 D8
10E2161961525530 E7
9F317207162661DecemF6
8G418218172772 G5
7A519229182883 A4
6B62023101929927Nove.B3
5C721241120301028 C2
4D822251221311129 D1
3E923261322June 11230 E*
2F10242714232131DecemF29
1G11252815243142 G28
*A1226Mar. 116254153 A27
29B13272172651627Nove.B26
28C14283182761728 C24
*D15Mar. 14192871829 D*
*E1625202981930 E*
*F173621309201DecemF*
*G1847223110212 G*
*A195823June 111223 A*
27B2069242122327Nove.B*
26C21710253132428 C23

A Table of Fixed Feasts
 JanuaryFebruaryMarchAprilMayJuneJulyAugustSeptembOctoberNovem.Decem.
1Circu. a [...]gnat. ddgP. & Ia. begLammas cAegyd. fRemigi. aAll Sa. df
2bPu. M. eeFrāde P acMarcel. fVisi M. adgbAll son. eBibinia g
3cBlasius ffbInv. cru. dgbeacfa
4dgLucius gceacfbFrancis. dVital. gBarbara b
5Telesph. eAgath. aadfbdDed. M. gceac
6Epfphā. fDoroth. bbeJo. p. latgceTransf. adfbd
7gccfadfbeMarc. p. gcAmbro. e
8addgAp. SM. begcNa. M. fadConc. M f
9bApollo. e40 Mar. eacPrimus fadgDionys. beg
10cffbdg7 fratr. bLaurenc eacTryph. fa
11Hygin. dggLeo Pa. ceBarnab. acfbdMartin gb
12eaGregor. adfbNabor dgceac
13fbbegAnton. ceadfbLucia d
14Hilari. gValent. ccT. V. M. fBonifa. aBasil. dBonav. fbExal. cr. eCallist. gce
15Paul Er. aFa. & J. ddgbegAss. M. cfadEusebius f
16Marcel. beeaUbald cfadCornel. gbeg
17Anton. cffAnicet. bdgAlexius beacGregor. fa
18Cut. S P dSimeon ggceacfbLucos dgb
19eaIos. con. adPrudent. fGervasi. bdgcePontia. ac
20Fab. & se fbbegcMargar. eBernar. adfbd
21Agnet. gcBenedi. cfadfbMat. E eHilariō. gOb. Ma. cTho. a. e
22Vincen. addSoter. c. gbeM Mag. gcfadf
23beeGeorge acfadLinus gbeg
24Timoth. cS. Ma. ffbdS. I. B gbBart. a. cacfa
25Con. P. dgAn. MagS Mar. cUrban. eaJam. a. cfbChrysa. dCathar. gNa. C. b
26Policar. eaadfbdgCyprian ceaStep [...]. c
27fbbeJo. pap. gceadfbJoh. E. d
28gccVitalis fadfAugust. beSi. Iu. gcInnoce. e
29a dCathar. gbLeo eMartha gDecoll. cMich. A fadT. Cant. f
30b eaFelix cPet. ap. fadHieron. gbAnd. a. eg
31c f Petrom. dgbe c Silvest. a

A Catalogue of some famous places with their Latitude, and distance in Longitude from the Meridian of London.
The Names of the Places.Difference of Meridia. H. PartsHeight of the Pole D. Parts
Aberden in ScotlandS0. 1166758. 66667
Adrionaplis in ThraceA2. 0666743. 3333 [...]
Ag [...]ia in HungarieA1. 3500047. 93333
Alba Julia in TransylvaniaA1. 5333347. 00000
Alepus in SyriaA2. 4166737. 33333
Alexandria in EgyptA2. 1833330. 96667
Algiers in AfricaA0. 3833335. 60000
Amsterdam in HollandA0. 3500052. 41667
Antwerp in BrabantA0. 2833351. 20000
Aracta in ChaldaeaA3. 3000036. 00000
Arbela in AssyriaA3. 7666737. 25000
Astracan upon Volgo in Tarta [...]iaA3. 9666750. 00000
Athens in GreeceA1. 8666737. 00000
Bamberge in FranconieA0. 7500049. 61667
Bononia in ItalyA0. 7166743. 81677
Brundusium in CalabriaA1. 2833349. 53333
Bulgaria in TartariaA4. 0333356▪00000
Burgos in SpaineS0. 2500042. 66667
Calecutum in IndiaA5. 8333311. 50000
Cambridge in EnglandA0. 0333352. 33333
Carthage in AfricaA0. 6833334. 83333
Casan in TartariaA4. 0000058. 00000
Cassels in HessiaA0. 7333351. 31667
Cair grand in EgyptA2. 2666729. 83333
ChalcedonA2. 3333343. 25000
Chester in EnglandS0. 1666753. 26667
Cochin in IndiaA5▪900009. 90000
Cola in LaplandA2. 3000069. 40000
Colberg in PomeraniaA1. 0333354. 46667
Compostella in SpaineS0. 6333343. 00000
Constantinople in ThraceA2. 3000043. 00000
Conymbre in LusitaniaS0. 5833340. 25000
Cracow in PolandA1. 3500049. 96667
Crim of Precopensis in Tart [...]ryA2. 7000047. 83333
Damascus in SyriaA3. 2666734. 00000
Dantzik of Borussia in PolandA1. 1333354. 38333
Doüay in ArtesiaA0. 2333350. 40000
Edenburgh in ScotlandS0. 0333355. 95000
Epidaurus in PeloponnesisA1. 8666735. 50000
Famagusta in CyprusA2. 9500035. 00000
[Page 9]Francford upon OdarA0. 5500050. 11667
Francford upon MaeneA0. 9666752. 33333
Fruenburg in BorussiaA1. 3666754. 36667
Grat [...]um in StiriaA1. 0666747. 03333
Groyning in FriziaA0. 4333353. 25000
Hamburg in HolsatiaA0. 6666753. 71667
Haphnia in DenmarkeA0. 8166755. 71667
Lipsia in MisniaA0. 8166751. 40000
Liverpoole in EnglandS0. 1666753. 36667
LONDON in England 0. 0000051. 53333
Lovaine in Brabant 0. 3333350. 83333
LeydenA0. 3166752. 18333
Middleburg in ZelandA0. 2666751. 50000
Manchester in EnglandA0. 1500053. 40000
Naples in ItalyS0. 9666740. 70000
Nicomedia in BythyniaA2. 3 [...]33342. 50000
Nidrosia in NorwayA0. 5666763. 20000
Newcastle in EnglandA0. 0166755. 05000
No [...]imberg in GermanyS0. 7666749. 43333
Orleans in FranceA0. 0000048. 13333
Oxford in England 0. 0500052. 06667
Paris in FranceS0. 1333348. 65000
corrected by BullialdusA0. 0333348. 85000
Patavium in LiburniaA0. 7666745. 10000
Prague in Bohemi [...]A0. 9333350. 10000
Rhodes an IslandA3. 4333336. 00000
Rochell in AquitainA0. 0666745. 81667
Rochester in EnglandS0. 0333351. 50000
Rome in ItalieA0. 8333342. 03333
Roan in Normandi [...]A0. 0000049. 63333
Smarcanda in TartariaA5. 6666745. 00000
Scutara in DalmatiaA1. 4333342. 38333
Sevill in SpaineS0▪3666737. 33333
Spahani in PersiaA4. 3333331. 50000
Stetin in PomeraniaA0. [...]666753. 60000
Syracusa in SicilieA1. [...]833386. 83333
Tolledo in SpaineS0. 2333339. 90000
Tubing WittenburgA0. 6333348. 56667
Valence in SpaineA0. 1000039▪50000
Ulme in SueviaA0. 7000048. 40000
Uraniburge in DenmarkA0. 8333855▪91667
Yorke in EnglandS0▪0500054. 03333

A Table to convert Sexagenary minutes,
′ ″P
000
. 3601
1. 1202
1. 4803
2. 2404
3. 005
3. 3606
4. 1207
4. 4808
5. 2409
6. 010
6. 3611
7. 1212
7. 4813
8. 2414
9. 015
9. 3616
10. 1217
10. 4818
11. 2419
12. 020
12. 3621
13. 1222
13. 4823
14. 2424
15. 025
15. 3626
16. 1227
16. 4828
17. 2429
18. 030
18. 3631
19. 1232
19. 4833
20. 2434
21. 035
21. 3636
22. 1237
22. 4838
23. 2439
24. 040
24. 3641
25. 1242
25. 4843
26. 2444
27. 045
27. 3646
28. 1247
28. 4848
29. 2449
30. 050
30. 3651
31. 1252
31. 4853
32. 2454
33. 055
33. 3656
34. 1257
34. 4858
35. 2459
36. 060
36. 3661
37. 1262
37. 4863
38. 2464
39. 065
39. 3666
40. 1267
40. 4868
41, 2469
42. 070
42. 3671
43. 1272
43. 4873
44. 2474
45. 075
45. [...]676
46. 1277
46 4878
47 2479
48. 080
48. 3681
49. 1282
49. 4883
50. 2484
51. 085
51. 3686
52. 1287
52. 4888
53. 2489
54. 090
54. 3691
55. 1292
55. 4893
56. 2494
57. 095
57. 3696
58. 1297
58. 4898
59. 2499
60. 0100

and seconds into Decimals and the contrary
03612482400000000
13713492502777778
23814502605555555
33915512708333333
44016522811111111
54117532913888889
64218543016666667
74319553119444444
84420563222222222
94521573325000000
104622583427777778
114723593530555555
1248241. 003633333333
13492513736111111
14502623838888889
15512733941666667
16522844044444444
17532954147222222
18543064250000000
19553174352777778
20563284455555555
21573394558333333
225834104661111111
235935114763888889
241. 0036124866666667
25137134969444444
26238145072222222
27339155175000000
28440165277777778
29541175380555555
30642185483333333
31743195586111111
32844205688888889
33945215791666667
341046225894444444
351147235997222222

 ThirdsFourthsFifths
1000004629600000007720000000013
292593157326
3138889231539
4185185304651
5231481385864
6277778463077
7324074540190
83703706173103
94166676944116
104629637716129
115092598488141
125555569259154
13601852100 1167
1464814810802180
1569444411574193
1674074112345206
1778 [...]03713117219
1883333313889232
1987963014660245
2092592615432258
2197222216204270
22101851816975283
23106481417747296
24111111118518309
25115740719290322
26120370320062335
27125000020833348
78129629621605360
29134259222376373
30138888823148386
[Page 13]31000143518400000239200000000399
32148148124691412
33152777725463425
34157407326234438
35162037027006450
36166666627778463
37171296328549476
38175925929321489
39180555630092502
40185185230864515
41189814831636527
42194444432407540
43199074033179553
44203703733950566
45208333334722579
46212962935494592
47217592536265605
48222222237037618
49226851837808630
50231481538580643
51236111139352656
52240740740123669
53245370340895682
54250000041666694
55254629642438707
56259250243210720
57263888943981733
58268518544753746
59273148145524759
60277777846296772

H. M.P
00
2. 241
4. 482
7. 123
9. 364
12. 005
14. 246
16. 487
19. 128
21. 369

A Table to convert the houres and minutes. of a day into Decimals and the contrary.
024481236000000000
125491337006944444
226501438013888889
327511539020833333
428521640027777778
529531741034722222
630541842041666667
731551943048611111
832562044055555555
933572145062500000
1034582246069444444
1135592347076388889
12365. 172448083333333
133712549090277778
143822650097222222
153932751104166667
164042852111111111
17415295311805555 [...]
184263054125000000
194373155131944444
204483256138888889
214593357145833333
2246103458152777778
2347113559159722222
2448123610. 22166666667
254913371173611111
265014382180555555
275115393187500000
285216404194444444
295317415201388889
305418426208333333
315519437215277778
325620448222222222
335721459229166667
3458224610236111111
3559234711243055555
363. 15244812250200000
[Page 15]371254913256944444
38226501426 [...]888889
393275115270833333
404285216277777778
415295317284722222
426305418291666667
437315519298611111
448325620305555555
459335721312500000
4610345822319444444
4711355923326388889
4812368. 2024333333333
491337125340277778
501438226347222222
511539327354166667
521640428361111111
531741529368055555
541842630375000000
551943731381944444
562044832388888889
572145933395833333
5822461034402777778
5923471135409722222
1. 124481236416666667
125491337423611111
226501438430555555
327511539437500000
428521640444444444
529531741451388889
630541842458333333
731551943465277778
832562044472222222
933572145479166667
1034582246486111111
1135592347493055555
12366. 182448500000000
[Page 16]133712549506944444
143822650513888889
153932751520833333
164042852527777778
174152953534722222
184263054541666667
194373155548911111
204483256555555555
214593357562500000
2246103458569444444
2347113559576388889
2448123611. 23583333333
254913371590277778
265014382597222222
275115393604166667
285216404611111111
295317415618055555
305418426625000000
315519437631944444
325620448638888889
335721459645833333
3458224610652777778
3559234711659722222
364. 16244812666666667
371254913673611111
382265014680555555
393275115687500000
404285216694444444
415295317701388889
426305418708333333
437315519715277778
448325620722222222
459335721729166667
4610345822736111111
4711355923743055555
4812369. 2124750000000
[Page 17]491337125756944444
501438226763888889
511539327770833333
521640428777777778
531741529784722222
541842630791666667
551943731798611111
562044832805555555
572145933812500000
5822461034819444444
5923471135826388889
2. 1424481236833333333
125491337840277778
226501438847222222
327511539854166667
428521640861111111
529531741868055555
630541842875000000
731551943881944444
832562044888888889
933572145895833333
1034582246902777778
1135592347909722222
12367. 192448916666667
133712549923611111
143822650930555555
153932751937500000
164042852944444444
174152953951388889
184263054958333333
194373155965277778
204483256972222222
214593357979166667
22461034589861 [...]1111
2347113559993055555
2448123600000000000

 Seconds.ThirdsFourthsFifths
10000115741000000192900000000320000000001
2231481385 [...]640000000001
33472225787962
4463963771600000001292
557870496451613
669444400000115741933
7810185135032254
8925926154322574
90001041666173612895
101157407192903215
111273148212193546
121388889231483877
131504630250774207
141620371270064538
151736112289354868
161851853398645189
171967593327935599
1820833333472258210
1921990743665161410
200002314815000003858000000006430000000011
2124305554050967511
2225462964243870712
2326620374436773912
2427777784629677113
2528935184822580313
2630092595025483614
2731250005218386914
2832407415411290215
2933564825604193415
300003472222000005787000000009650000000016
[Page 19]3100035879630000005979900000009970000000016
32370370461728103017
33381944463657106217
34393518565586109418
35405092667515112618
36416666769444115719
37428240771373118919
38439814873302122220
39451388975231125420
40462963077160128621
41474537079089131822
42486111181018135022
43497685282947138223
44509259284876141423
45520833386805144624
46532407488734147924
47543981490663151125
48555555592592154425
49567129694521167626
50578703796451168027
51590277898380164127
526018518100309167328
536134259102238170528
546250000104167173729
556365741106096177029
566481481108025180230
576597222109954183430
586712963111883186631
596828704113812189831
606944444115741192932

A Table converting Hours and parts into Degrees and parts of the Aequator.
  IV ‴ ″″ ′ 0
Ho.Deg.MD. Parts.
1150100, 15000
2300200, 30
3450300, 45
4600400, 60
5750500, 75
6900600, 90
71050701, 05
81200801, 20
91350901, 35
101501001, 50
111651101, 65
121801201, 80
131951301, 95
142101402, 10
15 [...]251502, 25
162401602, 40
172551702, 55
182701802, 70
192851902, 85
203002003, 00
213152103, 15
223302203, 30
233452303, 45
243602403, 60
  2503, 75
  2603, 90
  2704, 05
  2804, 20
  2904, 35
  3004, 50
  3104, 65
  3204, 80
  3304, 95
  3405, 10
  3505, 25
  3605, 40
  3705, 55
  3805, 70
  3905, 85
  4006, 00
  4106, 15
  4206, 30
  4306, 45
  4406, 60
  4506, 75
  4606, 90
  4707, 05
  4807, 20
  4907, 35
  5007, 50
  5107, 65
  5207, 80
  5307, 95
  5408, 10
  5508, 25
  5608, 40
  5708, 55
  5808, 70
  5908, 85
  6009, 00
  6109, 15
  6209, 30
  6309, 45
  6409, 60
  6509, 75
  6609, 90
  6710, 05
  6810, 30
  6910, 35
  7010, 50
  7110, 65
  7210, 80
  7310, 95
  7411, 10
  7611, 25
  7711, 40
  5711, 55
  7811, 70
  7911, 85
  8012, 00
  8112, 15
  8212, 30
  8312, 45
  8412, 60
  8512, 75
  8612, 90
  8713, 05
  8813, 20
  8913, 35
  9013, 50
  9113, 65
  9213 80
  9313, 93
  9414, 10
  9514, 25
  9614, 40
  9714, 55
  9814, 70
  9914, 85

A Perpetual Table for the Aequation of Time.
D♈ P. Add♉ P. Add♊ P. Add♋ P. Sub.♌ P. Sub.♍ P. Sub.D
000000140271463900000146391402730
100555143331436200611149171372229
201111145831405501194151671338928
30163814861137500180 [...]153891305527
402194151111341602416155831269426
502750153331305503000157781233325
603305155271266703583159441194424
703833157221227804361161111155523
804389158891186104750162221113822
904917160271144405333163331072221
1005444161671100005917164161030520
1105972162781055506472164720986119
1206472163891008307000165270938918
1307000164440961107555165550894417
1407500165000911108083165550847216
1507972165550861108611165550797215
1608472165550888309111165000750014
1708944165550755509611164440700013
1809389165270700010083163890647212
1909861164720647210555162780597211
2010305164160591711000161670544410
211072216333053331144416029049179
221113816222047501186215889043898
231155516111043611227815722038337
241194415944035831266715527033056
251233315778030001305515333027505
261269415583024161342615112021944
27130551538901805137501486 [...]016383
281338915167011941405514583011112
291372214917006111436114333005551
301402714639000001463914027000000
D♓ Sub.♒ Sub.♑ Sub.♐ Adde♏ Add♎ AddD

The Suns mean Motions.
EpochaeLongit. ☉ Deg. partsApog. ☉ Deg. parts [...] ♈ & Fix. Deg. Parts.
Christi.278. 9833170. 322644. 97537
1600290. 9485995. 5909427. 61667
1620291. 0981595. 9068027. 89968
1640291. 2477196. 2226528. 18270
1660291. 3972496. 5385128. 46571
1359. 761070. [...]15780. 01414
2359. 522130. 031560. 02828
3359. 283100. 047340. 04242
B 40. 029910. 063170. 05660
5359. 790980. 078950. 07074
6359. 552050. 094730. 0848 [...]
7359. 313110. 110510. 09903
B 80. 059820. 126340. 11321
9359. 820890. 142120. 12735
10359. 581960. 157900. 14149
11359. 343030. 173690. 15563
B 120. 089740. 189510. 16981
13359. 850810. 205290. 18395
14359. 611870. 221070. 19809
15359. 372940. 236860. 21223
B 160. 119650 252680. 22641
17359. 880720. 268640. 24055
18359. 641780. 284250. 25469
19359. 402850. 300030. 26884
B 200. 149560. 315850. 28302
400. 299130. 631710. 56603
600. 448700. 947560. 84905
800. 598261. 263421. 13206
1000. 747831. 579271. 41508

The Suns mean Motions.
Years.Longit. ☉ Deg. parts.Apog. ☉ Deg. parts.Fixed ✴. Deg. parts.
1000, 747831, 579271, 41508
2001, 495663, 158542, 830 [...]6
3002, 243494, 737814, 24524
4002, 991326, 317085, 66023
5003, 739157, 896357, 07540
6004, 486989, 475628, 49048
7005, 2348111, 054899, 90557
8005, 9826412, 6341511, 32065
9006, 7304714, 2134212, 73573
10007, 4783015, 7936914, 15081
200014, 9566031, 5853828, 30162
300022, 4349047, 3780842, 45242
400029, 9132063, 1707756, 60323
500037, 3915078, 9634670, 75404

Ianuary30, 555050, 001340, 00120
February58, 153150, 002550, 00228
March88, 708200, 003890, 00349
April118, 277600, 005190, 00465
May148, 832650, 006530, 00586
Iune178, 402050, 007830, 00701
Iuly208, 957100, 009170, 00821
August239, 512150, 010510, 00941
September267, 081550, 011800, 01058
October269, 636600, 013140, 01178
November329, 206000, 014440, 01294
December359, 761070, 015780, 01414

The Suns mean Motions.
In Dayes.
 ☉ Longit. Deg. Parts.☉ Apog. Parts.Fixed ✴ Parts
10. 98565. 00004, 00004
21. 97129. 00008, 00008
32. 95694. 00013, 00012
43. 94258. 00017, 00015
54. 92823. 00022, 00019
65. 91388. 00026, 00023
76. 89953. 00030, 00027
87. 88517. 00034, 00031
98. 87082. 00039, 00035
109. 85647. 00043, 00039
1110. 84211. 00048, 00043
1211. 82776. 00052, 00046
1312. 81341. 00056, 00050
1413. 79905. 00060, 00054
1514. 78470. 00065, 00058
1615. 77035. 00069, 00062
1716. 75599. 00073, 00066
1817. 74164. 00078, 00070
1918. 72729. 00082, 00074
2019. 71293. 00086, 00077
2120. 69858. 00091, 00081
2221. 68423. 00095, 00085
2322. 66987. 00099, 00089
2423. 65542. 00104, 00093
2524. 64117. 00108, 00097
2625. 62681. 90112, 00101
2726. 61246. 00117, 00105
2827. 59811. 00121, 00108
2928. 58375. 00125, 00112
3029. 56940. 00130, 00116
3130. 55505. 00134, 00120
3231. 54069. 00138, 00124

The Suns mean Motions. In Hours.
 ☉ Longit. Parts.
1, 04107
2, 08214
3, 12321
4, 16427
5, 20534
6, 24641
7, 28748
8, 32855
9, 36962
10, 41069
11, 45175
12, 49282
13, 53389
14, 57496
15, 61603
16, 65710
17, 69817
18, 73923
19, 78030
20, 82137
21, 86244
22, 90351
23, 94458
24, 98565

The Suns mean Motions.
In parts of an Hour.
 ☉ Long. Parts.
1, 00041
2, 00082
3, 00123
4, 00164
5, 00205
6, 00246
7, 00287
8, 00328
9, 00370
10, 00411
11, 00452
12, 00493
13, 00534
14, 00575
15, 00616
16, 00657
17, 00698
18, 00739
19, 00780
20, 00821
21, 00862
22, 00903
23, 00945
24, 00986
25, 01027
26, 01068
27, 01109
28, 01150
29, 01191
30, 01232
31, 01273
32, 01314
33, 01355
34, 01369
35, 01437
36, 01478
37, 01519
38, 01561
39, 01602
40, 01643
41, 01684
42, 01725
43, 01766
44, 01807
45, 01848
46, 01889
47, 01930
48, 01971
49, 02012
50, 02053
51, 02094
52, 02135
53, 02177
54, 02218
55, 02259
56, 02300
57, 02341
58, 02382
59, 02423
60, 02464
61, 02505
62, 02546
63, 02587
64, 02628
65, 02669
66, 02710
67, 02751
68, 02793
69, 02834
70, 02875
71, 02916
72, 02957
73, 02998
74, 03039
75, 03080
76, 03121
77, 03162
78, 03203
79, 03244
80, 03285
81, 03326
82, 03368
83, 03409
84, 03450
85, 03491
86, 03523
87, 03573
88, 03614
89, 03655
90, 03696
91, 03737
92, 03778
93, 03819
94, 03860
95, 03901
96, 03942
97, 03984
98, 04025
99, 04026

The Aequation of the Suns Excentrick.
DegreesAeq: Sub:☉ DistāceDegrees
 D. parts.Logarithm 
10, 0350250076781359
20, 0696650076767358
30, 1051250076752357
40, 1401250076724356
50, 1750650076695355
60, 2099650076464354
70, 2448050076253353
80, 2758050076041352
90, 3142650075829351
100, 3488650075561350
110, 3883650075292349
120, 4177650075023348
130, 4520250074782347
140, 4861650074540346
150, 5201450074298345
160, 5540050073888344
170, 5873050073478343
180, 6212050073068342
190, 6545250072656341
200, 6876650072245340
210, 7206250071834339
220, 75 [...]3450071347338
230, 7858650070859337
240, 8181650070372336
250, 8502050069833335
260, 8820050069294334
270, 9135650068755333
280, 9442450068246332
290, 9758650067736331
301, 0065050067244330
311, 037005. 0066482329
321, 067145. 0065720328
331, 096965. 0064958327
341, 126485. 0064216326
351, 155665. 0063474325
361, 184485. 0062732324
371, 212965. 0061917323
381, 241125. 0061102322
391, 268905. 0060287321
401, 296305. 0059457320
411, 323185. 0058615319
421, 349965. 0057779318
431, 376205. 0056904317
441, 402145. 0056029316
451, 427465. 0055154315
461, 452485. 0054194314
471, 477085. 0053230313
481, 501225. 0052273312
491, 5 [...]4945. 0051279311
401, 548205. 0050285310
511, 571 [...]03. 0049290309
521, 593365. 0048354308
531, 615225. 0047418307
541, 636625. 0046481306
551, 657545. 0045293305
561, 677965. 0044105304
571, 697905. 0042916303
581, 717325. 0041810302
591, 737845. 0040704301
601, 754645. 0039597300
[Page 27]611, 772545, 0038450299
621, 790005, 0037303298
631, 806705, 0036157297
641, 822405, 0035286296
651, 838765, 0034415295
661, 853965, 0033545294
671, 86862 [...], 0031985293
681, 882725, 0030425292
691, 896245, 0028866291
701, 909205, 0027615290
711, 920365, 0026364289
721, 933425, 0025113288
731, 944665, 0023831287
741, 955325, 0022549286
751, 965405, 0021268285
761, 974885, 0019971284
771, 983785, 0018674283
781, 992065, 0017378282
791, 999765, 0016069281
802, 006845, 0014760280
812, 013325, 0013451279
822, 019205, 0012217278
832, 024465, 0010984277
842, 029125, 0009753276
852, 033175, 0008067275
862, 036605, 0006681274
872, 039465, 0005296273
882, 041585, 0003993272
892, 043165, 0002690271
902, 044105, 0201387270
912, 044445, 0000038269
922, 044124, 9998690268
932, 043204, 9997342267
942, 041684, 9995972266
952, 039404, 9994602265
962, 036724, 9993231264
972, 033284, 9991886263
982, 029264, 9990542262
992, 024604, 9989198261
1002, 019324, 9987851260
1012, 013424, 9986506259
1022, 006904, 9985162258
1031, 999744, 9983844257
1041, 992004, 9982526256
1051, 983624, 9981208255
1061, 974684, 9979918254
1071, 965044, 9978628253
1081, 954864, 9977338252
1091, 944064, 9975992251
1101, 932644, 9974648250
1111, 920664, 9973304249
1121, 980824, 9972113248
1131, 896064, 6970824247
1141, 881064, 9969535246
1151, 866684, 9968355245
1161, 851724, 9967075244
1171, 836224, 9961795243
1181, 820004, 9964581242
1191, 803464, 9963366241
1201, 786224, 9962151240
[Page 28]1211, 768444, 9960958239
1221, 750104, 9959766238
1231, 731204, 9958574237
1241, 712904, 9957427236
1251, 691804, 9956279235
1261, 671304, 9955131234
1271, 651144, 9954018237
1281, 629544, 9952906232
1291, 606684, 9951794231
1301, 581004, 9950747230
1311, 561044, 9949700229
1321, 537484, 9948653228
1331, 513564, 9947664227
1341, 4 [...]8924, 9946676226
1351, 463944, 9945688225
1361, 438484, 9944696224
1371, 412584, 9943704223
1381, 386224, 9942712222
1391, [...]59444, 9941772221
1401, 332144, 9940832220
1411, [...]04584, 9939892219
1421, [...]76504, 9939076218
1431, 248044, 9938199217
144 [...], 219184, 9937322216
1451, 189944, 993651921 [...]
1461, 160 [...]04, 99 [...]5715214
1471, 130304, 9934911213
1481, 099944, 9934180212
1491, 069224, 9933448211
1501, 038184, 9932716210
1511, 006924, 9932045209
1520, 976104, 9931375208
1530, 943084, 9930705207
1540, 910764, 9930116206
1550, 8782049929527205
1560, 845264, 9928938204
1570, 812124, 09281 [...]8203
1580, 778684, 9927619202
1590, 745084, 9627140201
1600, 711164, 9926680200
1610, 676984, 9926239199
1620, 642644, 9925817198
16 [...]0, 608084, 9925412197
1640, 573324, 9925009196
1650, 538384, 9924606195
1660, 503564, 9924274194
1670, 468024, 992 [...]941193
1680, 432584, 9923609192
1690, 397304, 9923319191
1700, 361344, 9 [...]23029190
1710, 325544, 9922739189
1720, 294044, 9922573188
1730, 253664, 9922420187
1740, 217564, 9922268186
1750, 181404, 9922193185
1760, 145202, 9922119184
1770, 108964, 9622044183
1780, 072684, 9921970182
1790, 036364, 6921896181
1800, 000004, 9921822180
DAddeLogarith.D

The Moons mean Motions.
EpochaeLongit. ☽Anomaly. ☽Latitude ☽
 Deg. partsDeg. partsDeg. Parts.
Christi.135. 73167215. 54194226. 95833
160020. 69194151. 5711199. 19250
1620154. 25389191. 27138259. 59252
1640287. 81583230. 9719459. 99833
166061. 37805270. 67222220. 40139
1129. 3838988. 71889148. 71278
2258. 76805177. 43750297. 42555
328. 15194266. 1563986. 13833
B 4170. 712507. 93972248. 08028
5300. 0963996. 6586136. 79305
669. 48028 [...]85. 37750185. 50583
7198. 86444274. 09611334. 21889
B 8341. 4247215. 87972136. 16111
9110. 80861104. 59861284. 87389
10240. 1927819 [...]. 3175073. 58667
119. 57667282. 0 [...]639222. 29944
B 12152. 1372223. 8200024. 24167
13281. 52111112. 53889172. 97444
1450. 90500201. 25750321. 66722
15180. 28917288. 97639112. 38000
B 16322. 8494431. 76000272. 32222
1792. 23333120. 4788961. 03500
18221. 61750209. 19778209. 74778
19351. 00139297. 91667358. 46055
B 20133. 5619439. 70028160. 40278
40267. 1238979. 40083320. 80583
6040. 68611119. 15111121. 20889
80174. 24805158. 80139281. 61167
100307. 81000198. 5019482. 01472

The Moons mean Motions.
Years.Longit. ☽ Deg. parts.Anom. ☽ Deg. parts.Latitud. ☽ Deg: parts.
100307, 81000198, 5019482, 01472
200255, 6200037, 00361164, 02917
300203, 43000235, 50555246, 04389
400151, 2400074, 00722328, 05861
50099, 05000272, 5091750, 07333
60046, 86000111, 01083131, 08778
700354, 67000309, 51250214, 10250
800302, 48000148, 01444296, 11722
900250, 29027346, 5163918, 13194
1000198, 10027185, 01805100, 14639
200036, 2002710, 03639200, 29305
3000234, 30055195, 05444300, 43944
400072, 4005520, 0725040, 58611
5000270, 50083205, 09083140, 73250

Ianuary48, 4683345, 0144450, 10722
February57, 4072250, 8341760, 53167
March105, 8755595, 84861110, 64139
April141, 16722127, 79805147, 52194
May189, 63555172, 81250197, 63167
Iune224, 89417204, 76194234, 11222
Iuly273, 39555249, 77639284, 62194
August321, 86389294, 79055334, 73167
September357, 15555326, 7402811, 61222
October45, 6238711, 7547261, 72194
November80, 9158343, 7041798, 60250
December129, 3838788, 71889148, 71278

The Moons mean Motions.
DayesLongit. ☽ Deg. Parts.Anomaly ☽ Deg. Parts.Latitude ☽ Deg. parts.
113, 1763913, 0650013, 22944
226, 3527826, 1300026, 45861
339, 5291739, 1950039, 68805
452, 7055552, 2600052, 91722
565, 8819465, 3250066, 14667
679, 5083378, 3900079, 37611
792, 2347291, 4550092, 60528
8105, 41111104, 52000105, 83472
9118, 58750117, 58472119, 06417
10131, 76389130, 64972132, 29333
11144, 94028143, 71472145, 52278
12158, 11667156, 77972158, 75222
13171, 29305169, 84472171, 98139
14184, 46944182, 90972185, 21083
15197, 64583195, 97472198, 44028
16210, 82222209, 03972211, 66944
17223, 99861222, 10472224, 89889
18237, 17500235, 16972238, 12833
19250, 35139248, 23472251, 35750
20263, 52778261, 29972264, 58694
21276, 70417274, 36472277, 81639
22289, 88055287, 42972291, 04555
23303, 05694300, 49472304, 27500
24316, 23333313, 55972317, 50444
25329, 40972326, 62444330, 73361
26342, 58611339, 68944343, 96305
27355, 76250352, 75444357, 19250
288, 938895, 8194410, 42167
2922, 1152818, 8844423, 65111
3035, 2916731, 9494436, 88028
3148, 4680545, 0144450, 10972
3261, 6444458, 0794463, 33889

The Moons mean Motions.
In Hours.
 Longit. ☽ D. PartsAnomal. ☽ D. partsLatitude ☽ D. parts
10, 548890, 544440, 55139
21, 098051, 088611, 10278
31, 646941, 633051, 65389
42, 196112, 177502, 20528
52, 745002, 721942, 75639
63, 294173, 266113, 30750
73, 843053, 810553, 85889
84, 392224, 355004, 41000
94, 941114, 899444, 96139
105, 490005, 443615, 51250
116, 039175, 988056, 06361
126, 588056, 532506, 61500
137, 137227, 076947, 16611
147, 686117, 621117, 71750
158, 235288, 165558, 26861
168, 794178, 710008, 81972
179, 333059, 254449, 37111
189, 882229, 798619, 92222
1910, 4313910, 3430510, 47361
2010, 9802810, 8875011, 02472
2111, 5294411, 4319411, 57583
2212, 0783311, 9761112, 12722
2312, 6272212, 5 [...]05512, 67833
2413, 1763913, 0650013, 22944

The Moons mean Motions. In parts of an Hour.
 Long. ☽ Parts.Anom. Parts.Latit. Parts.
1, 00549, 00544, 00551
2, 01098, 01088, 01103
3, 01647, 01633, 01654
4, 02196, 02177, 02205
5, 02745, 02722, 02756
6, 03294, 03266, 03307
7, 03843, 03810, 03858
8, 04392, 04355, 04410
9, 04941, 04899, 04961
10, 05490, 05443, 05512
11, 06039, 05988, 06063
12, 06588, 06532, 06615
13, 07137, 07077, 07166
14, 07686, 07621, 07717
15, 08235, 08165, 08268
16, 08794, 08710, 08819
17, 09333, 09254, 09371
18, 09882, 09798, 09922
19, 10431, 10343, 10473
20, 10980, 10887, 11024
21, 11529, 11432, 11576
22, 12078, 11976, 12127
23, 12627, 12520, 12678
24, 13176, 13065, 13229
25, 13725, 13609, 13780
26, 14274, 14153, 14331
27, 14823, 14698, 14883
28, 15372, 15242, 15434
29, 15921, 15787, 15985
30, 16470, 16331, 16536
31, 17019, 16885, 17083
32, 17567, 17416, 17633
33, 18117, 17966, 18183
[Page 33]34, 18665, 18508, 18744
35, 19214, 19050, 19300
36, 19763, 19600, 19850
37, 20317, 20133, 20400
38, 20867, 20683, 20950
39, 21416, 21233, 21500
40, 21967, 21767, 22050
41, 22500, 223 [...]6, 22600
42, 23050, 22850, 23150
43, 23600, 23400, 23700
44, 24150, 23950, 24250
45, 24700, 24500, 24800
46, 25283, 25050, 25350
47, 25800, 25600, 25900
48, 26350, 26133, 26450
49, 26900, 26683, 27000
50, 27450, 27217, 27567
51, 28000, 27767, 28117
52, 28550, 28300, 28800
53, 29100, 28850, 29217
54, 29817, 29400, 29767
55, 30200, 29933, 30317
56, 30733, 30483, 30867
57, 31283, 31017, 31416
58, 31833, 31567, 31967
59, 32383, 32117, 32517
60, 32933, 32666, 33083
61, 33491, 33206, 33626
62, 34039, 33750, 34177
63, 34588, 34294, 34728
64, 35137, 34838, 35279
65, 35685, 35382, 35830
66, 36234, 35926, 36381
67, 36783, 36470, 36932
68, 37331, 37014, 37483
69, 37880, 37558, 38034
70, 38429, 38102, 38585
71, 38979, 38646, 39139
72, 39528, 39190, 39690
73, 40077, 39734, 40241
74, 40626, 40278, 40792
75, 41174, 40822, 41343
76, 41723, 41366, 41894
77, 42272, 41910, 42445
78, 42820, 42454, 42996
79, 43369, 42998, 43547
80, 43918, 43542, 44098
81, 44466, 44094, 44651
82, 45020, 44638, 45202
83, 45568, 45182, 45753
84, 46117, 45726, 46304
85, 46666, 46270, 46855
86, 47215, 46814, 47406
87, 47763, 47358, 47957
88, 48312, 47902, 48508
89, 48861, 48446, 49059
90, 49411, 48990, 49610
91, 49960, 49538, 50165
92, 50509, 50082, 50716
93, 51058, 50626, 51267
94, 51607, 51170, 51818
95, 52155, 51714, 52369
96, 52704, 52258, 52920
97, 53253, 52802, 53471
98, 53801, 53346, 54022
99, 54351, 53890, 54573

The Aequations of the Moons Excentrick.
DegreesAeq: Sub D. parts.☉ Distāce from Umb. 5, 085424Degrees
10, 083565, 0185341359
20, 167065, 0185258358
30, 250685, 0185174357
40, 334145, 0184826356
50, 417505, 0184479355
60, 500765, 0184131354
70, 584245, 0183845353
80, 666845, 0183560352
90, 749625, 0183274351
100, 832225, 0182718350
110, 914585, 0182163349
120, 996705, 0181607348
131, 078545, 0180979347
141, 160105, 0180352346
151, [...]41365, 0179724345
161, 322285, 0178897344
171, 402825, 0178071343
181, 483025, 0177244342
191, 562805, 0176271341
201, 642125, 0175298340
211, 721085, 0174325339
221, 799085, 0173200338
231, 877505, 0172075337
241, 954985, 0170950336
252, 031905, 0169696335
262, 108305, 0168443334
272, 184105, 0167189333
282, 295945, 0165775332
292, 333945, 0164362331
302, 407925, 0162948330
312, 481445. 0161416329
322, 553885. 0159884328
332, 625825. 0158351327
342, 696885. 0156656326
352, 767565. 0154962325
362, 837325. 0153267324
372, 906285. 0151439323
382, 975205. 0149611322
393, 041845. 0147782321
403, 128245. 0145848320
413, 174045. 0143915319
423, 227625. 0141961318
433, 302665. 0140007317
443, 365545. 0138052316
453, 427685. 0135901315
463, 488805. 0133649114
473, 548925. 0131474313
483, 608065. 0129254312
493, 666 [...]05. 0126977311
503, 733585. 0124700310
513, 779403. 0122423309
523, 834425. 0120012308
533, 888365. 0117601307
543, 941125. 0115189306
553, 992965. 0112631305
563, 043585. 0110073304
574, 093065. 0107514303
584, 141385. 0104891302
594, 188545. 0102269301
604, 234485. 0099646300
[Page 35]614, 279245, 0097259299
624, 322785, 0094872298
634, 365085, 0091485297
644, 406145, 0088671296
654, 447085, 0085856295
664, 484445, 0083041294
674, 521665, 0080136293
684, 547745, 0077231292
694, 592225, 0074326291
704, 625465, 0070981290
714, 656125, 0067637289
724, 689225, 0064292288
734, 716745, 0061720287
744, 745065, 0059148286
754, 771505, 0056575285
764, 796545, 0053376284
774, 820205, 0050177283
784, 842425, 0046977282
794, 863225, 0042544281
804, 895345, 0038111280
814, 900485, 0033678279
824, 916945, 0031731278
834, 931965, 0029785277
844, 945485, 0027838276
852, 957505, 0024588275
864, 968065, 0021339274
874, 977145, 0010809273
884, 984605, 0014811272
894, 990785, 0011534271
904, 995325, 0008256270
914, 998345, 0004952269
924, 999885, 0001649268
934, 999884, 9998345267
944, 998364, 9995032266
954, 995324, 9991719265
964, 990704, 9988405264
974, 984604, 9985193263
984, 976964, 9981982262
994, 967364, 9978770261
1004, 957064, 9972811260
1014, 944764, 9966852259
1024, 930964, 9960892258
1034, 915624, 9960119257
1044, 898744, 9959347256
1054, 880344, 9958574255
1064, 860424, 9955301254
1074, 829444, 9952028253
1084, 815944, 9948754252
1094, 791464, 9945474251
1104, 765444, 9942193250
1114, 737884, 9939013249
1124, 708844, 9935795248
1134, 678884, 9932577247
1144, 646324, 9929358246
1154, 612744, 9926191245
1164, 577784, 9923025244
1174, 541284, 9919859243
1184, 503504, 9916852242
1194, 163864, 9913845241
1204, 423004, 9910837240
[Page 36]1214, 380864, 9907779239
1224, 337204, 9904722238
1234, 292104, 9901664237
1244, 245604, 9899751236
1254, 197724, 9897838235
1264, 145464, 9895915234
1274, 097844, 9892117237
1284, 045504, 9888309232
1293, 992484, 9884500231
1303, 937984, 9881731230
1313, 882064, 9878962229
1323, 874864, 9876193228
1333, 766384, 9873574227
1343, 707384, 9870956226
1353, 645724, 9868337225
1363, 583564, 9865840224
1373, 520204, 9863343223
1383, 455644, 9860846222
1393, 389204, 9858146221
140 [...], 323104, 9855446220
1413, 255144, 9853746219
1423, 186104, 9851518218
1433, 115984, 9849290217
1443, 044784, 9847061216
1452, 972604, 9844966215
1462, 899384, 9842872214
1472, 825184, 9840777213
1482, 750044, 9838882212
1492, 673924, 9836987211
1502, 596864, 9835092210
1512, 510284, 9833262209
1522, 440304, 9831432208
1532, 360744, 9829601207
1542, 280304, 9828019206
1552, 191264 9826437205
1562, 117224, 9824855204
1572, 034584, 9823435203
1581, 951204, 9822015202
1591, 867184, 9820595201
1601, 782524, 9819334200
1611, 697244, 9818073199
1621, 611384, 9816811198
1631, 524944, 9815083197
1641, 438004, 9813356196
1651, 351184, 9811628195
1661, 263004, 9811425194
1671, 174304, 9811223193
1681, 085544, 9811020192
1690, 997684, 9810309191
1700, 906924, 9809599190
1710, 817144, 9808889189
1720, 727044, 9808391188
1730, 637244, 9807893187
1740, 546 [...]84, 9807 [...]94186
1750, 455464, 9807099185
1760, 365184, 9806804184
1770, 273524, 9806509183
1780, 182424, 9806441182
1790, 691264, 9806373181
1800, 000004, 9806304180
DAddeLogarith.D

A Table for the finding of the second and third inaequalities of the Moon.
 Subtense of the☽ double dist. from ☉ Log [...]rithm.Varia­tion Adde Parts. 
00, 0000000, 00000360
11, 5805276, 00119359
21, 8815410, 02389358
32, 0576047, 03555357
42, 1825049, 04722356
52, 2793653, 058 [...]7355
62, 3584859, 07055354
72, 4253610, 08222353
82, 4832702, 09389352
92, 5343290, 10555351
102, 5799817, 11722350
112, 6212586, 12889349
122, 6589203, 14055348
132, 6935445, 1 [...]194347
142, 7255502, 16333346
152, 7553834, 17472345
162, 7832410, 18611344
172, 8093878, 19750343
182, 8339081, 20861342
192, 8572949, 21972341
202, 8793554, 23083340
212, 9003187, 24194339
222, 9202845, 25278338
232, 9393410, 26361337
242, 9575646, 27444336
252, 9750225, 28528335
262, 9917737, 29583334
273, 0078710, 30638333
283, 0233609, 31694332
293, 0382853, 32722331
303, 0326819, 33750330
303, 0526819. 34750330
[...]13, 0665 [...]45. 34750329
323, 0800238. 35750328
333, 0900275. 36750327
343, 1056210. 37722326
353, 1178275. 38694325
363, 1296681. 39667324
373, 1411621. 40655323
383, 1523276. 41555322
393, 1630910. 42472321
403, 1737374. 43389320
413, 1840110. 44278319
423, 1940149. 45167318
433, 2037611. 46083317
443, 2132611. 46889316
453, 2225254. 47722315
463, 2315637. 48555314
473, 2403854. 49361313
483, 2489990. 50167312
493, 2574127. 50944311
503, 2655340. 51694310
513, 2706701. 52444309
523, 2815277. 53194308
533, 2892131. 53916307
543, 2967325. 54611306
553, 3040913. 55305305
563, 3012950. 55972304
573, 3183486. 56611303
583, 3252569. 57250302
593, 3320245. 57861301
603, 3386557. 58444300
[Page 38]603, 3386557, 58444300
613, 3451546, 59058299
623, 3515250, 59583298
633, 3577708, 60139297
643, 3638954, 60667296
653, 3699022, 61167295
663, 3757945, 61667294
673, 815752, 62139293
683, 3872474, 62583292
693, 3928137, 63000291
703, 3982770, 63417290
713, 4036397, 63805289
723, 4089044, 64167288
733, 4130733, 64500287
743, 4191487, 64861286
753, 4241328, 65194285
763, 4290277, 65500284
773, 4338353, 65778283
783, 4375575, 66028282
793, 7431962, 66250281
803, 4477532, 66427280
813, 4522301, 66667279
823, 4566282, 66833278
833, 4609503, 67000277
843, 4651966, 67139276
853, 4693690, 67250275
86 [...], 4704690, 67361274
873, 4465979, 67417273
883, 4814570, 67444272
893, 4853475, 67472271
903, 4891707, 67500270
903, 4891707, 67500270
913, 4929278, 67472269
923, 4966198, 67444268
933, 5002479, 67417267
943, 5038132, 67361266
953, 5073166, 67250265
963, 5107592, 67139264
973, 5141418, 67000263
903, 5174656, 66833262
913, 5207312, 66667261
1003, 5239397, 66472260
1013, 5270918, 66350259
1023, 5301883, 66028258
1033, 5332301, 65778257
1043, 5362178, 65500256
1053, 5391524, 65194255
1063, 5420343, 64861254
1073, 5448644, 64500253
1083, 5476433, 64167252
1093, 5503717, 63805251
1003, 5530502, 63417250
1113, 5556794, 63000249
1123, 5582599, 62583248
1133, 5607923, 62139247
1143, 5632771, 61667246
1153, 5656149, 61167245
1163, 5681062, 60667244
1173, 5704515, 60139243
1183, 5727513, 69583242
1193, 5750061, 59028241
1203, 5772163, 58444240
[Page 39]120 [...], 5772163, 58444240
1213, 5793825, 57861239
1223, 5815050, 57250238
1233, 5835842, 56611237
1243, 5856206, 55972236
1253, 5876126, 55305235
1263, 5895666, 54611234
1273, 5917769, 53916233
1283, 5933457, 53194232
2293, 5951739, 52444231
1303, 5969614, 51694230
1313, 5987086, 50944229
1323, 6004159, 50167228
1333, 6029834, 49361227
1 [...]43, 6037118, 48555226
1353, 6053010, 47722225
1363, 6068516, 46889224
1373, 6083636, 46083223
1383, 6098374, 45167222
1393, 6106733, 44278221
1403, 6126715, 43389220
1413, 6140323, 42472219
1423, 6153558, 41555218
1433, 6166423, 40611217
1443, 6178932, 39667216
1453, 6191052, 38694215
1463, 6208820, 37722214
1473, 6314227, 36750213
1483, 6325273, 35750212
1493, 6235962, 34750211
1502, 6246295, 33750210
1503, 624629. 33750210
1513, 6256273. 32722209
1523, 6265898. 31694208
1533, 6275172. 30638207
1543, 6284096. 29583206
1553, 6292672. 28528205
1563, 6300901. 27444204
1573, 6308784. 26361203
1583, 6316323. 25278202
1593, 6333518. 24194201
1603, 6330372. 23083200
1613, 6336884. 21972199
1623, 6343056, 20861198
1633, 6348890. 19750197
1643, 6354385. 18611196
1653, 6359543. 17472195
1663, 6364364. 16333194
1673, 6368850. 15194193
1683, 6373000. 14055192
1693, 6376817. 12889191
1703, 6380299. 11722190
1713, 6387448. 10555189
1723, 6386265. 09389188
1733, 6388749. 08222187
1743, 6390901. 07055186
1753, 6392722. 05889185
1763, 6394211. 04722184
1773, 6395369. 03555183
1783, 6396295. 02389182
1793, 6396792. 01194181
1803, 6396857. 00000180
DLogarithm.Subst.D

Bullialdus his Table of Evection.
 Evectiō Subst.Scrupl. of pro­portiō.Varia­tion Adde 
 D. Parts.Parts.Parts. 
00, 00000, 00000, 00000 [...]60
10, 04028, 00873, 01194359
20, 08055, 01745, 02389358
30, 12083, 02617, 03555357
40, 16083, 03489, 04722356
50, 20083, 04362, 05887355
60, 24111, 05234, 07055354
70, 28083, 06105, 08222353
80, 36028, 06975, 09389352
90, 36000, 07845, 10555351
100, 39944, 08715, 11722350
110, 43889, 09584, 12889349
120, 47833, 10453, 14055348
130, 51750, 11320, 15194347
140, 55667, 12187, 16333346
150, 59583, 13052, 17472345
160, 63472, 13917, 18611344
170, 67333, 14780, 19750343
180, 71222, 15643, 20861342
190, 75083, 16504, 21972341
200, 78917, 17364, 23083340
210, 82750, 18223, 24194339
220, 86528, 19081, 25278338
230, 9027 [...], 19936, 26361337
240, 94055, 20791, 274443 [...]6
250, 97805, 21643, 28528335
361, 01528, 22495, 29583334
271, 052 [...]2, 23344, 30638333
281, 08889, 24192, 31694332
291, 12527, 25038, 32722331
301, 161 [...]8, 25882, 33750330
301, 16138, 25882, 33750330
311, 19722, 2672334750329
321, 23278, 2756 [...], 35750328
331, 26833, 2840, 36750327
341, 30305, 29237, 37722326
351, 33750, 30072, 38694325
361, 37167, 30901, 39667324
371, 40556, 30730, 40655323
381, 43944, 32553, 41555322
391, 47222, 33380, 42472321
401, 50500, 34202, 43389320
411, 53750, 35020, 44378319
421, 56972, 35836, 45167318
431, 60139, 3665 [...], 46083317
441, 63278, 37460, 46889316
451, 66389, 38268, 4772 [...]315
461, 69444, 39073, 78555314
471, 72444, 39874, 49361313
481, 75444, 40673, 50167312
491, 78417, 41469, 50944311
501, 81 [...]61, 42262, 51694310
511, 84278, 4 [...]051, 52444309
521, 87139, 43837, 53194308
531, 89944, 44619, 53916307
541, 92695, 45 [...]99, 54611306
551, 95333, 46174, 55305305
561, 97917, 46 [...]47, 55972 [...]04
572, 00444, 47715, 56611303
582, 0 [...]917, 4848 [...], 57250302
592, 05333, 4924 [...], 57861301
602, 07694, 5000 [...], 58444300
[Page 39]602, 07694, 50000, 58444300
612, 10000, 50753, 59028299
622, 12250, 51903, 59583298
632, 14444, 52249, 60139297
642, 16583, 52991, 60667296
652, 18667, 53729, 61167295
662, 20694, 54463, 61667294
672, 22667, 55193, 62139293
682, 24583, 55919, 62583292
692, 26444, 56640, 63000291
702, 28222, 57357, 63417290
712, 29917, 58070, 63805289
722, 31527, 58778, 64167288
732, 33055, 59482, 64500287
742, 34527, 60181, 64861286
752, 35944, 60876, 65194285
762, 36750, 61566, 65500284
772, 38611, 62251, 65778283
782, 39889, 62932, 66028282
792, 41055, 63607, 66250281
802, 42222, 64278, 66472280
812, 43333, 64944, 66667279
822, 44361, 65605, 66833278
832, 45278, 66262, 67000277
842, 96083, 66913, 67139276
852, 46778, 67559, 67250275
862, 27417, 68199, 67361274
872, 48000, 68835, 67417273
882, 48500, 69465, 67444272
892, 48944, 70091, 67472271
902, 49333, 70711, 6750070
902, 4933370711, 67500270
912, 49667, 7132567472269
922, 49889, 71933, 67444268
932, 50000, 72537, 67417267
942, 49889, 73135, 67361266
952, 49778, 73727, 67250265
962, 49639, 74314, 67139264
972, 49444, 74895, 67000263
982, 49222, 75471, 66833262
992, 48972, 76040, 66667261
1002, 48667, 76604, 66472260
1012, 48333, 77162, 66250259
3022, 47944, 77714, 66028258
1032, 47139, 78260, 65778257
1042, 46917, 78801, 65600256
1052, 46278, 79335, 65194255
1062, 45500, 79863, 64861254
1072, 44611, 80385, 64500253
1082, 43611, 80901, 64167252
1092, 42556, 81411, 63805251
1102, 41389, 81915, 63417250
1112, 40139, 82412, 63000249
1122, 38861, 82903, 62583248
1132, 37583, 83388, 62139247
1142, 36194, 83867, 61667246
1152, 34722, 84339, 61167245
1162, 32972, 84805, 60667244
1172, 31222, 85264, 60139243
1182, 29472, 85716, 59583242
1192, 27722, 8616 [...], 59028241
1202, 25972, 8660 [...], 58444240
[Page 40]1202, 25972. 86602, 58444240
121 [...], 24083. 87135, 57861239
1222, 22111. 87462, 57250238
1232, 20038. 87882, 56611237
1242, 17833. 88295, 55972236
1252, 15555. 88701, 55305235
1262, 13167. 89100, 54611234
1272, 10694. 89493, 53916233
1282, 08138. 89879, 53194232
1292, 05500. 902 [...]8, 52444231
1302, 02805. 90631, 51694230
1312, 00055. 90996, 50944229
1321, 97222. 91354, 50167228
1331, 94333. 91706, 49 [...]612 [...]7
1341, 91389. 92050, 48555226
1351, 88138. 9 [...]38 [...], 47722225
1361, 85000. 92718, 46889224
1371, 81889. 93042, 46083223
1381, 78722. 93358, 45167222
1391, 75500. 93667, 44278221
1401, 72222. 93969, 43389220
1411, 68889. 94264, 42472219
1421, 65472. 94552, 41555218
1431, 62000. 94832, 40611217
1441, 58389. 95105, 39667216
1451, 54694. 95371, 38694215
1461, 50944. 95630, 37722214
1471, 47167. 95882, 36750213
1481, 43972. 96126, 35750212
1491, 39417. 96363, 34750211
1501, 35472. 9659 [...], 33750210
1501, 35472, [...]6592, 33750210
1511, 31472, 96814, 32722209
1521, 27417, 97029, 31694208
1531, 23305, 97237, 30638207
1541, 19167, 97437, 29583206
1551, 14972, 97629, 28528205
1561, 10722, 97815, 27444204
1571, 06417, 97992, 26361203
1581, 02056, 98163, 25278202
1590, 97667, 98325, 24194201
1600, 93250, 98481, 23083100
1610, 88778, 98628, 21972199
1620, 84278, [...]8769, 20861198
1630, 79750, 98901, 19750197
1640, 75167, 99027, 18611196
1650, [...]0556, 99144, 17472195
1660, 6 [...]944, 99254, 16333194
1670, 61305, 99357, 15194193
1680, 56667, 99452, 14055192
1690, 52000, 99535, 12889191
1700, 47333, 99619, 11722190
1710, 42667, 99692, 10555189
1720, 37972, 99756, 09389188
1730, 33278, 99813, 08222187
1740, 28556, 99863, 07055186
1750, 23833, 99905, 05889185
1760, 19083, 99939, 04722184
1770, 14333, 99966, 03555183
1780, 09556, 99985, 02389182
1790, 04778, 99996, 01194181
1800, 00000, 00000, 00000180
 Adde Sub: 

A Compounded Table of the ☽ Evection and Variation.
Degrees of Equation.36912151821Degrees.
SubSub:SubSubSubSubSub
00. 0580, 1160, 1710. 2240, 2730, 2990, 359360
50. 0590, 1200, 1780. 2350, 2900, 3210, 399355
100. 0590, 1200, 1810. 2420, 3010, 3380, 412350
150. 0580, 1190, 1810. 2450, 3080, 3490, 430345
200. 0570, 1170, 1790. 2430, 3090, 3540, 441340
250. 0540, 1120, 1750. 2390, 3060, 3530, 444335
300. 0500, 1060, 1660. 2320, 3000, 3490, 440330
350. 0450, 0970, 1550. 2190, 2870, 3390, 433325
400. 0390, 0870, 1410. 2020, 2700, 3210, 418320
450. 0320, 0740, 1240. 1840, 2480, 2980, 395315
500. 0240, 0590, 1030. 1580, 2210, 2710, 364310
550. 0150, 0420, 0800. 1290, 1880, 2370, 329305
600. 0060, 0240, 0550. 0970, 1500, 1960, 295300
650A0040, 0050, 0270. 0540, 2080, 1500, 234295
700. 0150A0160A0030. 0180, 0630, 0890, 157290
750. 0260, 0380, 0350A0280, 0130, 0460, 116285
800. 0380, 0620, 0690. 0620A0400A0140, 048280
850. 0500, 0860, 1050. 1090, 0960, 0840A024275
900. 0630, 1100, 1410. 1570, 1550, 1430, 101270
950. 0750, 1350, 1780. 2050, 2150, 1840, 182265
1000. 0870, 1600, 2160. 2650, 2760, 2820, 265160
1050. 1000, 1850, 2530. 3040, 3370, 3530, 349255
1100. 1120, 2090, 2890. 3530, 3990, 4 [...]50, 434250
1150. 1230, 2330, 3260. 4020, 4600, 4960, 520245
1200. 1340, 2560, 3610. 4490, 5200, 5660, 604240
1250. 1450, 2770, 3940. 4950, 5790, 6360, 688235
1300. 1550, 2980, 4260. 5330, 6350, 7930, 768230
1350. 1630, 3160, 4560. 5800, 6880, 7670, 848225
1400. 1710, 3330, 4830. 6180, 7380, 8290, 923220
1450. 1790, 3490, 5070. 6520, 8830, 8830, 992215
1500. 1850, 3630, 5370. 6840, 8240, 9341, 057210
1550. 1900, 3740, 5490. 7120, 8620, 9811, 114205
1600. 1940, 3830, 5640. 7360, 8950, 0221, 168200
1650. 1970, 3910, 5770. 7540, 9220, 0581, 215195
1800. 1990, 3960, 5880. 7590, 9450, 0861, 254190
1750. 2000, 3990, 5940 7710, 9620, 1111, 286185
1700. 201 [...], 4010, 5970. 7890, 9750, 1291, 312180
Degrees of Equ: Anom.SubSubSubSubSubSubSubFe [...]rees of Equ: Anom.
177174171168162162159

[Page 40] [...] [Page 39] [...] [Page 40] [...] [Page 41] [...]

A Compounded Table of the ☽ Evection and Variation.
Degrees of Equation.36912151821Degrees of Equation.
AddeAddeAddeAddeAddAddeAdd
1800. 2010, 4010, 5970, 7890, 9751, 1291, 312180
1850, 2000, 4010, 5990, 7940, 9811, 1391, 331175
1900, 1980, 3980, 5970, 7940, 9841, 1451, 341170
1950, 1950, 3940, 5930, 7940, 9831, 1461, 346165
2000, 1920, 3870, 5850, 7820, 9761, 1431, 346160
2050, 1870, 3800, 5750, 7700, 9641, 1331, 338155
2100, 1820, 3710, 5620, 7550, 9481, 1171, 323150
2150, 1760, 3590, 5470, 7360, 9281, 0961, 300145
2200, 1690, 3470, 5290, 7150, 9031, 0711, 275140
2250, 1620, 3330, 5090, 6900, 8751, 0411, 242135
2300, 1540, 3170, 4870, 6630, 8431, 0061, 204130
2350, 1450, 3000, 4630, 6330, 7070, 9671, 161125
2400, 1360, 2830, 4380, 6000, 7680, 9241, 112120
2450, 1270, 2650, 4120, 5660, 7270, 8781, 059115
2500, 1170, 2460, 3840, 5300, 7840, 8291, 002110
2550, 1070, 2270, 3550, 4930, 6380, 7780, 943105
2600, 0970, 2060, 3260, 4540, 5910, 7240, 880100
2650, 0870, 1860, 2950, 4140, 5420, 6680, 81595
2700, 0760, 1650, 2640, 3740, 4920, 6110, 74890
2750, 0660, 1440, 2370, 3310, 4410, 5520, 67985
2800, 0550, 1210, 2020, 2910, 3890, 4930, 60980
2850, 0450, 1020, 1700, 2490, 3370, 4330, 53875
2900, 0350, 0820, 14 [...]0, 2090, 2860, 3720, 46670
2950, 0250, 0620, 1090, 1690, 2340, 3120, 39465
3000, 0160, 0420, 0790, 1260, 1830, 2530, 32260
3050, 0060, 0230, 0490, 0870, 1330, 1940, 25255
3100S0020, 0040, 0210, 0480, 0840, 1360, 17650
3150, 0110S0130S0050, 0110, 0370, 0800, 11445
3200, 0190, 0300, 0310S0250S0090, 0260, 04840
3250, 0270, 0450, 0560, 0580, 0520S0250S01535
3300, 0340, 0600, 0790, 0910, 0930, 0750, 07230
3350, 0400, 0730, 1000, 1200, 1320, 1220, 13425
3400, 0450, 0850, 1190, 1470, 1680, 1660, 18720
3450, 0500, 0960, 1360, 1710, 2000, 2060, 23815
3500, 0540, 1050, 1510, 1920, 2290, 2410, 28410
3550, 0570, 1110, 1610, 2100, 2530, 2730, 32505
3600, 0590, 1160, 1710, 2240, 2730, 2960, 35900
Deg: of E­quated A­nomaly.AddAddAddAddAddAddAddDegrees of Equated Anomaly.
177174171108165162159

A Compounded Table of the ☽ Evection and Variation.
Deg: of Eq▪ Anomaly.21242780333639Deg. of Eq▪ Anomaly.
Sub.SubSubSubSubSub:Sub:
00, 3590, 3960, 4270, 4540, 4750, 4910. 499360
50, 3990, 4330, 4730, 5090, 5400, 5650. 585355
100, 4120, 4610, 5110, 5560, 5960, 6320. 661350
150, 4300, 4870, 5420, 5950, 6440, 6890. 728345
200, 4410, 5050, 5670, 6260, 6830, 7370. 786340
250, 4440, 5130, 5810, 6490, 7140, 7750. 829335
300, 4400, 5130, 5880, 6620, 7340, 8050. 870330
350, 4330, 5080, 5850, 6640, 7440, 8220. 896325
400, 4180, 4960, 5750, 6590, 7420, 8270. 910320
450, 39 [...]0, 4750, 5590, 6470, 7340, 8220. 910315
500, 3640, 4450, 5320, 6220, 7150, 8100. 002310
550, 3290, 4090, 4950, 5890, 6840, 7840. 884305
600, 2950, 3650, 4520, 5450, 6420, 7470. 850300
650, 2340, 3120, 3980, 4930, 5930, 6970. 805295
700, 1570, 2500, 3360, 4300, 5310, 6390. 749290
750, 1160, 1840, 2650, 3560, 4570, 5660. 681285
800, 0480, 1120, 2890, 2770, 3740, 4830. 598280
850A0240, 0330, 1070, 1890, 2840, 3890. 503275
900, 1010A0510, 0130, 1040, 1840, 2890. 402270
950, 1820, 1400A0830A0100, 0770, 1780. 289265
1000, 2650, 2330, 1850, 1180A0370, 0590. 166260
1050, 3490, 3270, 2890, 2320, 1570A0670. 036255
1100, 43 [...]0, 4240, 3950, 3480, 2900, 1990A102250
1150, 5200, 5210, 5030, 4650, 4100, 3360. 246245
1200, 6040, 6180, 6110, 5840, 5380, 4310. 392240
1250, 6880, 7130, 7180, 7030, 6680, 6130. 540235
1300, 7680, 8070, 8240, 8210, 7980, 7540. 690230
1350, 8480, 8990, 9280, 9370, 9250, 8920. 839225
1400, 9230, 9861, 0291, 0511, 0510, 8290. 987220
1450, 9920, 0681, 1241, 1591, 1711, 1631. 133215
1501, 0571, 1461, 2141, 2731, 2881, 2921. 274210
1551, 1141, 2171, 2801, 3581, 4011, 4141. 41020 [...]
1601, 1681, 2801, 3531, 4451, 4991, 5291. 537200
1651, 2151, 3371, 4411, 5251, 5901, 6341. 657195
1701, 2541, 3871, 5021, 5981, 6751, 7291. 764190
1751, 2861, 4271, 5541, 6621, 7501, 8171. 864185
1801, 3121, 4621, 5951, 7141, 8151, 8941. 953180
Deg: of Equated Anomaly.SubSubSubSubSubSubSubDegree of Equated A­oumaly.
159156153150147144141

A Compounded Table of the ☽ Evection and Variation.
Deg [...]ees of Eq: Anom. [...]2 [...]4273 [...]333639Degrees of Eq: Anom.
AddeAddeAddeAddeAddAddeAdd
1801, 3211, 4621, 5951, 7141, 8151, 8941, 953180
1851, 3311, 4881, 5301, 7581, 8661, 9592, 031175
1901, 3411, 5061, 6561, 7911, 9112, 0112, 093170
1951, 3461, 5131, 6711, 8161, 9432, 0532, 146165
2001, 3461, 5171, 6781, 8281, 9632, 0842, 186160
2051, 3381, 5141, 6801, 8331, 9742, 1012, 214155
2101, 3231, 5021, 6721, 8311, 9782, 1092, 227150
2151, 3001, 4821, 66 [...]1, 8181, 9702, 1092, 232145
2201, 2751, 4551, 6291, 7951, 9522, 0962, 226140
2251, 2421, 4221, 6191, 7651, 9232, 0722, 208135
2301, 2041, 3321, 5571, 7251, 8862, 0332, 177130
2351, 1611, 3361, 5091, 67 [...]1, 8401, 9932, 136125
2401, 1121, 2851, 4561, 6231, 7851, 9392, 085120
2451, 0551, 2271, 3961, 5611, 7221, 8762, 023115
2501, 0021, 1651, 3291, 4911, 6511, 8051, 952110
2550. 943 [...], 0001, 2581, 4161, 5761, 7251, 872105
2600, 8801, 0311, 1841, 3371, 4 [...]91, 6371, 782100
2650, 8150, 9591, 1061, 2531, 4011, 5441, 68795
2700, 7480, 8841, 0241, 1701, 3071, 4481, 58690
2750, 6790, 8070, 9391, 0731, 2101, 3451, 48085
2800, 6090, 7180, 8520, 9791, 1081, 2381, 36880
2850, 5 [...]80, 6480, 7630, 8 [...]21, 0041, 1281, 25275
2900, 4660, 5670, 6740, 7840, 8981, 0151, 13270
2950, 3940, 4850, 5640, 6850, 7910, 8991, 01065
3000, 3220, 40 [...]0, 4850, 5840, 6820, 7830, 88760
3050, 2520, [...]230, 40 [...]0, 4840, 5730, 6650, 77455
3100, 1760, 2430, 3120, 3840, 4640, 5470, 64550
3150, 1140, 1650, 2230, 2860, 3970, 4300, 50845
3200, 0480, 0890, 1 [...]70, 1890, 2500, 3140, 38440
3250S0150, 0150, 0520, 0940, 1450, 2000, 26035
3300, 0720S0440S0300, 0000, 0430, 0890, 03930
3350, 1340, 1230, 1070S0840S0530S0190, 020. 25
3400, 1870, 1880, 1800, 1680, 1470, 1240S09320
3450, 2380, 2480, 2500, 2470, 2420, 2230, 20315
3500, 2840, 3030, 3160, 3220, 3230, 3180, 30510
3550, 3250, 3530, 3860, 3920, 4030, 4070, 40605
3600, 3590, 3960, 4270, 4540, 4750, 4910, 4 [...]900
Deg: of E­quated A­nomaly.AddAddAddAddAddAddAddDegrees of Equtead Anomaly.
15915615315 [...]147144141

A Compounded Table of the ☽ Evection and Variation.
Equated Anomaly.39414548515457Equated Anomaly.
Sub:Sub.SubSubSubSubSub:
00. 4990, 5020, 5010, 4950, 4810, 4680, 447360
50. 5850, 5990, 6060, 6100, 6090, 6000, 591355
100. 6610, 6860, 7050, 7190, 7260, 7290, 651350
150. 7280, 7630, 7930, 8180, 8370, 7680, 854345
200. 7860, 83 [...] [...], 8700, 9060, 9350, 9590, 976340
250. 8290, 8870, 9380, 9831, 0231, 0571, 085335
300. 8700, 9330, 9921, 0491, 0991, 1441, 182330
350. 8960, 969 [...], 0371, 1021, 1621, 2181, 266325
400. 9100, 99 [...]1, 0691, 1441, 2131, 2741, 337320
450. 9101, 001 [...], 0871, 1711, 2521, 3271, 4013 [...]5
500. 9020, 9961, 0901, 0851, 2741, 3601, 440310
550. 8840, 9821, 0821, 1821, 2821, 3781, 467305
600. 8500, 9581, 0661, 1711, 2751, 3781, 480300
650. 8050, 9181, 0311, 1461, 2591, 3671, 473295
700. 7490, 8630, 9741, 1031, 2251, 3441, 455290
750. 6810, 800 [...], 9221, 1101, 1751, 3011, 426285
800. 5980, 7710, 84 [...]0, 9791, 109 [...], 2431, 375280
8 [...] [...]. 5030, 628 [...], 7580, 8941, 0331, 1671, 307275
900. 4020, 5240, 6550, 7940, 9371, 0631, 228270
9 [...]0. 2890, 4120, 5420, 6800, 8270, 9771, 128265
1000. 1660, 2920, 4180, 5580, 7040, 8451, 053260
1050. 0360, 1530, 2820, 4220, 5680, 7 [...]51, 88 [...]255
1100A1020, 01 [...]0, 1370, 2750, 4230, 5790, 742250
1150. 2460A1370A0160, 1190, 2660, 4420, 591245
1200. 3920, 2920, 1770A0450, 0910, 2540, 417240
1250. 5400, 4490, 3410, 2160A0760, 0770, 239235
1300. 6900, 6070, 5370, 3890, 2560A1080, 052230
1350. 8390, 7660, 6750, 5650, 4480, 2960A141225
1400. 9870, 9250, 8430, 3420, 6230, 4870, 337220
1451. 1331, 0811, 0100, 9180, 8080, 6800, 536215
1501. 2741, 235 [...], 1741, 0940, 9920, 8720, 737210
1551. 4101, 3831, 2341, 2631, 1721, 0620, 935205
1601. 5371, 5411, 4881, 4291, 3501, 2491, 131200
1651. 6571, 6561, 6331, 5871, 5201, 4311, 323195
1701. 7641, 7781, 7681, 7411, 6821, 6051, 509190
1751. 8641, 8881, 8921, 8751, 8331, 7691, 685185
1801. 9531, 9912, 0051, 9991, 9731, 9231, 851180
Equated Anomaly.SubSubSubSubSubSubSubEquated A­nomaly.
141138135132129126123

A Compounded Table of the ☽ Evection and Variation.
Equated Anomaly.3942454 [...]515457Equated Anomaly.
AddAddAddAddAddAddAdd
1801. 9531, 9912, 0051. 9991, 9731, 9231, 851180
1852. 0312, 0812, 1082. 1032, 0982, 0612, 004175
1902. 0932, 1572, 1992. 2182, 2152, 1802, 142170
195 [...]. 1462, 2182, 2722. 3062, 3172, 3032, 270165
2002. 1862, 2692, 3342. 3762, 4022, 4032, 383160
2052. 2142, 3072, 3822. 4362, 4712, 4842, 479155
2102. 2272, 3302, 4162. 4822, 5262, 5522, 555150
2152. 2322, 3402, 4332. 5072, 5682, 6032, 620145
2202. 2262, 34 [...]2, 4412. 5232, 5902, 6392, 668140
2252. 2082, 3302, 4 [...]72. 5292, 6002, 6732, 696135
2302. 1772, 3002, 4192. 5182, 6002, 6632, 708130
2352. 1362, 2672, 3872. 4942, 5832, 6552, 712125
2402. 0852, 2202, 3432. 4542, 5512, 6322, 696120
2452. 0232, 1612, 2882. 4032, 5002, 5912, 666115
2501. 9522, 0912, 2192. 3402, 4462, 5392, 572110
2551. 8722, 0122, 1432. 2652, 3752, 4732, 558105
2601. 7821, 9232, 0562. 1792, 2922, 3932, 484100
2651. 6871, 8251, 9572. 0832, 1982, 3022, 38795
2701. 5861, 7211, 8511. 9752, 0942, 1902, 29790
2751. 4801, 6111, 7391. 8611, 9752, 0852, 18685
2801. 3681, 4961, 6201. 7411, 8531, 9622, 06380
2851. 2521, 3751, 4961. 6141, 7261, 8321, 93375
2901. 1321, 2501, 3661. 4801, 4901, 6951, 79570
2951. 0101, 1111, 2331. 3421, 4491, 5521, 65065
3000. 8870, 9911, 0961. 2001, 3031, 4021, 49960
3050. 7740, 8840, 9571. 0561, 1531, 2491, 34255
3100. 6450, 7250, 8140. 9091, 0011, 0941, 18150
3150. 5080, 5900, 6750. 7610, 8720, 9331, 01845
3200. 3840, 4570, 5370. 6210, 6910, 7940, 85240
3250. 2600, 3250, 4930. 4620, 5160, 6090, 68435
3300. 0390, 1950, 2540. 3230, 3800, 4460, 51530
3350. 0200, 0670, 1170. 1700, 2270, 2860, 34825
3400S0930S0570S0160. 0280, 0760, 1280, 18320
3450. 2030, 1770, 1460S1100S0710S0280, 01915
3500. 3050, 2910, 2700. 2450, 2140, 1790S14110
3550. 4060, 4000, 3880. 3730, 4520, 3270, 29605
3600. 4990, 5020, 5010. 4950, 4810, 4680, 447200
Equated Anomaly.AddAddAddAddAddAddAddEquated Anomaly▪
141138135 [...]32129126123

A Compounded Table of the ☽ Evection and Variation.
Equated Anomaly.576863666972 [...]5Equated Anomaly.
SubSub:SubSubSubSubSub
00. 4470, 4210, 3910. 3580, 3200, 2800, 237360
50. 5910, 5740, 5520. 5500, 4960, 4620, 424355
100. 6510, 7190, 6060. 6880, 6650, 6390, 607350
150. 8540, 8560, 7520. 8430, 8280, 8090, 784345
200. 9760, 9860, 9900. 9900, 9810, 9720, 954340
251. 0851, 1071, 1211. 1271, 1291, 1261, 116335
301. 1821, 2141, 2401. 2581, 2681, 2271, 269330
351. 2661, 3091, 3451. 3741, 3961, 4021, 413325
401. 3371, 3921, 3481. 4771, 5081, 5931, 549320
451. 4011, 4591, 5171. 5671, 6081, 6421, 668315
501. 440 [...], 5131, 5801. 6401, 6941, 7391, 774310
551. 4671, 5891, 6311. 7001, 7581, 8201, 866305
601. 4801, 5751, 6631. 7461, 8191, 8851, 941300
651. 4731, 5791, 6801. 7721, 8571, 9362, 001295
701. 4551, 5691, 6761. 7811, 8781, 9662, 046290
751. 4261, 5491, 6631. 7721, 8781, 9812, 070285
801. 3751, 5061, 63 [...]1. 7541, 9661, 9732, 074280
851. 3071, 4481, 5621. 7131, 8391, 9532, 074275
901. 2281, 3731, 5141. 6551, 7491, 9202, 035270
951. 1281, 2821, 4331. 5781, 6221, 8631, 993265
1001. 0131, 1721, 3311. 4871, 6391, 7851, 929260
1050. 8821, 0451, 2111. 3751, 5381, 6961, 845255
1100. 7420, 9071, 0741. 2461, 4241, 5831, 744250
1150. 5910, 7550, 8941. 1011, 2751, 4511, 621245
1200. 4170, 5890, 7650. 9451, 1241, 3031, 479240
1250. 2390, 4110, 5890. 7720, 9571, 1941, 325235
1300. 0520, 2230, 4020. 5870, 7750, 9731, 156230
1350A1410, 0260, 2040. 3900, 5810, 7760, 970225
1400. 3370A1750, 0000. 1840, 3770, 5740, 772220
1450. 5360, 3780A2080A0260, 1630, 3610, 563215
1500. 7370, 5840, 4190. 2400A0630, 1420, 344210
1550. 9350, 7900, 6310. 4580, 2730A0800, 119205
1601. 1310, 9940, 8420. 6750, 4950, 3060A107200
1651. 3231, 1951, 0510. 8910, 7170, 5330, 337195
1701. 5091, 3921, 2571. 1040, 9370, 6830, 568190
1751. 6851, 5801, 4551. 3221, 1530, 9790, 784185
1801. 85 [...]1, 7581, 6451. 5131, 3631, 1981, [...]19180
Equated Anomaly.SubSubSubSubSubSubSubEquated Anomaly.
123120117 [...]14111108105

A Compounded Table of the ☽ Evection and Variation▪
Equated Anomaly.57606366697275Equated Anomaly.
AddeAddeAddeAddeAddAddeAdd▪
1801, 8511, 7581, 6451, 5131, 3631, 1981, 1 [...]9180
1852, 0041, 9241, 8291, 7 [...]21, 5641, 4091, 2 [...]8175
1902, 1422, 07 [...]1, 9901, 8801, 7531, 6081, 44817 [...]
1952, 2702, 2142, 1392, 0441, 9301, 7961, 646165
2002, 3832, 3412, 2782, 1912, 0901, 9701, 831160
2052, 4792, 4512, 4012, 3 [...]92, 2382, 1262, 0011 [...]5
2102, 5552, 5412, 5072, 4482, 3692, 2722, 154150
2152, 6202, 6172, 5912, 5482, 4832, 4002, 296145
2202, 6682, 6752, 6632, 6292, 5762, 5092, 419140
2252, 6962, 7172, 7172, 6952, 6562, 5962, 520135
2302, 7082, 7382, 7482, 7442, 7152, 6682, 604130
2352, 7122, 7482, 7672, 7692, 7562, 7232, 669125
2402, 6962, 7442, 7742, 7812, 7752, 7552, 711120
2452, 6602, 7582, 7602, 7822, 7842, 129 [...], 739115
2502, 5722, 6822, 7272, 7612, 7742, 7732, 750110
2552, 5582, 6282, 6842, 7242, 7482, 7552, 746105
2602, 4842, 56 [...]2, 623 [...], 6872, 7012, 7 [...]2, 721100
2652, 3872, 4782, 5472, 6012, 6402, 6662, 67795
2702, 2972, 3832, 4572, 5172, 56 [...]2, 6002, 61690
2752, 1862, 2762, 3542, 4192, 4732, 5142, 54185
2802, 0632, 1552, 2382, 3092, 3682, 4152, 44980
2851, 9332, 0252, 109 [...], 1852, 2412, 3032, 34375
2901, 7951, 8881, 97 [...]2, 0482, 1172, 1762, 22470
2951, 6501, 7431, 8291, 9041, 9752, 0362, 08865
3001, 4991, 5901, 6761, 7541, 7981, 8891, 94460
3051, 3421, 4311, 5161, 5951, 6631, 7331, 79155
3101, 1811, 2681, 3501, 4161, 5021, 5691, 62950
3151, 0181, 1001, 1811, 2571, 3291, 3971, 45945
3200, 8520, 9301, 0071, 0811, 1521, 2191, 28140
3250, 6840, 7580, 8310, 9020, 9711, 0371, 09935
3300, 5150, 5840, 6540, 7170, 7870, 8410, 91330
3350, 3480, 4100, 4740, 5380, 6020, 6640, 72325
3400, 1830, 2380, 2950, 3330, 4240, 4730, 53120
3450, 0190, 0670, 1190, 1720, 2260, 2820, 33715
3500S1410S0990S0540S0060, 0420, 0920, 14410
3550, 2960, 2620, 2240, 1840S1400S0950S04805
3600, 4470, 4210, 3910, 3580, 3200, 2800, 23700
Equated Anomaly.AddAddAddAddAddAddAddEquated Anomaly.
12312 [...]117114 [...]11108105

A Compounded Table of the ☽ Evection and Variation.
Equated Anomaly.75788184 [...]790 Equated Anomaly:
Sub:Sub.SubSubSubSub 
00. 2370, 1930, 1460, 0990, 0500, 000 360
50. 4240, 3840, 3410, 2950, 2490, 201 355
100. 6070, 5710, 5320, 4900, 4460, 399 350
150. 7840, 7540, 7200, 6820, 6400, 596 345
200. 9540, 9310, 9020, 8690, 8310, 789 340
251. 1161, 1001, 0781, 0501, 0161, 978 335
301. 2691, 260 [...], 2451, 2241, 1981, 161 330
351. 4131, 4121, 4031, 3511, 3661, 337 325
401. 5491, 5551, 5531, 5441, 5281, 505 320
451. 6681, 6861, 6941, 6921, 6811, 664 315
501. 7741, 8011, 8191, 8271, 8261, 813 310
551. 8661, 9031, 9301, 9471, 9551, 953 305
601. 9411, 9902, 0282, 0542, 0712, 077 300
652. 0012, 0592, 1002, 1462, 1722, 186 295
702. 0462, 1152, 1712, 2132, 2572, 282 290
752. 0702, 1512, 2212, 2792, 3252, 359 285
802. 0742, 1702, 2492, 3192, 3782, 422 280
852. 0742, 1652, 2592, 3422, 4112, 467 275
902. 0352, 1502, 2502, 3422, 4262, 493 270
951. 9932, 1182, 2292, 3292, 4182, 498 265
1001. 9292, 0602, 1862, 3002, 3972, 487 260
1051. 8451, 9872, 1232, 2422, 3622, 463 255
1101. 7441, 8972, 0402, 1762, 3022, 414 250
1151. 6211, 7861, 9422, 0872, 2212, 347 245
1201. 4791, 6541, 8211, 9792, 1272, 259 240
1251. 3251, 5041, 6811, 8482, 0082, 155 235
1301. 1561, 3441, 5241, 6991, 8702, 000 230
1350. 9701, 16 [...]1, 3551, 5391, 7141, 881 225
1400. 7720, 9721, 1681, 3601, 5471, 722 220
1450. 5630, 7660, 9681, 1661, 3671, 547 215
1500. 3440, 5500, 7550, 9601, 1611, 355 210
1550. 1190, 3250, 5330, 7420, 9491, 149 20 [...]
1600A1070, 1970, 3040, 5150, 7261, 932 200
1650. 3370A0680, 0730, 2830, 4950, 705 195
1700. 4680, 3670A1610, 0490, 2610, 473 190
1750. 7840, 5990, 3970A1880, 0250, 238 185
1801. 0190, 8280, 6300, 4240A2140, 000 180
Equated Anomaly.SubSubSubSubSubSub Equated A­nomaly.
105102099969390 

A Compounded Table of the ☽ Evection and Variation.
Equated Anomaly.757 [...]81848790 Equated Anomaly.
 AddeAddeAddeAddeAddeAdde  
1801, 0190, 8280, 6300, 4240, 2140, 000 180
1851, 2381, 0540, 8600, 6580, 4500, 238 175
1901, 4481, 2711, 0850, 8880, 6840, 473 170
1951, 6461, 4801, 3021, 1120, 9120, 705 165
2001, 8311, 6821, 5071, 3261, 1330, 932 160
2052, 0011, 8581, 6991, 5271, 3431, 146 155
2102, 1542, 0221, 8861, 7161, 5401, 355 150
2152, 2962, 1752, 0351, 8861, 7191, 547 145
2202, 1492, 3102, 1842, 0441, 8871, 722 140
2252, 5202, 4262, 3132, 1842, 0401, 881 135
2302, 6042, 5182, 4122, 3072, 1752, 000 130
2352, 9662, 5982, 5092, 4052, 2942, 155 125
2402, 7112, 6572, 5802, 4892, 3802, 259 120
2452, 7392, 6612, 6332, 5532, 4562, 347 115
2502, 7502, 7122, 6612, 5962, 5132, 414 110
2552, 7462, 7192, 6742, 6162, 5522, 463 105
2602, 7212, 7052, 6742, 6262, 5612, 487 100
2652, 6772, 6732, 6522, 6162, 5662, 498 95
2702, 6162, 6212, 6112, 5882, 5472, 493 90
2752, 5412, 5542, 5462, 5382, 5112, 467 85
2802, 4492, 4712, 4792, 4732, 4532, 422 80
2852, 3432, 3712, 3882, 3922, 3832, 359 75
2902, 2242, 2592, 2822, 2942, 2942, 282 70
2952, 0882, 1322, 1632, 1822, 1902, 186 65
3001, 9441, 9902, 0282, 0572, 07 [...]2, 077 60
3051, 7911, 8401, 8821, 9151, 9391, 953 55
3101, 6291, 6821, 7251, 7641, 7921, 813 50
3151, 4591, 5151, 5611, 6051, 6381, 664 45
3201, 2811, 3351, 3911, 4361, 4741, 505 40
3251, 0991, 1571, 21 [...]1, 2601, 3021, 337 35
3300, 9130, 9711, 0261, 0761, 1241, 161 30
3350, 7230, 7800, 8350, 8870, 9340, 978 25
3400, 5310, 5870, 6380, 6940, 7430, 789 20
3450, 3370, 3920, 4470, 4990, 5480, 596 15
3500, 1440, 1960, 2480, 3000, 3510, 399 10
3550S0480S0000S0500S1080, 1490, 201 05
3600, 2730, 1930, 1460, 0990S0500, 000 00
Equated Anomaly.AddAddAddAddAddAdd Equated Anomaly.
 10510299969390  

A Table of the Aequations of Nodes and Moons Latitude.
  Eq: Nod: AddeScruples of prop.Latit. ☽Eccesse Adde  
  D. Parts.Parts.D. parts.Parts.  
01800. 00000, 000000, 00000, 00000180360
11810, 06389, 000300, 08694, 00556179359
21820, 12750, 001200, 17361, 01111178358
31830, 19083, 002740, 26000, 01639177357
41840, 25389, 004870, 34639, 02194176356
51850, 31667, 007600, 43278, 02750175355
61860, 37944, 010930, 51917, 03305174354
71870, 44139, 014850, 60528, 03861173353
81880, 50250, 019370, 69139, 04389172352
91890, 56305, 024470, 77722, 04917171351
101900, 62305, 030150, 86278, 05472170350
111910, 68222, 036410, 94806, 06000169 [...]49
121920, 74056, 043231, 03972, 06528168348
131930, 79778, 050601, 11778, 07083167347
141940, 85389, 058531, 20222, 07611166346
151950, 90889, 066991, 28611, 08139165345
161960, 96307, 075981, [...]6972, 08694164344
171971, 01556, 085481, 45278, 09222163343
181981, 06 [...]67, 095491, 53556, 09750162342
191991, 11639, 105991, 61778, 10278161341
202001, 16472, 116981, 69944, 10778160340
212011, 21167, 128431, 78083, 11305159339
222021, 25694, 140331, 86139, 11833158338
232031, 30056, 152671, 94167, 12333157337
242041, 34250, 1654 [...]2, 02139, 12833156336
252051, 38944, 178612, 10028, 13333155335
262061, 42111, 192172, 17861, 13833154334
272071, 45778, 206112, 25639, 14 [...]06153333
282081, 39278, 222872, 33333, 14806152332
292091, 52611, 235042, 40944, 15306151331
302101, 55778, 250002, 48500, 15778150330
[Page 52]302101. 55778, 250002, 48500, 15778150330
312111, 58667, 265262, 56000, 16250149329
322121, 61306, 280812, 63417, 16722148328
332131, 63667, 296632, 70722, 17 [...]67147327
342141, 65861, 312702, 77944, 17639146326
352151, 67833, 328992, 85111, 18083145325
362161, 69583, 345492, 92194, 18528144324
372171, 71222, 362182, 99167, 18972143323
382181, 72722, 379043, 06056, 19417142322
392191, 74139, 396403, 12861, 19861141321
402201, 75222, 413183, 19556, 20306140320
412211, 75944, 430413, 26167, 20732139319
422221, 76389, 447743, 32667, 21139138318
432231, 76556, 465123, 39056, 21556137317
442241, 76639, 482553, 45361, 21944136316
452251, 76667, 500003, 51564, 22346135315
462261, 76472, 517443, 57639, 22722134314
472271, 76000, 534873, 63611, 23111133313
482281, 75361, 552263, 69500, 23472132312
492291, 74472, 569533, 75194, 23833131311
502301, 733 [...]3, 586823, 80833, 24194130310
512311, 71944, 603953, 86444, 24556129309
522321, 70389, 620963, 91917, 24917128308
532331, 68611, 637813, 97194, 25250127307
542341, 66639, 654514, 02306, 25583126306
552351, 64500, 671014, 07333, 25917125305
562361, 62167, 687304, 12250, 26194124304
572371, 59611, 703364, 17083, 26500123303
582381, 56889, 719184, 21806, 26806120302
592391, 5397 [...], 7347 [...]4, 26306, 27083101301
602401, 50889, 750004, 30722, 27361120300
[Page 53]602401, 50889, 750004, 30722, 27361120300
612411, 47611, 764964, 34972, 27639119299
622421, 44167, 779594, 39111, 27917118298
632431, 40583, 793894, 43139, 28194117297
642441, 36833, 807834, 47028, 28444116296
652451, 32917, 824394, 50778, 28667115295
662461, 28833, 834564, 54389, 28889114294
672471, 24667, 847324, 57861, 29111113293
682481, 20250, 859674, 61194, 29333112292
692491, 15750, 871524, 64389, 29528111291
702501, 11139, 883024, 67417, 29750110290
712511, 06361, 894004, 70306, 29944109289
722521, 01417, 904504, 73056, 30139108288
732530, 96389, 914514, 75639, 30333107287
742540, 91306, 924024, 78111, 30500106286
752550, 86167, 933014, 80500, 30639105285
762560, 80889, 941474, 32639, 30750104284
772570, 75500, 949394, 84694, 30861103283
782580, 70000, 951774, 86611, 30944102282
792590, 64444, 963594, 88333, 31056101281
802600, 58833, 969844, 89917, 31167100280
812610, 53139, 975524, 91 [...]61, 3125099279
822620, 47389, 980634, 92667, 3133398278
832630, 41583, 985144, 9 [...]806, 3141797277
842640, 35722, 989074, 94778, 3147296276
852650, 29833, 992404, 95611, 3152895275
862660, 23917, 995134, 96278, 3155694274
872670, 17944, 997264, 96833, 3158393273
882680, 11972, 998784, 97167, 3161192272
892690, 06000, 999644, 97389, 3163991271
902700, 00000, 000004, 97500, 3166790270
  Subst.     

A Table of the Moons Reductions to the Ecliptick.
  Reduct. Subst.  
  D. parts.  
0180, 00000180360
1181, 00417179359
2182, 00833178358
3183, 01250177357
4184, 01639176356
5185, 02028175355
6186, 02417174354
7187, 02833173353
8188, 03222172352
9189, 03611171351
10190, 04000170350
11191, 04389169349
12192, 04778168348
13193, 05 [...]67167347
14194, 05528166346
15195, 05889165345
16196, 06194164344
17197, 06556163343
18198, 06 [...]89162342
19199, 07194161341
20200, 07500160340
21201, 07806159339
22202, 08111158338
23203, 08389157337
24204, 08694156336
25205, 08944155335
26206, 09194154334
27207, 09444153333
28208, 09694152332
29209, 09944151331
[...]0210, 10278150330
30210, 10167150330
31211, 10333149329
32212, 10500148328
33213, 10667147327
34214, 10806146326
35215, 10972145325
36216, 11111144324
37217, 11222143323
38218, 11306142322
39219, 11417141321
40220, 11500140320
41221, 11556139219
42222, 11583138318
43223, 11611137317
44224, 11639136316
45225, 11667135315
46226, 11639134314
47227, 11611133313
48228, 11583132212
49229, 11556131311
50230, 11500130310
51231, 11417129309
52232, 11306128308
53233, 11222127307
54234, 11111126306
55235, 10972125305
56236, 10778124304
57237, 1063912 [...]303
58238, 10472122302
59239, 10306121391
60240, 10139120300
[Page 55]60240, 10139120300
61241, 09917119299
62242, 09667118298
63243, 09417117297
64244, 09167116296
65245, 08917115295
66246, 08667114294
67247, 08361113293
68248, 08083112292
69249, 07778111291
70250, 07472110290
71251, 07167109289
72252, 06833108288
73253, 06528107287
74254, 06167106286
75255, 05861105285
76256, 05500104284
77257, 05139103283
78258, 04750102282
79259, 04389101281
80260, 03972100280
81261, 0358399279
82262, 0319498278
83263, 0280697277
84264, 0238996276
85265, 0200095275
86266, 0161194274
87267, 0125093273
88268, 0083392272
89269, 0041791271
90270, 0000090270
  Adde  

The difference of the true ☌ or ☍ from the middle of the Obscuration.
Lat. ☽Differ.
D. parParts.
0, 10, 00861
0, 20, 01722
0, 30, 02611
0, 40, 03500
0, 50, 04361
0, 60, 05222
0, 70, 06083
0, 80, 06972
0, 90, 07833
1, 00, 08722
1, 10, 09583
1, 20, 10472
1, 30, 11361
1, 40, 12222
1, 50, 13083
1, 60, 13944
Latitude. ☽
  • North Desc. Adde
  • South Asc. Adde
  • North Asc. Subst.
  • South Desc. Subst.
A Table of the Meane Lunations.
YeersHours: PartsMonths.Common.Bissextile.DaiesHours
1255, 18944complea.Hours: parts.Hours: Parts.
2510, 37889January0035, 265560035, 26556124
3056, 83417Februa.0707, 265560022, 531 [...]9248
B4336, 02361March.0043, 7972 [...]0057 79722372
5591, 21306April.0045, 063060069, 06306496
6137, 66833May.0080, 328890104, 328895120
7392, 85778June.0091, 594720115, 594726144
B8673, 04722July.0126, 860280150, 860287168
9218, 50250August0162, 126110186, 126118192
10473, 69194Septem.0173, 391940197, 391949216
11020, 14722October0208, 657780232, 6577810240
B12299, 33667Novem0219, 923610243, 9236111264
13554, 52611Decem.0255, 189440279, 1894412288
14100, 98139   13312
15356, 17083Canonion Syzygiarum.14336
B16635, 36028 15360
17181, 81556   16384
18437, 00500 Hours: PartsHours: Parts.17408
19692, 19444I0708, 734170354, 3672218432
B20262, 64972II1417, 468331063, 1013919456
40525, 29944III2126, 202501771, 8355620480
60079, 21528IV2834, 036672480, 5697221504
80341, 86500V3543, 670833189, 3036122528
100604, 51472VI4252, 405003898, 0380623552
200500, 29556VII4961, 139444606, 7722224576
300396, 07639VIII5669, 873615315, 5066725600
400291, 85694   26624
500187, 63778Epochae.27648
600083, 41861Yeares Compleat.Hours: Parts.28672
700687, 93361   29696
800583, 71417 Christi.0425, 7066730720
900479, 49500 16000176, 06694  
1000375, 27583 16200439, 31667  
2000041, 81750 16400701, 96639  
3000417, 09333 16600255, 88194  

The Horizontal Parallaxes, Semidiameters, and Hourly motions of the Sun and Moon.
DegreesHoriz. Paral. ☉Semi­diam. ☉Hourly motion. ☉Semia. Cone Shad.Horizō. Paralax. ☽Semi­diam. ☽Hourly motion ☽Degrees
 Parts.Parts.Parts.Parts.Parts.Parts.Parts. 
0, 03855, 26936, 03972, 22948, 92692. 25964, 49444360
6, 03859, 26968, 03981, 22980, 92982. 26043, 49916354
12, 03863, 27001, 03990, 23013, 93273. 26122, 50388348
18, 03868, 27033, 03999, 23046, 93564. 26201, 50860342
24, 03872, 27066, 04008, 23078, 93854. 26280, 51332336
30, 03876, 27099, 04017, 23111, 94145. 26359, 51804330
36, 03881, 27131, 04026, 2 [...]144, 94436. 26438, 52276324
42, 03885, 27164, 04035, 23176, 94727. 26517, 52748318
48, 03889, 27196, 04044, 23209, 95018. 26596, 53220312
54, 03894, 27239, 04052, 23242, 95308. 26679, 53682306
60, 03898, 27271, 04061, 23274, 95599. 26754, 54164300
66, 03902, 27304, 04070, 23307, 95889. 26833, 54636294
72, 03907, 27337, 04079, 23340, 96180. 26912, 55108288
78, 03911, 27369, 04088, 23372, 96471. 26991, 55581282
84, 03915, 27401, 04097, 23405, 96762. 27069, 55953276
90, 03919, 27433, 04106, 23438, 97052. 27148, 56425270
96, 03924, 27466, 04115, 23470, 97343. 27227, 56897264
102, 03928, 27498, 04124, 23503, 97634. 27306, 57369258
108, 03932, 27531, 04132, 23536, 97925. 27385, 57841252
114, 03937, 27564, 04141, 23568, 98215. 27464, 58313246
120, 03941, [...]7596, 04150, 23601, 98506. 27543, 58785240
126, 03945, 27629, 04159, 23634, 98797. 27622, 59257234
132, 03950, 27661, 04168, 23666, 99087. 27701, 59729228
138, 03954, 27694, 04177, 23699, 99378. 27780, 60201222
144, 03958, 27727, 04186, 23732, 99669. 27859, 60673216
150, 03963, 27759, 04195, 23764, 99960. 27938, 61145210
156, 03967, 27792, 04204, 237971, 00250. 28017, 616172 [...]4
162, 03971, 27824, 04213, 238301, 00541. 28096, 62089198
168, 03976, 27857, 04222, 238631, 00832. 28175, 62461192
174, 03981, 27889, 04231, 238961, 01123. 28254, 6 [...]933186
180, 03988, [...]7916, 04250, 239281, 01414. 28333, [...]3611180
Dist▪43293329179472erēc

The Declination and Meridian Angles.
  
 Declina.Ang.Declina.Ang.Declina.Ang. 
 D. partsD. P.D. Parts.D. P.D. Parts.D. P. 
00, 0000066. 4711, 5116769, 3320, 2227877. 7030
10, 3988966. 4711, 8633369, 5220, 4391778. 0729
20, 7980656. 4812, 2111169, 7220, 6358378. 4328
31, 1969466. 5012, 5558369, 9220, 8327878. 8027
41, 5952866. 5212, 8969470, 1321, 0236179. 1826
51, 9936166. 5513, 2347270, 3521, 2080679. 5725
62, 3911166. 5813, 5686170, 5821, 3852879. 9524
72, 7877866. 6313, 8991770, 8121, 5561180. 3323
83, 1844466. 6814, 2255671, 0521, 7208380. 7222
93, 5797266. 7314, 5480671, 3021, 8783381. 1221
103, 9744466. 7814, 8663971, 5522, 0291781. 5120
114, 3677866. 8515, 1805671, 8022, 1727881. 9219
124, 7602866. 9215, 4905672, 0722, 3097282. 3118
135, 1513967. 0015, 7963972, 3322, 4394482. 7317
145, 5413967. 0816, 0975072, 6022, 5622283. 1516
155, 9297267, 1816, 3941772, 8822, 6775083. 5715
166, 3161167. 2816, 6886173, 1722, 7861183. 9814
176, 7016767. 4016, 9727873, 4522, 8869484. 4013
187, 0850067. 5217, 2550073, 7522, 9808384. 8312
197, 4666767. 6317, 5316774, 0523, 0675085. 2511
207, 8461167. 7517, 8038974, 3523, 1463985. 6810
218, 2238967. 8818, 0705674, 6723, 2180686. 1009
228, 5994468. 0218, 3325074, 9823, 2822286. 5308
238, 9722268. 1518, 5883375, 3023, 3388986. 9707
249, 3427868. 3018, 8391775, 6323, 3883387. 4006
259, 7113968. 4719, 0844475, 9723, 4300 [...]87. 8305
2610, 0772268. 6319, 3238976, 3023, 4641788. 2604
2710, 4400068. 8019, 5575076, 6523, 4908388. 7003
2810, 8005668. 9719, 7852877, 0023, 5097289. 1302
2911, 1575069. 1520, 0072277, 3523, 5213989. 5701
3011, 5116769. 3320, 2227877, 7023, 5250090. 0000
  

Tycho's Table of Refractions.
Altitude✴ ✴
 Parts.Parts.Parts.
0, 56667, 55000, 50000
1, 43333, 41667, 35833
2, 33333, 33333, 25833
3, 28333, 28333, 20833
4, 25833, 25556, 18333
5, 24167, 23889, 16667
6, 22500, 23056, 15000
7, 21250, 21250, 13750
8, 18750, 20000, 11250
9, 17500, 18889, 10000
10, 16667, 17917, 09167
11, 15833, 16944, 08333
12, 15000, 15972, 07500
13, 14167, 15000, 06667
14, 13333, 14167, 05833
15, 12500, 13333, 05000
16, 11667, 12500, 04167
17, 10833, 11667, 03333
18, 09583, 10833, 02083
19, 08333, 10000, 00833
20, 07500, 09167, 00000
21, 06667, 08333, 00000
22, 05833, 07639, 00000
23, 05278, 06944 
24, 04722, 06250 
25, 04167, 05556 
26, 03750, 05000 
27, 03333, 04444 
28, 02917, 03889 
29, 02639, 03333 
30, 02361, 02778 
31, 02083, 02500 
32, 01806, 0222 [...] 
33, 01528, 01944 
34, 01250, 01667 
35, 00972, 01389 
36, 00833, 01250 
37, 00694, 01111 
38, 00556, 00972 
39, 00417, 00833 
40, 00278, 00694 
41, 00250, 00556 
42, 00222, 00417 
43, 00194, 00278 
44, 00167, 00139 
45, 00139, 00000 

Saturns Mean Motions.
EpochaeLongit. ♄Apheliō. ♄Node ♄
Deg. partsDeg. partsDeg. Parts.
Christi.73. 13056215. 2572298. 98861
1600208. 43944265. 99722110. 51389
162093. 13083266. 63139110. 65778
1640337. 81722267. 26583110. 80194
1660222. 50111267. 88333110. 94583
112. 226110. 031670. 00722
224. 452500. 063330. 01444
336. 678610. 095000. 02167
B 448. 938330. 126940. 02889
561. 164440. 158610. 03611
673. 390560. 190780. 04306
785. 616940. 221940. 05028
B 897. 876670. 253610. 05750
9110. 102780. 285280. 06472
10122. 328890. 316940. 07194
11134. 555000. 348890. 07917
B 12146. 814720. 380560. 08639
13159. 041110. 412220. 09361
14171. 267220. 443890. 10083
15183. 493330. 475560. 10806
B 16195. 753060. 507220. 11528
17207. 979170. 539170. 12250
18220. 205560. 570830. 12944
19232. 431670. 602500. 13667
B 20244. 691390. 634170. 14389
40129. 382781 268610. 28806
6014. 074171. 902780. 43222
80258. 765282. 536940. 57611
100143. 456673. 171110. 72028

Saturns mean Motions.
Years.Longit. ♄Aphel. ♄Node ♄
Deg. parts.Deg. parts.Deg. parts.
100143, 456673, 271110, 72028
200286, 913616, 342501, 44056
30080, 370569, 513612, 16111
40021 [...], 8272212, 685002, 88139
500357, 2841715, 856113, 60 67
600140, 7408319, 027504, 32194
700284, 1977822, 198615, 04222
80067, 6544425, 370015, 76278
900211, 1113928, 54116, 48306
1000354, 5608631, 712507, 20333
2000349, 1363963, 4250014, 40667
3000343, 7044495, 1375021, 61000
4000338, 27278126, 8500028, 81333
5000332, 84083158, 5625036, 01667

January1, 038330, 002780, 00056
February1, 976390, 005280 00139
March3, 014720, 007780, 00194
April4, 019440, 010280, 00250
May5, 058060, 013330, 00333
June6, 062780, 015560, 00389
July7, 101110, 018330, 00444
August8, 139720, 021390, 00500
September9, 144440, 023610, 00556
October10, 182780, 026390, 00611
November11, 187780, 029170, 00667
December12, 226110, 031670, 00722

Saturns Mean Motions.
In Daies. In Hours.
 Long. ♄Aphel. ♄N [...]d. ♄    Long. ♄
 D. partsParts.Parts.    Parts.
10, 03361, 00000, 00002   1, 00139
20, 06694, 00000, 00003   2, 00278
30, 10056, 00028, 00005   3, 00417
40, 13389, 00028, 00007   4, 00556
50, 16750, 00056, 00009   5, 00694
60, 20111, 00056, 00011   6, 00833
70, 23444, 00056, 00013   7, 00972
80, 26806, 00083, 00015   8, 01111
90, 30139, 00083, 00017   9, 01250
100, 33500, 00083, 00019   10, 01389
110, 36861, 00111, 00020   11, 01528
120, 40194, 00111, 00022   12, 01667
130, 43556, 00111, 00024   13, 01806
140, 46889, 00139, 00026   14, 01944
150, 50250, 00139, 00028   15, 02083
160, 53583, 00139, 00030   16, 02222
170, 56944, 00167, 00032   17, 02361
180, 60306, 00167, 00034   18, 02500
190, 63639, 00167, 00036   1902639
200, 67000, 00194, 00038   20, 02778
210, 70333, 00194, 00040   21, 02917
220, 73694, 00194, 00041   22, 03083
230, 77056, 00222, 00042   23, 03222
240, 80389, 00222, 00043   24, 03361
250, 83750, 00222, 00045     
260, 87083, 00250, 00047     
270, 90444, 00250, 00049     
280, 93806, 00250, 00051     
290, 97139, 00278, 00053     
301, 00500, 00278, 00055     
311, 03833, 00278, 00057     
321, 07194, 00306, 00059     

Saturn's mean Motions in the parts of an Hour.
 Long. ♄
 Parts.
1, 00001
2, 00002
300004
4, 00005
5, 00006
6, 00008
7, 00009
8, 00011
9, 00012
10, 00013
11, 00015
12, 00016
13, 00018
14, 00019
15, 00020
16, 00022
17, 00023
18, 00025
19, 00026
20, 00027
21, 00029
22, 00030
23, 00032
24, 00033
25, 00035
26, 00036
27, 00037
28, 00039
29, 00040
30, 00042
31, 00043
32, 00044
33, 00046
34, 00047
35, 00048
36, 00050
37, 00051
38, 00052
39, 00054
40, 00055
41, 00056
42, 00058
43, 00059
44, 00061
45, 00062
46, 00063
47, 00065
48, 00066
49, 00068
50, 00069
51, 00070
52, 00072
53, 00074
54, 00075
55, 00076
56, 00078
57, 00079
58, 00081
59, 00082
60, 00083
61, 00085
62, 00086
63, 00087
64, 00089
65, 00090
66, 00091
67, 00093
68, 00094
69, 00095
70, 00097
71, 00098
72, 00099
73, 00101
74, 00102
75, 00103
76, 00105
77, 00106
78, 00107
79, 00109
80, 00111
81, 00112
82, 00113
83, 00115
84, 00116
85, 00118
86, 00119
87, 00120
88, 00122
89, 00123
90, 00125
91, 00126
92, 00127
93, 00129
94, 00130
95, 00131
96, 00133
97, 00134
98, 00136
99, 00137

Jupiter's mean Motions.
EpochaeLongit. ♃Aphel. ♃Node ♃
 Deg. parts.Deg. Parts.Deg. Parts.
Christi.179, 91583148, 4238987, 67722
1600160, 80556188, 0233398, 62306
162048, 06667188, 5183398, 76000
1640295, 32778189, 0133398, 89667
1660182, 58889189, 5083399, 03333
130, 342220, 024720, 00694
260, 684440, 049440, 01361
391, 026670, 074170, 02056
B 4121, 452220, 098890, 02722
5151, 794440, 123610, 03417
6182, 136670, 148330, 04111
7212, 478890, 173330, 04778
B 8242, 904440, 198060, 05472
9273, 246670, 222780, 06167
10303, 588890, 247500, 06833
11333, 931390, 272220, 07528
B 124, 356670, 296940, 08194
1334, 698890, 321670, 08889
1465, 041110, 346390, 09583
1595, 383610, 371110, 10250
B 16125, 808890, 396110, 10944
17156, 151110, 420830, 11639
18186, 493610, 445560, 12306
19216, 835830, 470280, 13000
B 20247, 261110, 495000, 13694
40134, 522220, 990000, 27361
6021, 783331, 485000, 41056
80269, 044441, 980000, 54722
100156, 305562, 475000, 68417

Jupiters mean Motions.
Years.Longit. ♃Aphelion. ♃Node. ♃
 Deg. parts.Deg. Parts.Deg. Parts.
100156, 305562, 475000, 68417
200312, 611114, 950001, 36833
300108, 916947, 425002▪05222
400265, 222509, 899722, 73639
50061, 5280612, 374723, 42056
600217, 8336114, 849724, 10472
70014, 1394417, 324724, 78861
800170, 4450019, 799725, 47278
900326, 7505622, 274726, 15694
1000123, 0561124, 749726, 84111
2000246, 1125049, 4997213, 68222
30009, 1686174, 2488920, 52306
4000132, 2250098, 9983327, 36417
5000255, 28111123, 7480634, 20500

January.2. 576940, 001940, 00056
February.4. 904720, 004170, 00111
March.7. 481670, 006110, 00167
April.9. 975560, 008060, 00222
May.12. 552500, 010280, 00278
June.15. 046390, 012220, 00333
July.17. 623330, 014440, 00389
August.20. 200560, 016670, 00444
Septemb.22. 694440, 018610, 00500
October.25. 271390, 020830, 00556
Novemb.27. 765280, 022780, 00611
Decemb.30. 342220, 024720, 00694

Jupiter's mean Motions.
In Dayes. In Hours.
 Long. ♃Aphel. ♃Nod. ♃  Long. ♃
 D. partsParts.Parts.  Parts.
10, 08306, 00006, 00002 1, 00333
20, 16611, 00013, 00003 2, 00722
30, 24944, 00020, 00005 3, 01028
40, 33250, 00026, 00007 4, 01389
50, 41556, 00033, 00009 5, 01722
60, 49861, 00039, 00011 6, 02083
70, 58194, 00046, 00013 7, 02417
80, 66500, 00053, 00015 8, 02722
90, 74816, 00059, 00017 9, 03111
100, 83141, 00066, 00019 10, 03472
110, 914 [...]4, 00072, 00020 11, 03806
120, 99750, 00079, 00022 12, 04167
131, 08056, 00085, 00024 13, 04500
141, 16361, 00091, 00026 14, 04861
151, 24694, 00098, 00028 15, 05194
161, 33000, 00104, 00030 16, 05556
171, 41306, 00111, 00032 17, 05889
181, 49611, 00117, 00034 18, 06222
191, 57944, 00123, 00036 19▪ 06583
201, 66250, 00130, 00038 20, 06917
211, 74556, 00136, 00039 21, 07278
221, 82861, 00142, 00041 22, 07611
231, 91194, 00149, 00043 23, 07972
241, 99500, 00155, 00045 24, 08306
252, 07806, 00162, 00047   
262, 16111, 00168, 00049   
272, 24444, 00174, 00051   
282, 32750, 00181, 00053   
292, 41056, 00197, 00055   
302, 49389, 00203, 00057   
312, 57694, 00 [...]09, 00059   
32 [...], 66000, 00216, 00061   

Jupiters mean Motions in the parts of an Hour.
Long. ♃
Parts.
1, 00003
2, 00007
3, 00010
4, 00013
5, 00017
6, 00020
7, 00024
8, 00027
9, 00031
10, 00034
11, 00038
12, 00041
13, 00045
14, 00048
15, 00052
16, 00055
17, 00058
18, 00062
19, 00065
20, 00069
21, 0007 [...]
22, 00076
23, 00079
24, 00083
25, 00086
26, 00090
27, 00093
28, 00097
29, 0010 [...]
30, 00104
31, 00107
32, 00111
33, 00114
34, 00117
35, 00121
36, 00124
37, 00128
38, 00131
39, 00135
40, 00138
41, 00142
42, 00145
43, 00149
44, 00152
45, 00156
46, 00159
47, 00162
48, 00166
49, 00169
50, 00173
51, 00176
52, 00180
53, 00183
54, 00187
55, 00190
56, 00194
57, 00197
58, 00201
59, 00204
60, 00208
61, 00211
62, 00214
63, 00218
64, 00221
65, 00225
66, 00228
67, 00232
68, 00235
69, 00238
70, 00241
71, 00245
72, 00248
73, 00251
74, 00255
75, 00258
76, 00262
77, 00265
78, 00269
79, 00272
80, 00276
81, 00279
82, 00283
83, 00286
84, 00290
85, 00293
86, 00297
87, 00300
88, 00303
89, 00307
90, 00311
91, 00314
92, 00318
93, 00321
94, 00325
95, 00328
56, 00332
97, 00335
98, 00339
99, 00342

The Mean Motions of Mars.
EpochaeLongit. ♂Apheliō. ♂Node ♂
 Deg. partsDeg. partsDeg. Parts.
Christi.40. 71611113. 9708325. 30583
1600307. 27611148. 9983346. 74222
1620175. 60778149. 4361147. 01028
164043. 94000149. 8738947. 27806
1660272. 27194150. 2116747. 54639
1191. 285560. 021940. 01333
222. 571110. 043890. 02667
3213. 856670. 065560. 04028
B 445. 666390. 087500. 05361
5236. 951670. 109440. 06694
668. 237500. 131390. 08028
7259. 522780. 153060. 09361
B 891. 332780. 175000. 10722
9282. 618330. 197220. 12056
10113. 903890. 218890. 13389
11305. 189440. 240560. 14722
B 12136. 999170. 262500. 16056
13328. 284720. 284440. 17417
14159. 570280. 306390. 18778
15350. 855830. 328060. 20111
B 16182. 665560. 350280. 21444
1713. 951110. 372220. 22778
18205. 236670. 394170. 24139
1936. 522220. 415830. 25472
B 20228. 331940. 437780. 26806
4096. 663890. 475560. 53583
60324. 99 [...]111. 313330. 80389
80193. 327781. 751391. 07194
10061. 660002. 189171. 33972

The mean Motions of Mars.
Years.Longit. ♂Aphel. ♂Node ♂
 Deg. parts.Deg. parts.Deg: parts.
10061, 660002, 189171, 17306
200123, 320004, 378332, 67944
300184, 980006, 567784, 01944
400246, 640008, 756945, 35917
500308, 3000010, 946116, 69889
6009, 9600013, 135288, 03861
70071, 6200015, 324449, 37833
800133, 2800017, 5136110, 71806
900194, 9400019, 7030612, 05806
1000256, 6000021, 8922213, 39778
2000153, 2002843, 7844426, 79528
300049, 8002865, 6763940, 19306
4000306, 400568 [...], 5688953, 59056
5000203, 00056109, 4608366, 98833

January16, 246110, 001940, 00111
February30, 920280, 003610, 00222
March47, 166390, 005560, 00333
April62, 888330, 007220, 00444
May79, 134720, 009170, 00556
June94, 856670, 010830, 00667
July111, 103060, 012500, 00778
August127, 349170, 014440, 00889
September143, 071110, 016390, 01000
October159, 317500, 018330, 01111
November175, 039440, 020280, 01222
December191, 285560, 021940, 01333

The mean Motions of Mars.
In Dayes. In Hours.
 Long. ♂Apha. ♂Node ♂  Long. ♂
 D. Parts.Parts.Parts.  Parts.
10, 52417. 00006, 00003 1, 02194
21, 04806, 00012, 00007 2, 04361
31, 57222, 00018, 00010 3, 06556
42, 09611, 00024, 00014 4, 08722
52, 62111, 00030, 00018 5, 10917
63, 14444, 00036, 00021 6, 13111
73, 66833, 00042, 00025 7, 15278
84, 19250, 00048, 00028 8, 17472
94, 71667, 00054, 00032 9, 19667
105, 24083, 00060, 00036 10, 21833
115, 76472, 00066, 00039 11, 24028
126, 28889, 00072, 00043 12, 26194
136, 81278, 00078, 00046 13, 28389
147, 33694, 00084, 00050 14, 30583
157, 86111, 00090, 00054 15, 32750
168, 38500, 00096, 00057 16, 34944
178, 90917, 00102, 00061 17, 37111
189, 43333, 00108, 00064 18, 39306
199, 95750, 00114, 00068 19, 41500
2010, 48139, 00120, 00072 20, 43667
2111, 00556, 00126, 00075 21, 45861
2211, 52944, 00132, 00079 22, 48028
2312, 05361, 00138, 00082 23, 50222
2412, 57778, 00144, 00086 24, 52417
2513, 10167, 00150, 00090   
2613, 62583, 00156, 00093   
2714, 15000, 00162, 00097   
2814, 67417, 00168, 00100   
2915, 19861, 00174, 00104   
3015, 72222, 00180, 00108   
3116, 24611, 00186, 00111   
3216, 77028, 00192, 00115   

The mean Motions of Mars in parts of an Hour.
 Long. ♂
 Parts.
1, 00022
2, 00043
3, 00065
4, 00087
5, 00109
6, 00131
7, 00152
8, 00174
9, 00196
10, 002 [...]8
11, 00240
12, 00262
13, 00284
14, 00306
15, 00327
16, 00349
17, 00371
18, 00393
19, 00415
20, 00436
21, 00458
22, 00480
23, 00502
24, 00524
25, 00545
26, 00567
27, 00589
28, 00611
29, 00633
30, 00655
31, 00676
32, 00698
33, 00720
34, 00742
35, 00764
36, 00785
37, 00807
38, 00829
39, 00851
40, 00873
41, 00894
42, 00916
43, 00938
44, 00960
45, 00982
46, 01003
47, 01025
48, 01047
49, 01069
50, 01091
51, 01112
52, 01134
53, 01156
54, 01178
55, 01200
56, 01221
57, 01243
58, 01265
59, 01287
60, 01309
61, 01330
62, 01352
63, 01374
64, 01396
65, 01418
66, 01439
67, 01461
68, 01483
69, 01505
70, 01527
71, 01548
72, 01570
73, 01592
74, 01614
75, 01636
76, 01657
77, 01679
78, 01701
79, 01723
80, 01746
81, 01768
82, 01789
83, 01811
84, 01833
85, 01855
86, 01877
87, 01898
88, 01920
89, 01942
90, 01966
91, 01988
92, 02009
93, 02031
94, 02053
95, 02075
56, 02097
97, 02118
98, 02140
99, 02162

The mean Motions of Venus.
EpochaeLongit. ♀Aphel. ♀Node ♀
 Deg. parts.Deg. Parts.Deg. Parts.
Christi.42, 77917282, 8455660, 72111
1600352, 47278305, 3850074, 12722
1620176, 34389305, 6666774, 29472
16400, 21500305, 9483374, 46222
1660184, 08611306, 2300074, 62972
1224, 793060, 014170. 00833
289, 586110, 028060, 01667
3324, 379170, 042220, 02500
B 4180, 774170, 056390, 03361
545, 567220, 070280, 04194
6270, 360280, 084440, 05028
7135, 153330, 098610, 05861
B 81, 548330, 112500, 06694
9226, 341390, 126670, 07528
1091, 134440, 140830, 08361
11315, 927500, 154720, 09222
B 12182, 322780, 168890, 10056
1347, 115830, 183060; 10889
14271, 908610, 197220, 11722
15136, 701670, 211110, 12556
B 163, 096940, 225280 13389
17227, 890000, 239440, 14222
1892, 683060, 253330, 15083
19317, 476110, 267500, 15917
B 20183, 871110, 281670, 16750
407, 742220, 563610, 33528
60191, 613610, 845288, 50278
8015, 484721, 126940, 67028
100199, 355831, 408610, 83778

The mean Motions of Venus.
Years.Longit. ♀Aphelion. ♀Node. ♀
 Deg. parts.Deg. Parts.Deg. Parts.
100199, 355831, 408610, 83778
20038, 711672, 817501, 67583
300238, 067504, 226112, 51361
40077, 423335, 635002, 35167
500276, 779177, 043614, 18944
600116, 135008, 452225, 02750
700315, 490839, 861115, 86528
800154, 8463911, 269726, 70333
900354, 2025012, 678337, 54111
1000193, 5583314, 087228, 37889
200027, 1163928, 1744416, 75778
3000220, 6747242, 8613928, 13694
400054, 2327846, 3488933, 51611
5000247, 7911161, 4358341, 89500

January.49. 667500, 001110, 00083
February.94. 528330, 002220, 00139
March.144. 195560, 003610, 00222
April.192. 260830, 004720, 00278
May.241. 928330, 005830, 00361
June.289. 993610, 006940, 00417
July.339. 658330, 008060, 00500
August.29. 328330, 009170, 00556
Septemb.77. 393610, 010560, 00611
October.127. 060830, 011670, 00694
Novemb.171. 126110, 012780, 00750
Decemb.224. 793060, 014170, 00833

The mean Motions of Venus.
In Dayes. In Hours.
 Long. ♀Aphel. ♀Node ♀  Long. ♀
 D. Parts.Parts.Parts.  Parts.
11, 6022 [...], 00004, 00002 10, 06667
23, 20444, 00007, 00004 20, 13361
34, 80639, 00011, 00006 30, 20028
46, 40861, 00015, 00009 40, 26722
58, 01083, 00019, 00011 50, 33389
69, 61306, 00023, 00013 60, 40056
710, 21528, 00027, 00016 70, 46750
812, 81750, 00031, 00018 80, 53417
914, 41944, 00035, 00020 90, 60083
1016, 02167, 00038, 00023 100, 66778
1117, 62389, 00042, 00025 110, 73444
1219, 22611, 00046, 00027 120, 80139
1320, 8 [...]833, 00050, 00030 130, 86806
1422, 43056, 00054, 00032 140, 93472
1524, 03250, 00058, 00034 151, 00167
1625, 63472, 00062, 00037 161, 06833
1727, 23694, 00066, 00039 171, 13500
1828, 83917, 00069, 00041 181, 20194
1930, 44139, 00073, 00044 191, 26861
2032, 04361, 00077, 00046 201, 33556
2133, 64556, 00081, 00048 211, 40222
2235, 24778, 00085, 00051 221, 46889
2336, 85000, 00089, 00053 231, 53583
2438, 45222, 00093, 00055 241, 60250
2540, 05444, 00097, 00058   
2641, 65639, 00100, 00060   
2743, 25861, 00104, 00062   
2844, 86083, 00108, 00065   
2946, 4630 [...], 00112, 00067   
3048, 06528, 00116, 00069   
3149, 66750, 00120, 00072   
3251, 26972, 00124, 00074   

The mean Motions of Venus in parts of an Hour.
 Long. ♀
 Parts.
1, 00067
2, 00133
3, 00200
4, 00267
5, 00334
6, 00401
7, 00468
8, 00534
9, 00601
10, 00667
11, 00734
1200801
13, 00868
14, 00935
15, 01002
16, 01068
17, 01135
18, 01202
19, 01268
20, 01335
21, 01402
22, 01469
23, 01536
24, 01603
25, 01669
26, 01736
27, 01803
28, 01869
29, 01936
30, 02003
31, 02070
32, 02137
33, 02204
34, 02270
35, 02337
36, 02404
37, 02470
38, 02537
39, 02604
40, 02671
41, 02738
42, 02805
43, 02871
44, 02938
45, 03005
46, 03071
47, 03138
48, 03205
49, 03272
50, 03339
51, 03406
52, 03472
53, 03539
54, 03606
55, 03672
56, 03739
57, 03806
58, 03873
59, 03940
60, 04007
61, 04073
62, 04140
63, 04207
64, 04273
65, 04340
66, 04407
67, 04474
68, 04541
69, 04608
70, 04674
71, 04741
72, 04808
73, 04874
74, 04941
75, 05008
76, 05075
77, 05142
78, 05209
79, 05276
80, 05342
81, 05408
82, 05475
83, 05542
84, 05609
85, 05676
86, 05743
87, 05810
88, 05876
89, 05943
90, 06009
91, 06076
92, 06143
93, 06210
94, 06277
95, 06344
96, 06410
97, 06477
98, 06544
99, 06610

Mercuries mean Motion.
EpochaeLongit. ☿Apheliō. ☿Node ☿
Deg. partsDeg. partsDeg. Parts.
Christi.316. 26111205. 31361000. 0 [...]000
160066. 95583251. 6302842. 51139
162081. 83944252. 2061143. 04250
164096. 72306252. 7880643. 57361
1660111. 6 [...]694253. 3502844. 10472
153. 721110. 028890. 02667
2107. 442220. 057780. 05306
3161. 163330. 086670. 07972
B 4218. 976670. 115830. 10611
5272. 697780. 144720. 13278
6326. 418890. 173610. 15917
720. 140000. 202500. 18583
B 877. 953610. 231670. 21250
9131. 674440. 260560. 23889
10185. 395560. 289440. 26556
11239. 116670. 318330. 29194
B 12296. 926940. 347500. 31861
13350. 651390. 376390. 34528
1444. 372500. 405270. 37167
1598. 093610. 434170. 39833
B 16155. 906940. 463330. 42472
17209. 628060. 492220. 45139
18263. 349170. 521110. 47778
19317. 070280. 550000. 50444
B 2014. 883610. 578890. 53111
4029. 767221. 157781. 06194
6044. 650831. 736671. 59306
8059. 534722. 316112. 12417
10074. 418332. 894722. 65500

Mercuries mean Motions
Years.Longit. ☿Aphel. ☿Node ☿
Deg. parts.Deg. parts.Deg: parts.
10074, 418332, 894722, 65500
200148, 836945, 789725, 31028
300223, 255278, 684447, 96528
400297, 6736111, 5791710, 62028
50012, 0922214, 473891 [...], 27556
60086, 510 [...]617, [...]688915, 93056
700160, 9288920, 2636118, 58556
800235, [...]475023, 1583 [...]21, 24083
900309, 7825026, 0533323, 89583
100024, 18417 [...]8, 9480626, 55083
200048, 368615 [...], 896114 [...], 10194
300072, 5527886, 8441779, 65278
400096, 73694115, 79222106, 20333
5000120, 9 [...]47 [...]144, 74861132, 75472

January126, 86 [...]890, 002500, 00222
February241, 450830, 004720, 00444
March8, 314720, 007220, 00667
April131, 086390, 009720, 00861
May257, 950280, 012220, 01083
June20, 721940, 014440, 01306
July147, 585830, 016940, 01528
August274, 449720, 019170, 01778
September37, 221390, 021670, 02000
October164, 085560, 024170, 02222
November286, 857220, 026390, 02417
December53, 721390, 028890, 02667

The Mean Motions of Mars.
In Dayes.In Hours.
 Long. ☿Aphel. ☿Node. ☿ Long. ☿
 Deg. parts.Parts.Parts. Parts.
14, 09222, 00008, 0000710, 17056
28, 18472, 00015, 0001420, 34111
312, 27722, 00023, 0002130, 51167
416, [...]6944, 00031, 0002940, 68222
520, 46194, 00039, 0003650, 85250
624, 55444, 00047, 0004361, 02306
728, 64667, 00055, 0005171, 19361
832, 73917, 00063, 0005881, 36417
936, 83193, 00071, 0006591, 53472
1040, 92389, 00079, 00073101, 70528
1145, 01611, 00086, 00080111, 87556
1249, 1086 [...], 00094, 00087122, 04611
1353, 20111, 00102, 00095132, 21667
1457, 29333, 00110, 00102142, 37822
1561, 38583, 00118, 00109152, 55778
1665, 47806, 00126, 00117162, 72806
1769, 57056, 00134, 00124172, 89861
1873, 66306, 00142, 00131183 06917
1977, 75528, 00150, 00139193, 23972
2081, 84778, 00158, 00146203, 41028
2185, 94000, 00165, 00153213, 58083
2290, 03250, 00173, 00161223, 75111
2394, 12500, 00181, 00168233, 92167
2498, 21722, 00189, 00175244, 09222
25102, 30972, 00197, 00182  
26106, 40194, 00205, 00190  
27110, 49444, 00213, 00197  
28114, 58694, 00221, 00204  
29118, 67917, 00229, 00212  
30122, 77167, 00237, 00219  
31126, 86389, 00243, 00226  
32130, 95611, 00251, 00233  

Mercuries mean Motions in parts of an Hour.
 Long. ☿
 Parts.
1, 00170
2, 00341
3, 00511
4, 00682
5, 00852
6, 01023
7, 01193
8, 01364
9, 01534
10, 01705
11, 01875
12, 02046
13, 02217
14, 02387
15, 02557
16, 02728
17, 02898
18, 03069
19, 03239
20, 03410
21, 03580
22, 03751
23, 03921
24, 04092
25, 04262
26, 04433
27, 04603
28, 04774
29, 04944
30, 05115
31, 05285
32, 05456
33, 05626
34, 05797
35, 05967
36, 06138
37, 06 [...]08
38, 06479
39, 06649
40, 06820
41, 06990
42, 07161
43, 07331
44, 07502
45, 07672
46, 07843
47, 08013
48, 08184
49, 08354
50, 08525
51, 08695
52, 08866
53, 09036
54, 09207
55, 09377
56, 09548
57, 09718
58, 09889
59, 10059
60, 10230
61, 10400
62, 10571
63, 10741
64, 10912
65, 11082
66, 11253
67, 11423
68, 11594
69, 11764
70, 11935
71, 12106
72, 12276
73, 12446
74, 12617
75, 12787
76, 12958
77, 13128
78, 13299
79, 13469
80, 13640
81, 13811
82, 13981
83, 14152
84, 14322
85, 14493
86, 14663
87, 14834
88, 15004
89, 15175
90, 15345
91, 15516
92, 15687
93, 15857
94, 16028
95, 16198
96, 16369
97, 16540
98, 167 [...]1
99, 16882

[Page 78] [...] [Page 79] [...]

A Table of Declinations.
♈ North Latitude.♎ South Latitude.
 0123456 
00, 000, 921, 832, 753, 674. 586. 0030
10, 401, 322, 233, 154, 074. 986. 2029
20, 801, 722, 633, 554, 475. 386. 3028
31, 202, 123, 033, 954, 875. 786. 7027
41, 602, 513, 434, 355, 276. 187. 1026
52, 002, 913, 834, 755, 836. 587. 5025
62, 403, 314, 235, 156, 066. 987. 8824
72, 783, 714, 635, 556, 467. 388. 2823
83, 184, 115, 035, 956, 867. 788. 6822
93, 584, 505, 426, 337, 258. 179. 0821
103, 974, 905, 806, 737, 658. 579. 4820
114, 375, 306, 207, 138, 058. 979. 8819
124, 775, 706, 607, 538, 459. 3610. 2718
135, 156, 087, 007, 928, 839. 7610. 6717
145, 556, 487, 408, 329, 2310. 1611. 0716
155, 936, 877, 788, 709, 6210. 5511. 4515
166, 327, 238, 159, 0810, 0010. 9311. 8514
176, 707, 628, 539, 4710, 3811. 3212. 2313
187, 088, 008, 939, 8510, 6811. 701 [...]. 6212
197, 478, 389, 3010, 2311, 1512. 0813. 0011
207, 858, 779, 7010, 6311, 5512. 4713. 3810
218, 229, 0810, 1511, 0 [...]11, 9312. 8513. 809
228, 609, 5310, 4711, 3812, 3213. 2314. 158
238, 979, 9210, 8511, 7712, 7013. 6214. 537
249, 3510, 2811, 2212, 1313, 0714. 0014. 906
259, 7210, 6511, 5812, 5013, 4314. 3715. 285
2610, 0811, 0211, 9512, 8713, 8014. 7315. 654
2710, 4311, 3812, 3213, 2314, 1715. 1016. 023
2810, 8011, 7512, 6813, 6014, 5315. 4716. 382
2911, 1512, 0813, [...]313, 9514, 8815. 8216. 751
3011, 5112, 4513, 3814, 3115, 2516. 1817. 100
♓ North Latitude.♍ South Latitude.

A Table of Declinations.
♈ South Latitude.♎ North Latitude
 0123456 
0 0, 921, 832, 753, 674, 585, 5030
1 0, 521, 452, 353, 274, 185, 1029
2 0, 121, 051, 952, 873, 784, 7028
3 0▪280, 651, 572, 483, 404, 3227
4 0, 680, 251, 172, 083, 003, 9226
5 1, 080, 150, 771, 682, 603, 5225
6 1, 470, 550, 371, 282, 033, 1224
7 1, 870, 950, 030, 8 [...]1, 802, 7223
8 2, 271, 350, 430, 481, 422, 3322
9 2, 481, 730, 820, 101, 031, 9521
10 3, 052, 131, 220, 300, 631, 5520
11 3, 452, 531, 610, 680, 231, 1519
12 3, 852, 932, 011, 070, 170, 7718
13 4, 233, 322, 401, 470, 550, 3817
14 4, 623, 682, 951, 870, 930, 0016
15 5, 004, 083, 172, 251, 320, 3815
16 5, 384, 473, 532, 631, 680, 7714
17 5, 774, 853, 923, 002, 071, 1513
18 6, 155, 234, 303, 382, 451, 5312
19 6, 535, 624, 683, 772, 831, 9211
20 6, 925, 985, 074, 133, 202, 2810
21 7, 286, 355, 454, 503, 572, 659
22 7, 676, 735, 834, 883, 953, 028
23 8, 057, 126, 205, 254, 323, 387
24 8, 427, 506, 575, 634, 703, 756
25 8, 787, 876, 936, 005, 074, 125
26 9, 158, 237, 306, 375, 434, 484
27 9, 518, 587, 836, 725, 784, 833
28 9, 888, 958, 027, 076, 135, 182
29 10, 239, 308, 377, 426, 485, 531
30 10, 589, 658, 727, 776, 835, 880
♓ North Latitude.♍ South Latitude.

A Table of Declinations.
♉ North Latitude.♏ South Latitude.
 0123456 
011, 5112, 4513, 3814, 3115, 2516, 1817, 1030
111, 8712, 8013, 7314, 6715, 6016, 5517, 4729
212, 2213, 1514, 0815, 0215, 9516, 1917, 8228
312, 5513, 4814, 4215, 3516, 3017, 2318, 1727
412, 9013, 8314, 7815, 7016, 6517, 5818, 5226
513, 2314, 1815, 1216, 0517, 0017, 9318, 8725
613, 5714, 5215, 4516, 4017, 3318, 2819, 2024
713, 9014, 8515, 7816, 7317, 6718, 5819, 5323
814, 2315, 1816, 1217, 0718, 0018, 9519, 8722
914, 5515, 5016, 4317, 3818, 3319, 2820, 2021
1014, 8715, 8216, 7517, 7018, 6519, 6020, 5320
1115, 1816, 1317, 0718, 0218, 9719, 9220, 8519
1215, 4816, 4317, 3818, 3319, 2320, 2321, 1718
1315, 8016, 7517, 7018, 6519, 6020, 5521, 4817
1416, 1017, 0518, 0018, 9519, 9020, 8721, 8016
1516, 4017, 3518, 3019, 2520, 2021, 1722, 1015
1616, 6817, 6318, 6019, 5520, 5021, 6322, 4014
1716, 9717, 9218, 8819, 8520, 8021, 7722, 7013
1817, 2518, 2019, 1720, 1321, 0822, 0522, 9812
1917, 5318, 4819, 4520, 4221, 3722, 3323, 2711
2017, 8018, 7719, 7 [...]20, 6821, 6522, 6223, 5510
2118, 0719, 0 [...]20, 0020, 9521, 9222, 8823, 839
2218, 3 [...]19, 3020, 2721, 2222, 1823, 1524, 108
2318, 5819, 5720, 5321, 4822, 4523, 4224, 377
2418, 8319, 8220, 7821, 7522, 722 [...], 6824, 636
2519, 0820, 0521, 0322, 0022, 9723, 9324, 885
2619, 3220, 2821, 2722, 2323, 2024, 1825, 134
2719, 5520, 5221, 5022, 4723, 4324, 4225, 373
2819, 7820, 7521, 7322, 7023, 6724, 6525, 602
2920, 0020, 9821, 9522, 9323, 9024, 8825, 831
3020, 2221, 2022, 1723, 1524, 1225, 1026, 050
♌ North Latitude.♒ South Latitude.

A Table of Declinations.
♉ South Latitude.♏ North Latitude
 0123456 
0 10, 5809, 658, 727, 776, 835, 8830
1 10, 9310, 009, 078, 127, 186, 2329
2 11, 2810, 339, 408, 477, 526, 5728
3 11, 6210, 679, 738, 807, 856, 9027
4 11, 9711, 0210, 079, 138, 187, 2326
5 12, 3011, 3510, 409, 478, 527, 5725
6 12, 6311, 6810, 739, 808, 877, 8324
7 12, 9712, 0111, 0710, 129, 178, 2023
8 13, 2812, 3311, 3810, 479, 488, 5222
9 13, 6012, 6511, 7010, 759, 808, 8321
10 13, 9212, 9712, 0211, 0710, 129, 1520
11 14, 2313, 2812, 3311, 3810, 489, 4519
12 14, 5313, 5812, 6311, 6810, 729, 7518
13 14, 8313, 8812, 9311, 9811, 0210, 0517
14 15, [...]314, 181 [...], 2312, 2811, 3210, 3516
15 15, 4314, 4813, 5312, 5711, 6010, 6 [...]15
16 15, 7214, 7713, 8012, 8511, 8810, 9214
17 16, 0015, 0514, 0813, 1312, 1711, 2013
18 16, 2815. 3314, 3713, 4012, 4311, 4712
19 16, 5715. 6014, 6313, 6712, 7011, 7311
20 16, 8315. 8714, 9013, 9312, 9712, 0010
21 17, 1016. 1315, 1714, 2013, 2312, 259
22 17, 3716. 4015, 4314, 4713, 481 [...], 508
23 17, 6216. 6515, 6814, 7213, 7312, 757
24 17, 8716. 9015, 9314, 9713, 9813, 006
25 18, 1217. 1516, 1715, 2014, 2213, 235
26 18, 3517. 3816, 4215, 4314, 4513, 484
27 18, 5817. 6016, 6315, 6514, 6813, 683
28 18, 8017. 8316, 8515, 8714, 9013, 902
29 19, 0218. 0517, 0716, 0815, 1214, 121
30 19, 2318. 2717, 2816, 3015, 3314, 350
♌ South Latitude.♏ North Latitude.

A Table of Declinations.
♊ North Latitude.♐ South Latitude.
 0123456 
020, 2221, 2022, 1723, 1524, 1225, 1026, 0530
120, 4321, 4222, 3823, 3724, 3325, 3226, 2729
220, 6321, 6222, 6023, 5824, 5525, 5326, 4828
320, 8321, 8222, 8023, 7824, 7525, 7326, 7027
421, 0222, 0022, 9823, 9724, 9525, 9226, 9026
521, 2222, 1823, 1724, 1525, 1326, 1227, 0825
621, 3822, 3723, 3524, 3525, 3226, 3027, 3524
721, 5522, 5323, 5224, 5225, 5026, 4827, 4523
821, 7222, 7023, 6824, 6825, 6726, 6527, 6222
921, 8822, 8723, 8524, 8525, 8326, 8227, 7821
1022, 0323, 0224, 0025, 0025, 9826, 9727, 9320
1122, 1723, 1724, 1525, 1526, 1327, 1228, 0819
1222, 3223, 3224, 3025, [...]026, 2827, 2728, 2318
1322, 4523, 4524, 4325, 4326, 4227, 4028, 3717
1422, 5723, 5724, 5525, 5526, 5327, 5228, 5016
1522, 6823, 6824, 6725, 6526, 6527, 6328, 6215
1623, 7823, 7224, 7725, 7526, 7527, 7528, 7214
1722, 8823, 8824, 8825, 8726, 8727, 8728, 8213
1822, 9823, 9814, 9825, 9726, 9727, 9728, 9212
192 [...], 0724, 0725, 0726, 0527, 0528, 0529, 0311
2023, 1524, 1525, 1526, 1327, 1328, 1329, 1210
2123, 2224, 2225, 2226, 2227, 2028, 2029, 209
2223, 2824, 2825, 2826, 2827, 2728, 2729, 258
2323, 3324, 3325, 3 [...]26, 3327, 3228, 3229, 307
2423, 3824, 3825, 3826, 3827, 3728, 3729, 376
2523, 4324, 4325, 4326, 4327, 4228, 4229, 425
2623, 4724, 4725, 4726, 4727, 4728, 4729, 474
2723, 4924, 5025, 5026, 5027, 5028, 5029, 503
2823, 5024, 5125, 5126, 5127, 5128, 5129, 512
2923, 5124, 5225, 5226, 5227, 5228, 5229, 521
3023, 5224, 5225, 5226, 5227, 5228, 5229, 520
♑ South Latitude.♋ North Latitude.

A Table of Declinations.
♊ South Latitude.♐ North Latitude.
 0123456 
0 19, 2318, 2717, 2816, 3015, 3314. 3530
1 19, 4518, 4717, 4816, 5015, 5314. 5529
2 19, 5218, 6717, 6816, 7015, 7314. 7528
3 19, 8518, 8717, 8816, 9015, 9214. 9527
4 20, 0319, 0518, 0517, 1016, 1215. 1 [...]26
5 20, 2219, 2518, 2717, [...]816, 3015. 3025
6 20, 4019, 4218, 4317, 4516, 4715. 4724
7 20, 5719, 5818, 6017, 6216, 6315. 6323
8 20, 7319, 7518, 7717, 7816, 7815. 8022
9 20, 9019, 9218, 9317, 9316, 9315. 9521
10 21, 0520, 0719, 0818, 0817, 1016. 0820
11 21, 1820, 1819, 2218, 2217, 2316. 2219
12 21, 3220, 3319, 3518, 3517, 3716. 3518
13 21, 4520, 4719, 4718, 4817, 4816. 4717
14 21, 5820, 5819, 5818, 6017, 6016. 5816
15 21, 6820, 6819, 6818, 7017, 7016. 7015
16 21, 7820, 7819, 7818, 8017, 8016. 8014
17 21, 8820, 8819, 8818, 9017, 9016. 9013
18 21, 9820, 9819, 9819, 0018, 0016. 9812
19 22, 0721, 0720, 0719, 0818, 0817. 0711
20 22, 1521, 1520, 1519, 1718, 1717. 1510
21 22, 2221, 2220, 2219, 2318, 2317. 239
22 22, 2821, 2820, 2819, 2818, 2817. 2 [...]8
23 22, 3321, 3320, 3319, 3318, 3317. 337
24 22, 3821, 3820, 3819, 3818, 3817. 386
25 22, 4 [...]21, 4320, 4319, 4318, 4317. 435
26 22, 4722, 4720, 4719, 4718, 4717. 474
27 22, 5021, 5020, 5019, 5018, 5017. 503
28 22, 5121, 5120, 5119, 5118, 5117. 512
29 22, 5221, 5220, 5219, 5218, 5217. 521
30 22, 5221, 5220, 5219, 5218, 5217. 520
♑ North Latitude.♋ South Latitude.

A Table of Declinations.
♈ North Latitude.♌ South Latitude.
 0123456
00, 00359, 62359, 22358, 82358, 42358. 02357. 62
10, 920, 530, 13359, 73359, 33358. 93358. 53
21, 831, 451, 050, 650, 25359. 85359. 45
32, 752, 371, 971, 571, 170. 770. 37
43, 673, 282, 882, 482, 081. 681. 28
54, 584, 203, 804, 403, 002. 602. 20
65, 505, 124, 724, 323, 9 [...]3. 523. 12
76, 426, 035, 635, 234, 834. 434. 03
87, 356, 956, 556, 155, 755. 354. 95
98, 277, 877, 477, 076, 676. 275. 87
109, 188, 788, 387, 987, 587. 186. 78
1110, 109, 709, 308, 928, 528. 127. 72
1211, 0310, 6310, 239, 859, 459. 058. 65
1311, 9511, 5511, 1510, 7710, 379. 979. 57
1412, 8812, 4812, 0811, 7011, 3010. 9010. 50
1513, 8013, 4213, 0212, 6312, 2311. 6711. 43
1614, 7 [...]14, 3 [...]13, 9513, 5713, 1712. 7712. 37
1715, 6715, 2714, 8814, 5014, 1013. 7013. 30
1816, 5816, 2015, 8215, 4315, 0314. 6514. 25
1917, 5217, 1316, 7516, 3715, 9715. 5815. 18
2018, 4518, 0717, 6817, 3016, 9016. 5216. 12
2119, 3819, 0018, 6218, 2317, 8517. 4717. 07
2220, 3319, 9319, 5519, 1818, 8018. 4218. 01
2321, 2720, 8820, 5020, 1319, 7519. 3719. 97
2422, 2021, 8321, 4521, 0820, 7020. 3220. 92
2523, 1522, 7822, 4022, 0321, 6511. 2721. 87
2624, 1023, 7323, 3522, 9822, 6022. 2222. 83
2725, 0324, 6844, 3223, 9523, 5723. 1823. 80
2825, 9825, 6325, 2724, 9024, 5224. 1524. 77
2926, 9526, 5826, 2225, 8525, 4825. 1225. 73
3027, 9027, 5527, 1826, 8226, 4526. 0826. 70

A Table of Right Ascensions.
♈ South Latitude♎ North Latitude. 180. Adde.
 0123456
0 0. 380, 781, 181, 581, 982, 38
1 1. 301, 702, 102, 502, 903, 30
2 2. 222, 623, 023, 423, 824, 22
3 3. 133, 533, 934, 334, 735, 13
4 4. 054, 454, 855, 255, 656, 05
5 4. 975, 375, 776, 176, 576, 97
6 5. 906, 306, 707, 107, 507, 88
7 6. 827, 227, 628, 028, 428, 80
8 7. 738, 138, 538, 939, 339, 72
9 8. 669, 079, 479, 8510, 2510, 63
10 9. 589, 9810, 3810, 7711, 1711, 55
11 10. 5010, 9011, 3011, 6812, 0812, 47
12 11. 4211, 8212, 2212, 6013, 0013, 38
13 12. 3312, 7313, 1313, 5213, 9214, 30
14 13. 2713, 6514, 0514, 4314, 8315, 22
15 14. 2014, 5814, 9715, 3515, 7516, 13
16 15. 1215, 5015, 8816, 2716, 6717, 05
17 16. 0316, 4216, 8017, 1817, 5817, 97
18 16. 9717, 3517, 7318, 1218, 5018, 88
19 17. 9018, 2818, 6719, 0319, 4219, 80
20 18. 8319, 2219, 6019, 9720, 3520, 72
21 19. 7620, 1520, 5320, 9021, 2821, 65
22 20. 7021, 0821, 4721, 8322, 2022, 57
23 21. 6322, 0122, 4022, 7723, 1323, 50
24 22. 5822, 9523, 3323, 7024, 0724, 43
25 23. 5223, 8824, 2724, 6325, 0025, 35
26 24. 4724, 8325, 2025, 5725, 9326, 28
27 25. 4225, 7826, 1526, 5026, 8727, 22
28 26. 3726, 7227, 0827, 4327, 8028, 15
29 27. 3227, 6728, 0228, 3728, 7329, 08
30 28. 2728, 6328, 9729, 3229, 6730, 02

A Table of Right Ascensions.
♉ North Latitude.♏ South Latitude. 180 Adde.
 0123456
027, 9027, 5527, 1826, 8226, 4526, 0825, 70
128, 8528, 5028, 1327, 7827, 4227, 0526, 67
229, 8229, 4529, 1028, 7528, 3828, 0227, 63
330, 7730, 4230, 0729, 7229, 3528, 9828, 62
431, 7231, 3831, 0330, 6830, 3229, 9729, 60
532, 7032, 3732, 0031, 6531, 3030, 9530, 58
633, 6733, 3332, 9732, 6332, 2831, 9331, 57
734, 6334, 3033, 9633, 6233, 2732, 9232, 56
835, 6035, 2834, 9534, 6134, 2633, 9133, 55
936, 5736, 2735, 9335, 6035, 2534, 9034, 55
1037, 5537, 2536, 9236, 5936, 2535, 9035, 55
1138, 5538, 2337, 9137, 5837, 2536, 9136, 56
1239, 5339, 2338, 9038, 5838, 2537, 9237, 57
1340, 5240, 2239, 9039, 5839, 2638, 9338, 58
1441, 5141, 2140, 9040, 5940, 2739, 9539, 60
1542, 5142, 2141, 9041, 6041, 2840, 9740, 63
1643, 5143, [...]142, 9142, 6142, 3041, 9841, 65
1744, 5144, 2243, 9243, 6243, 3243, 004 [...], 67
1845, 5245, 2344, 9344, [...]344, 3344, 0243, 70
1946, 5346, 2445, 9545, 6545, 3545, 0544, 73
2047, 5347, 2546, 9746, 6746, 3846, 0845, 77
2148, 5548, 2747, 9847, 7047, 4247, 1246, 82
2249, 5749, 2849, 0048, 7348, 4548, 1547, 87
2350, 5850, 3050, 0349, 7749, 4849, 2048, 92
2451, 6051, 3351, 0750, 8050, 5350, 2549, 97
2552, 6352, 3752, 1051, 8551, 5851, 3051, 03
2653, 675 [...], 4053, 1552, 9052, 6352, 3752, 10
2754, 7054, 4554, 2053, 9553, 7053, 4353, 17
2855, 7 [...]55, 4855, 2555, 0054, 7554, 5054, 23
2956, 7756, 5356, 3056, 0555, 8255, 5755, 30
3057, 8057, 5857, 3557, 1256, 8856, 6356, 38

A Table of Right Ascensions.
♉ South Latitude.♏ North Latitude. 180. Adde.
 0123456
0 28, 2728. 6228, 9729, 3229, 6730, 02
1 29, 2229. 5729, 9230, 2730, 6230, 95
2 30, 1730. 5230, 8731, 2231, 5731, 90
3 31, 1231. 4731, 8232, 1732, 5232, 85
4 32, 0832. 4 [...]32, 7733, 1233, 4533, 78
5 33, 0533. 3833, 7234, 0734, 4034, 73
6 34, 0234. 3534, 6835, 0235, 3535, 68
7 34, 9835. 3235, 6535, 9736, 3036, 63
8 35, 9536. 2836, 6256, 9337, 2537, 5 [...]
9 36, 9337. 2537, 5837, 9038, 2238, 5 [...]
10 37, 9038. 2238, 5538, 8739, 1839, 48
11 38, 8839, 2039, 5239, 8340, 1540, 45
12 39, 8740. 1840, 5040, 8041, 1241, 42
13 40, 8541. 1741, 4741, 7742, 0842, 38
14 41, 8342, 1542, 4542, 7543, 0543, 35
15 42, 8243, 1343, 4343, 7344, 0344, 32
16 43, 8144, 1244, 4244, 7245, 0045, 28
17 44, 8145, 1145, 4045, 7045, 9846, 25
18 45, 8146, 1046, 3946, 6846, 9747, 23
19 46, 8247, 1047, 3847, 6747, 9548, 22
20 47, 8248, 1048, 3848, 6648, 9349, 20
21 4 [...], 8349, 1049, 3849, 6549, 9250, 18
22 49, 8450, 1050, 3850, 6450, 9051, 17
23 50, 8551, 1151, 3851, 6351, 8952, 15
24 51, 8752, 1252, 3952, 6352, 8853, 14
25 52, 8853, 1353, 3953, 635 [...], 8854, 13
26 53, 9254, 1554, 4054, 6454, 8855, 12
27 54, 9355, 1855, 4255, 6555, 8956, 12
28 55, 9756, 2056, 4356, 6756, 9057, 11
29 57, 0057, 2257, 4557, 6857, 9158, 12
30 58, 0358, 2558, 4858, 7058, 9259, 12

A Table of Right Ascensions.
♊ North Latitude♐ South Latitude.180 Adde.
 0123456
057, 8057. 5857, 3557, 1256, 8856, 6356, 38
158, 8558. 6358, 4058, 1757, 9557, 7057, 47
259, 8859. 6859, 4559, 2359, 0258, 7858, 55
360, 9360. 7366, 5260, 3060, 0859, 8759, 63
461, 9861. 7861, 5861, 3761, 1760, 9560, 73
563, 0562. 8562, 6562, 4562, 2562, 0361, 83
664, 1063. 9263, 7263, 5363, 3363, 1362, 93
765, 1564. 9864, 7864, 6264, 4264, 2264, 03
866, 2266. 0565, 8765, 7065, 5065, 3265, 13
967, 2867. 1266, 9566, 7866, 6066, 4266, 23
1068, 3568. 1868, 0367, 8767, 7067, 5267, 35
1169, 4269. 2769, 1268, 9568, 8068, 6368, 47
1270, 4870. 3570, 2070, 0569, 9069, 7569, 58
1371, 771. 4371, 2871, 1571, 0070, 8570, 70
1472, 6372. 5272, 3772, 2572, 1071, 9771, 82
1573, 7073. 6073, 4773, 3573, 2273, 0872, 95
1674, 7874. 6874, 5574, 4574, 3274, 2074, 07
1775, 8775. 7775, 6575, 5575, 4375, 3275, 20
1876, 9576. 8576, 7576, 6576, 5576, 4576, 33
1978, 0377. 9377, 8577, 7577, 6777, 5777, 47
2079, 1279. 0378, 9578, 8778, 7878, 6878, 60
2180, 2080. 1380, 0579, 9879, 9079, 8279, 73
2281, 2881. 2281, 1581, 0881, 0280, 9380, 87
2382, 3782. 3082, 2582, 1882, 1382, 0782, 00
2483, 4783. 4083, 3583, 3083, 2583, 2083, 15
2584, 5584. 5084, 4584, 4284, 3784, 3384, 28
2685, 6384. 6085, 5585, 5385. 4885, 4785, 38
2786, 7386. 7086, 6786, 6586. 6 [...]86, 6086, 57
2887, 8287. 8087, 7787, 7387. 7887, 7387, 70
2988, 9288. 9088, 8888, 8888:8788, 8788, 85
3090, 0090. 0090, 0090, 0090. 0090, 0090, 00

A Table of Right Ascensions.
♊ South Latitude.♐ North Latitude.180 Adde.
 0123456
0 58, 0358, 2558, 4858, 7058, 9259, 12
1 59, 0759, 2859, 5059, 7259, 9260, 13
2 60, 1060, 3260, 5260, 7360, 9361, 13
3 61, 1561, 3561, 5561, 7761, 9562, 14
4 62, 1862, 3862, 5862, 8062, 9763, 15
5 63, 2363, 4263, 6263, 8363, 9864, 17
6 64, 2864, 4764, 6564, 8765, 0265, 18
7 65, 3365, 5265, 6865, 9066, 0366, 20
8 66, 3866, 5766, 7366, 9367, 0767, 22
9 67, 4567, 5267, 7767, 9768, 1068, 25
10 68, 5068, 6768, 8268, 9869, 1269, 27
11 69, 5769, 7269, 8770, 0170, 1570, 28
12 70, 6370, 7770, 9217, 0571, 1871, 32
13 71, 7071, 8271, 9772, 0872, 2272, 35
14 72, 7772, 8873, 0273, 1373, 2573, 38
15 73, 8373, 9574, 0774, 1874, 3074, 42
16 74, 9075, 0275, 1275, 2375, 3375, 45
17 75, 9776, 0876, 1876, 2876, 3876, 48
18 77, 0577, 1577, 2577, 3377, 4377, 52
19 78, 1278, 2278, 3078, 3878, 4778, 55
20 79, 2079, 2879, 3579, 4379, 5279, 58
21 80, 2880, 3580, 4280, 4880, 5780, 63
22 81, 3581, 4281, 4781, 5381, 6081, 67
23 82, 4282, 4882, 5382, 5882, 6582, 70
24 83, 5083, 5583, 6083, 6583, 7083, 75
25 84, 5884, 6284, 6784, 7084, 7584, 78
26 85, 6785, 6885, 7385, 7585, 8085, 82
27 86, 7586, 7786, 8086, 8286, 8586, 87
28 87, 8387, 8387, 8787, 8787, 9087, 90
29 88, 9288, 9288, 9388, 9388, 9588, 95
30 90, 0090, 0090, 0090, 0090, 0090, 00

A Table of Right Ascensions.
♋ North Latitude♑ South Latitude.180 Adde.
 0123456
090, 0090, 0090, 0090. 0090, 0090, 0090, 00
191, 0891, 1091, 1291. 1291, 1391, 1391, 15
292, 1892, 2092, 2392. 2392, 2792, 2792, 30
393, 2793, 3093, 3393. 3593, 3893, 4093, 43
494, [...]794, 4094, 4594. 4794, 5294, 5394, 62
595, 4595, 5095, 5595. 5895, 6395, 6795, 72
696, 5396, 6096, 6596. 7096, 7596, 8096, 85
797, 6397, 7097, 7597. 8297, 8797, 9398, 00
898, 7298, 7898, 8598. 9299, 9899, 0799, 13
999, [...]099, 8799, 95100. 02100, 10100, 18100, 27
10100, [...]8100, 97101, 05101. 13101, 22101, 32101, 40
11101, 97102, 07102, 15102. 25102, 33102, 43102, 53
12103, 05103, 15103, 25103. 35103, 45103, 55103, 67
13104, 13104, 2 [...]104, 35104. 45104, 57104, 68104, 80
14105, 22105, 32105, 45105. 55105, 68105, 80105, 93
15106, 30106, 40106, 53106. 65106, 78106, 92107, 05
16107, 37107, 48107, 63107. 75107, 90108, 0 [...]108, 18
17108, 43108, 57108, 72108. 85108, 00109, 15109, 30
18109, 52109, 65109, 80109. 95110, 10110, 25110, 42
19110, 58110, 73110, 88111. 05111, 20111, 37111, 53
20111, 65111, 82111 97112. 13112, 30112, 48112, 65
21112, 72112, 88113, 05113. 22113, 40113, 58113, 77
22113, 78113, 95114, 13114. 30114, 50114, 68114, 87
23114, 85115, 02115, 22115. 38115, 58115, 78115, 97
24115, 90116, 08116, 28116 47116, 67116, 87117, 07
25116, 95117, 15117, 35117. 55117, 75117, 97118. 17
26118, 02118, 22118, 42118. 63118, 83119, 05119. 27
27119, 07119, 27119, 48119. 70119, 92120, 13120. 37
28120, 12120, 32120, 55120. 77120, 98122, 22121. 45
29121, 15121, 37121, 60121. 83122, 05122, 30122. 53
30122, 20122, 42122, 65122. 88123, 12123, 37123. 62

A Table of Right Ascensions.
♋ South Latitude.♑ North Latitude.180 Adde.
 0123456
0 90, 0090, 0090, 0090, 0090, 0090, 00
1 91, 0891, 0891, 0791, 0791, 0591, 05
2 92, 1792, 1792, 1392, 1392, 1092, 10
3 93, 2593, 2393, 2093, 1893, 1593, 13
4 94, 3 [...]94, 3294, 2794, 2594, 2094, 18
5 95, 4295, 3895, 3395, 3095, 2595, 22
6 96, 5096, 4596, 4096, 3596, 3096, 25
7 97, 5897, 5297, 4797, 4297, 3597, 30
8 98, 6598, 5898, 5398, 4798, 4098, 33
9 99, 7299, 6599, 5899, 5299, 4399, 37
10 100, 80100, 72100, 65100, 57100, 48100, 42
11 101, 88101, 78101, 70101, 62101, 53101, 45
12 102, 95102, 85102, 75102, 67102, 57102, 48
13 104, 03103, 92103, 82103, 72103, 62103, 52
14 105, 10104, 98104, 88104, 77104, 67104, 55
15 106, 17106, 05105, 93105, 82105, 70105, 58
16 107▪23107, 12106, 98106, 87106, 75106, 62
17 108, [...]0108, 18108, 0 [...]107, 92107, 78107, 65
18 109, 37109, 23109, 08108, 95108, 82108, 68
19 110, 43110, 28110, 13110, 99110, 85109, 72
20 111, 50111, 33111, 18111, 02111, 88110, 73
21 112, 55112, 38112, 2 [...]112, 03112, 90111, 75
22 113, 62113, 4 [...]113, 27113, 07113, 93112, 78
23 114, 67114, 48114, 32114, 10114, 97113, 80
24 115, 72115, 53115, 35115, 13115, 98114, 82
25 116, 77116, 58116, 38116, 17116, 02115, 83
26 117, 82117, 62117, 42117, 20117, 03116, 85
27 118, 85118, 65118, 45118, 23118, 05117, 86
28 119, 90119, 68119, 48119, 27119, 07118, 87
29 120, 93120, 72120, 50120, [...]8120, 08119, 88
30 121, 97121, 75121, 52121, 30121, 08120, 88

A Table of Right Ascensions.
♌ North Latitude♒ South Latitude.180 Adde.
 0123456
0122, [...]0122, 42122, 65122, 88123, [...]2123. 37123. 62
1123, [...]3123, 47123, 70123, 95124, [...]8124. 43124. 70
2124, 27124, 52124, 75125, 00125, 25125. 50125. 77
3125, 30125, 55125, 80126, [...]5126, 30126. 57126. 83
4126, 33126, 60126, 85127, 10127, 37127. 63127. 90
5127, 37127, 63127, 90128, 15128, 42128. 70128. 97
6128, 40128, 67128, 93129, 20129, 47129. 75130. 03
7129, 42129, 70129, 97130, 23130, 52130. 80131. 08
8130, 43130, 72131, 00131, 27131, 55131. 85232. 13
9131, 45131, 73132, 02132, 30132, 58132. 88133. 18
10132, 46132, 75133, 03133, 33133, 62133. 92134. 23
11133, 47133, 77134, 05134, 35134, 65134. 95135. 27
12134, 48134, 78135, 07135, 37135, 67135. 98136. 30
13135, 48135, 78136, 08136, 38136, 68137. 00137. 33
14136, 49136, 79137, 09137, 39137, 70138. 02138. 35
15137, 4 [...]237, 79138, 09138, 40138, 72139. 03139. 37
16138, 48138, 78139, 10139, 41139, 73140. 05140. 40
17139, 47139, 78140, 10040, 41140, 74141. 07141. 42
18140, 46140, 77141, 09141, 42141, 74142. 08142. 43
19141, 45141, 76142, 09142, 41142, 75143. 09143. 44
20142, 43142, 75143, 08143, 41143, 75144. 10144. 44
21143, 41143, 73144, 07144, 40144, 74145. 10145. 45
22144, 38144, 72145, 05145, 39145, 74146. 09146. 45
23145, 36145, 70146, 03146, 38146, 73147. 08147. 44
24146, 33146, 67147, 02147, 37147, 72148. 07148. 43
25147, 30147, 65148, 00148, 35148, 70149. 05149. 42
26148, 27148, 62148, 97149, 32149, 68150. 03150. 40
27149, 23149, 58149, 93150, 28150, 65151. 01151. 38
28150, 18150, 55150, 90151, 25151, 62151. 98152. 37
29151, 15551, 50151, 87152, 22152, 52152. 95153. 33
30152, 10152, 45152, 82153, 18153, 55153. 92154. 30

A Table of Right Ascensions.
♌ South Latitude♒ North Latitude.180. Adde.
 0123456
0 121, 97121, 75121, 52121, 30121, 08120. 88
1 123, 00122, 78122, 55122, 32122, 09121. 88
2 124, 03123, 80123, 57123, 33123, 10122. 89
3 125, 07124, 82124, 58124, 35124, 11123. 88
4 126, 08125, 85125, 60125, 36125, 12123. 88
5 127, 12126, 87126, 61126, 37126, 12125. 87
6 128, 13127, 88127, 61127, 37127, 12126. 86
7 129, 15128, 89128, 62128, 37128, 11127. 85
8 130, 16129, 90129, 62129, 36129, 10128. 83
9 131, 17130, 90130, 62130, 35130, 08129. 82
10 132, 18131, 90131, 62131, 34131, 07130. 80
11 133, 18132, 90132, 62132, 33132, 05131. 78
12 134, 19133, 90133, 61133, 32133, 03132. 77
13 135, 19134, 89134, 60134, 30134, 02133. 75
14 136, 19135, 88135, 58135, 28135, 00134. 72
15 137, 18136, 87136, 57136, 27135, 97135. 68
16 138, 17237, 85137, 55137, 25136, 95136. 65
17 139, 15138, 83138, 53138, 23137, 92137. 6 [...]
18 140, 13139, 82139, 50139, 20138, 88138. 5 [...]
19 141, 12140, 80140, 48140, 17139, 85139. 55
20 142, 10141, 78141, 45141, 13140, 82140. 52
21 143, 07142, 75142, 42142, 10141, 78141. 47
22 144, 05143, 72143, 38143, 07142, 75142. 4 [...]
23 145, 02144, 68144, 35144, 03143, 50143. 37
24 145, 98145, 65145, 32144, 98144, 65144. 3 [...]
25 146, 95146, 62146, 28145, 93145, 60145. [...]7
26 147, 92147, 58147, 23146, 88146, 55146. 22
27 148, 88148, 53148, 18147, 83147, 48147. 15
28 149, 83149, 48149, 13148, 78148, 43148. 1 [...]
29 150, 77150, 43150, 08149, 73149, 38149. [...]
30 151, 73551, 38151, 03150, 68150, 33149. 9 [...]

A Table of Right Ascensions.
♈ North Latitude.♓ South Latitude.180 Adde.
 0123456
0152, 10152, 45152, 82153. 18153, 55153, 92154, 30
1153, 05153, 42153, 78154. 15154, 52154, 88155, 27
2154, 02154, 37154, 73155. 10155, 48155, 85156, 23
3154, 97155, 32155, 68156, 0 [...]156, 43156, 82157, 20
4155, 90156, 27156, 65157. 02157, 40157, 78158, 17
5156, 85157, 22157, 60157. 97158, 35158, 73159, 13
6157, 80258, 17158, 55158. 92159, 30159, 68160, 08
7158, 73159, 12159, 50159. 87160, 25160, 63161, 03
8159, 67160, 07160, 45160. 82161, 20161, 58161, 99
9160, 62161, 00161, 38161. 77162, 15162, 53162, 93
10161, 55161, 93162, 32162. 70163, 10163, 48163, 88
11162, 48162, 87163, 25163. 63164, 03164, 42164, 82
12163, 42163, 80164, 18164. 57164, 97165, 35165, 75
13164, 33164, 73165, 21165. 50165, 90166, 30166, 70
14165, 27165, 67166, 05166. 43166, 83167, 23167, 63
15166, 20166, 58166, 98167. 37167, 77168, 33168, 57
16167, 12167, 52167, 92168. 30168, 70169, 10169, 50
17168, 05168, 45168, 85569. 23169, 62170, 03170, 43
18168, 97169, 37169, 77170. 15170, 55170, 95171, 35
19169, 90170, 30170, 70171. 08171, 48171, 88172, 28
20170, 82171, 22171, 62172. 02172, 42172, 82173, 22
21171, 73172, 13172, 53172. 93173, 33173, 73174, 13
22172, 65173, 05173, 45173. 85174, 25174, 65175, 05
23173, 58173, 97174, 37174. 77175, 17175, 57175, 97
24174, 50174, 88175, 28175. 68176, 08176, 48176, 88
25175, 42175, 80176, 20176. 60177, 00177, 40177. 80
26176, 33176, 72177, 12177. 52177, 92178, 32178. 72
27177, 25177, 63178, 03178. 43178, 83179, 23179. 63
28178, 17178, 55178, 95179. 35579, 75180, 15180. 55
29179, 08179, 47179, 87180 27180, 67181, 07181. 47
30180, 00180, 38180, 78181. 18181, 58181, 98182. 38

A Table of Right Ascensions.
♍ South Latitude♓ North Latitude.180 Adde.
 0123456
0152151, 73151, 37151, 03150, 68150, 33149, 98
1153152, 68152, 33151, 98551, 63151, 27150, 92
2154153, 62153, 28152, 92152, 57152, 20151, 85
3154154, 58154, 22153, 85153, 50153, 13152, 78
4155155, 52155, 17154, 80154, 43154, 07153, 72
5156156, 48156, 12155, 73155, 37155, 00154, 65
6157157, 42157, 05156, 67156, 30155, 93155, 57
7158158, 37157, 99157, 60157, 23156, 87156, 50
8159159, 30158, 92158, 53158, 17157, 80157, 43
9160160, 23159, 85159, 47159, 10158, 72158, 35
10161161, 17160, 78160, 40160, 03159, 65159, 28
11162162, 10161, 72161, 33160, 97160, 58160, 20
12163163, 03162, 65162, 27161, 88161, 50161, 12
13164163, 97163, 58163, 20162, 82162, 42162, 03
14165164, 88164, 50164, 12163, 73163, 33163, 95
15166165, 80165, 42165, 03164, 65164, 25163, 87
16167166, 73166, 35165, 95165, 57165, 17164, 78
17168167, 67167, 27166, 87166, 48166, 08165, 70
18168168, 58168, 18167, 78167, 40167, 00166, 62
19169169, 50169, 10168, 70168, 32167, 92167, 53
20170170, 42170, 02169, 62169, 23168, 83168, 45
21171171, 34170, 93170, 53170, 15169, 75169, 37
22172172, 27171, 87171, 47171, 07170, 67170, 28
23173173, 18172, 78172, 38171, 98171, 58171, 20
24174174, 10173, 70173, 30172, 90172, 50172, 12
25175175, 03174, 63174, 23173, 83173, 43173, 03
26176175, 95175, 55175, 15174, 75174, 35173, 95
27177176, 87176, 47176, 07175, 67175, 27174, 87
28178177, 78177, 38176, 98176, 58176, 18175, 78
29179178, 70178, 30177, 90177, 50177, 10176, 70
30179179, 62179, 32178, 82178, 42178, 02177, 62

A Table of Ascensional Differences.
Poles.1234567
Degrees of Declination.100. 0100. 0 [...]00, 0500, 0700, 0800, 1000, 12
20. 030. 060, 100, 130, 1700, 220, 25
30. 050. 100, 150, 220, 270, 320, 37
40. 060. 130, 220, 280, 350, 420, 50
50. 080. 160, 270, 350, 430, 530, 62
60. 100. 210, 320, 420, 530, 630, 73
70. 110. 250, 370, 500, 620, 730, 87
80. 130. 280, 420, 570, 700, 850, 98
90. 150. 320, 480, 630, 800, 951, 12
100. 180. 350, 530, 700, 881, 071, 23
110. 200. 380, 580, 780, 971, 171, 37
120. 210. 420, 630, 851, 071, 281, 50
130. 230. 470, 700, 931, 151, 381, 62
140. 250. 500, 751, 001, 251, 501, 75
150. 260. 530, 801, 071, 351, 621, 88
160. 280. 570, 871, 151, 431, 732, 01
170. 300. 620, 921, 231, 531, 832, 15
180. 320. 650, 981, 301, 631, 952, 28
190. 350. 681, 031, 381, 732, 072, 42
200. 360. 731, 101, 451, 822, 202, 57
210. 380. 771, 151, 531, 922, 322, 70
220. 400. 821, 221, 622, 032, 432, 85
230. 420. 851, 281, 702, 132, 552, 98
240. 440. 881, 331, 782, 232, 683, 03
250. 460. 931, 401, 872, 332, 823, 28
260. 480. 981, 471, 952, 452, 933, 43
270. 511. 021, 532, 052, 553, 073, 58
280. 531. 071, 602, 132, 673, 203, 75
290. 551. 131, 672, 222, 783, 333, 90
300. 581. 151, 732, 322, 903, 484, 07
310. 601. 201, 802, 403, 013, 624, 23
320. 621. 251, 882, 503. 133, 774, 40

A Table of Ascensional Differences.
Height.891011121314
Degrees of Declination.100, 1300. 1500, 1800, 2000, 2200, 2300, 25
20, 280. 320, 350, 380, 420, 470, 50
30, 420. 480, 530, 580, 630, 700, 75
40, 570. 630, 700, 780, 850, 931, 00
50, 700. 800, 880, 971, 071, 151, 25
60, 850. 951, 071, 171, 281, 381, 50
70, 981. 121, 231, 371, 501, 621, 73
81, 131. 271, 421, 571, 721, 872, 00
91, 271. 431, 601, 771, 932, 102, 27
101, 421. 601, 781, 972, 152, 332, 52
111, 571. 771, 972, 172, 372, 572, 78
121, 721. 932, 152, 372, 582, 823, 03
131, 872. 102, 332, 572, 823, 053, 30
142, 002. 272, 5 [...]2, 783, 033, 303, 57
152, 172. 432, 702, 983, 273, 553, 83
162, 322. 602, 903, 203, 503, 804, 10
172, 472. 783, 083, 403, 734, 054, 37
182, 622. 953, 283, 623, 974, 304, 65
192, 773. 13 [...], 483, 834, 284, 574, 92
202, 933. 303, 684, 054, 434, 825, 20
213, 103. 483, 884, 284, 685, 085, 50
223, 253. 674, 084, 504, 935, 355, 78
233, 423. 854, 304, 7 [...]5, 185, 626, 12
243, 584. 054, 504, 635, 435, 906, 37
253, 754. 234, 725, 205, 686, 186, 68
263, 934. 434, 935, 435, 956, 476, 98
274, 104. 635, 155, 686. 226, 757, 30
284, 284. 835, 385, 936. 487, 057, 62
294, 475. 035, 626, 186. 777, 357, 95
304, 655. 255, 856, 457: 057, 678, 28
314, 855. 476, 086, 707. 337, 978, 62
325, 035. 686, 336, 987. 638, 308, 97

A Table of Ascensional Differences.
Poles.15161718192021
Degrees of Declination.100, 2700, 2800; 3000, 3200, 3500, 3700, 38
20, 530, 570, 620, 650, 680, 730, 77
30, 800, 870, 920, 981, 031, 101, 15
41, 071, 151, 231, 301, 381, 451, 53
51, 351, 271, 531, 631, 731, 821, 92
61, 621, 731, 831, 952, 072, 202, 32
71, 952, 012, 152, 282, 422, 572, 70
82, 152, 322, 472, 622, 772, 933, 10
92, 432, 602, 782, 953, 133, 303, 48
102, 702, 903, 083, 283, 483, 683, 88
112, 983, 203, 403, 623, 834, 054, 28
123, 273, 503, 733, 974, 204, 434, 68
133, 553, 804, 054, 304, 574, 825, 08
143, 834, 104, 374, 654, 925, 205, 50
154, 124, 404, 705, 005, 305, 605, 90
164, 404, 725, 035, 355, 675, 986, 32
174, 705, 035, 375, 706, 036, 386, 73
185, 005, 355, 706, 076, 426, 787, 17
195, 305. 676, 056, 426, 827, 207, 60
205, 605. 986, 386, 787, 207, 628, 03
215, 906. 326, 737, 177, 608, 038, 47
226, 226. 657, 107, 558, 008, 458, 92
236, 5 [...]6. 987, 457, 938, 408, 889, 37
246, 857. 337, 828, 328, 829, 329, 83
257, 187. 688, 208, 729, 239, 7710, 32
267, 528. 038, 589, 129, 6710, 2310, 78
277, 858. 408, 979, 5310, 1010, 6811, 28
288, 188. 779, 359, 9510, 5511, 1511, 78
298, 539. 159, 7510, 3811, 1711, 6312, 28
308, 909. 5310, 1710, 8211, 4712, 1312, 80
319, 279. 9210, 5811, 2711, 9312, 6313, 33
329, 6310. 3211, 0111, 7212, 4213, 1513, 88

A Table of Ascensional Differences.
Height.22232425262728
Degrees of Declination.100, 4000. 4200, 4500, 4700, 4800, 5100, 53
20, 820. 850, 880, 930, 981, 021, 07
31, 221. 281, 331, 401, 471, 531, 60
41, 621. 701, 781, 871, 952, 052, 13
52, 032. 132, 232, 332, 452, 552, 67
62, 432. 552, 682, 822, 933, 073, 20
72, 852. 983, 133, 283, 433, 583, 75
83, 253. 423, 583, 753, 934, 104, 28
93, 673. 854, 054, 234, 434, 634, 83
104, 084. 304, 504, 724, 935, 155, 38
114, 504. 734, 975, 205, 455, 685, 93
124, 935. 185, 435, 685, 956, 226, 48
135, 355. 635, 906, 186, 476, 757, 05
145, 786. 086, 376, 686, 987, 307, 62
156, 226. 536, 857, 187, 537, 858, 18
166, 656. 987, 337, 688, 058, 408, 77
177, 107. 457, 828, 208, 588, 979, 35
187, 557. 938, 328, 729, 129, 539, 85
198, 008. 408, 829, 239, 6710, 1010, 55
208, 458. 889, 329, 7710, 2310, 6811, 15
218, 929. 389, 8310, 3210, 7811, 2811, 77
229, 409. 8810, 3710, 8711, 3711, 8812, 40
239, 8810. 3810, 9011, 4211, 9512, 4813, 05
2410, 3710. 9011, 4311, 9812, 5513, 1213, 70
2510, 8711. 4211, 9812, 5713, 1513, 8014, 35
2611, 3711. 9512, 5513, 1514, 7714, 3815, 03
2711, 8812. 4813, 1213, 7314, 3815, 0515, 72
2812, 4013. 0513, 7014, 3515, 0315, 7216, 42
2912, 9313. 6214, 2814, 4815. 6816, 4017, 13
3013, 4814. 1814, 9015, 6216. 3517, 1217, 88
3114, 0514. 7815, 5216, 2717, 0317, 8318, 63
3214, 6215. 3816, 1516, 9317, 7518, 5719, 40

A Table of Ascensional Differences.
Poles.29303132333435
Degrees of Declination.100, 5 [...]00, 5800, 6000, 6200, 6500, 6700, 70
21, 121, 151, 201, 251, 301, 351, 40
31, 671, 731, 801, 881, 952, 032, 10
42, 222, 322, 402, 502, 602, 702, 80
52, 782, 903, 013, [...]33, 253, 383, 52
63, 333, 483, 623, 773, 924, 074, 22
73, 904, 074, 234, 404, 574, 754, 93
84, 474, 654, 855, 035, 235, 435, 65
95, 035, 255, 475, 685, 906, 136, 37
105, 625, 856, 0 [...]6, 336, 586, 837, 10
116, 186, 456, 706, 987, 257, 537, 82
126, 777, 057, 337, 637, 938, 258, 57
137, 357, 677, 978, 308, 628, 979, 30
147, 938, 288, 628, 979, 329, 6810, 05
158, 538, 909, 279, 6310, 0210, 4210, 82
169, 139, 539, 9210, 3210, 7 [...]11, 1511, 58
179, 7510, 1710, 5811, 0211, 4511, 9012, 37
1810, 3810, 8 [...]11, 2711, 7212, 1812, 6713, 15
1911, 0011, 4711, 9312, 4212, 9213, 4313, 85
2011, 6312, 1312, 6313, 1513, 6714, 2214, 77
2112, 2812, 8013, 3313, 8814, 4315, 0015, 65
2212, 9313, 4814, 0514, 6215, 2215, 8216, 45
2313, 6214, 1814, 7815, 3816, 0016, 6317, 28
2414, 2814, 9015, 5216, 1516, 8017, 4818, 17
2514, 9815, 6216, 2716, 9317, 6318, 3319, 05
2615, 6816, 3517, 0317, 7518, 4719, 2019, 97
2716, 4017, 1017, 8318, 5719, 3220, 1020, 90
2817, 1317, 8818, 6319, 4020, 2021, 0121, 85
2917, 9018, 6719, 4520, 2721, 1021, 9522, 83
3018, 6719, 4720, 3021, 1522, 0222, 9223, 85
3119, 4520, 3021, 1722, 0522, 9723, 9224, 88
3220, 2721, 1522, 0523, 9823, 9324, 9325, 95

A Table of Ascensional Differences.
Height.36373839404142
Degrees of Declination.100, 7300, 7500, 7800, 8200, 8300, 8700, 90
21, 451, 531, 571, 621, [...]81, 731, 80
32, 182, 272, 352, 432, 522, 622, 70
42, 923, 013, 133, 253, 373, 483, 62
53, 653, 783, 924, 074, 224, 374, 52
64, 384, 554, 724, 875, 075, 255, 43
75, 125, 325, 505, 705, 926, 136, 35
85, 876, 086, 306, 536, 777, 027, 27
96, 606, 857, 107, 477, 637, 888, 20
107, 377, 637, 928, 228, 508, 829, 1 [...]
118, 128, 428, 739, 059, 389, 7310, 08
128, 889, 229, 579, 9210, 2710, 6511, 0 [...]
139, 6510, 0210, 4010, 7711, 1711, 5812, 00
1410, 4310, 8311, 2311, 6512, 0812, 5312, 97
1511, 2311, 6512, 0812, 5313, 0013, 4713, 97
1612, 0312, 4812, 9513, 4313, 9214, 4314, 97
1712, 8313, 3213, 8214, 3314, 8715, 4215, 98
1813, 6514, 1714, 7015. 2515, 8216, 4017, 01
1914, 4815, 0315, 6016. 1816, 8017, 4218, 07
2015, 3315, 9216, 3217. 1317, 7818, 4519, 13
2116, 1816, 8217, 4518. 1218, 7819, 5020, 22
2217, 0817, 7318, 4019. 1019, 8220, 5721, 33
2317, 9718, 6519, 3720. 1020, 8721, 6522, 47
2418, 8719, 6020, 3521. 1321, 9322, 7723, 63
2519, 8020, 5721, 3522. 1823, 0323, 9224, 83
2620, 7521, 5722, 4023. 2724, 1725, 0826, 05
2721, 7322, 5823, 4724. 3725, 3226, 2827, 30
2822, 7223, 6124, 5525. 5026, 5027, 5228, 60
2923, 7524, 6825, 6726. 6727, 7228, 8029, 95
3024, 8025, 7826, 8227. 8728, 9830, 1231, 32
3125, 8026, 9228, 0029. 1230, 2831, 483 [...], 75
3227, 0028, 0829, 2230. 9031, 5232, 9034, 23

A Table of Ascensional Differences.
Poles.43444546474849
Degrees of Declination.100, 9300, 9701, 0001, 0301, 0701, 1201, 15
21, 871, 932, 002, 072, 152, 222, 30
32, 802, 903, 003, 123, 223, 333, 45
43, 7 [...]3, 874, 014, 154, 304, 454, 62
54, 684, 855, 025, 205, 385, 585, 78
65, 625, 836, 036, 256, 476, 706, 95
76, 576, 827, 057, 307, 577, 838, 12
87, 537, 808, 088, 378, 678, 989, 30
98, 508, 809, 129, 439, 7810, 1310, 50
109, 479, 8010, 1510, 5310, 9011, 3011, 70
1110, 4510, 8211, 2211, 6212, 0312, 4712, 92
1211, 4311, 8512, 2712, 7213, 1813, 6514, 15
1312, 4312, 8813, 3513, 8314, 3314, 8515, 40
1413, 4513, 9314, 4314, 9715, 5016, 0816, 67
1514, 4715, 0015, 5316, 1216, 7017, 3217, 95
1615, 5116, 0816, 6717, 2717, 9018, 5719, 27
1716, 5717, 1717, 8018, 4519, 1319, 8520, 60
1817, 6318, 2818, 9719, 6720, 3821, 1521, 95
1918, 7319, 4220, 1520, 8821, 6722, 4823, 33
2019, 8320, 5821, 3522, 1322, 9723, 8524, 75
2120, 9821, 7722, 5723, 4224, 3025, 2326, 20
2222, 1322, 9723, [...]324, 7325, 6726, 6727, 70
2323, 3224, 2024, 1226, 0827, 0828, 1329, 23
2424, 5325, 4726, 4327, 4528, 5229, 6330, 80
2525, 7826, 7727, 8028, 8730, 0031, 2032, 43
2627, 0328, 1029, 1830, 3331, 5332, 8034, 13
2728, 3729, 4830, 6331, 8533 1234, 4735, 88
2829, 7330, 9032, 1233, 4234, 7736, 2037, 70
2931, 1332, 3733, 6735, 0336, 4738, 0039, 62
3032, 5833, 8835, 2736, 7238, 2539, 8841, 62
3133, 9735, 4736, 9338, 4840, 1241, 8743, 73
3235, 6337, 1238, 6740, 3242, 0743, 9545, 9 [...]

A Table of Ascensional Differences.
Height.50515253545556
Degrees of Declination.101. 2001. 2301, 2801, 3301, 3801, 4301, 48
22. 382. 472, 572, 652, 752, 872, 97
33. 583. 723, 853, 984, 134, 284, 45
44. 784. 955, 135, 325, 525, 735, 95
55. 986. 206, 436, 676, 927, 187, 45
67. 207. 457, 738, 018, 328, 638, 97
78. 428. 729, 039, 389, 7310, 2710, 48
89. 6310. 0010, 3710, 7511, 1511, 5812, 02
910. 8811. 2811, 7012, 1312, 5813, 0713, 58
1012. 1312. 5813, 0513, 5314, 0514, 5815, 15
1113. 4013. 8814, 4014, 9515, 5216, 1216, 75
1214. 6715. 2215, 7816, 3817, 0217, 6718, 37
1315. 6316. 5717, 1817, 0818, 5319, 2520, 01
1417. 2817. 9318, 6219, 3220, 0720, 8721, 70
1518. 6219. 3220, 0720, 8321, 6322, 5023, 40
1619. 9820. 7321, 5322, 3723, 2524, 1725, 15
1721. 3722. 1823, 0323, 9324, 8825, 8826, 95
1822. 7823. 6524, 5725, 5526, 5727, 6528, 80
1924. 2325. 1726, 1527, 1828, 2829, 4530, 68
2025. 7226. 7227, 7728, [...]830, 0731, 3232, 65
2127. 2328. 3029, 4330, 6231, 9033, 2534, 68
2228. 8029. 9331, 1332, 4233, 7835, 2336, 80
2330. 4031. 6232, 9034, 2835, 7537, 3239, 00
2432. 0533. 3534, 7336, 2237, 8039, 4841, [...]0
2533. 7735. 1736, 6538, 2339, 9341, 7543, 73
2635. 5337. 0538, 6340, 3340, 1744, 154 [...], 30
2737. 3839. 0040, 7042, 5544, 7046, 6849, 07
2839. 3241. 0342, 8844, 8847, 0349, 4052, 02
2941. 3543. 2045, 2047, 3549, 7352, 3355, 27
3043. 4845. 4847, 6550, 0252, 6255, 5358, 87
3145. 7347. 9050, 2752, 8855, 8059, 1062, 97
3248. 1350. 5053, 1256, 0259, 3263, 1767, [...]8

A Table of oblique Ascensions.
S.D.123456
0000, 00000, 00000, 00000, 00000, 00000, 00
 43, 633, 603, 583, 553, 533. 48
 87, 287, 237, 177, 127, 077, 00
 1210, 9510, 8710, 7710, 6810, 6010, 53
 1614, 6214, 5014, 3814, 2814, 1714, 07
 2018, 3218, 1718, 0317, 9017, 7717, 62
 2422, 0521, 8721, 7021, 5521, 3821, 22
 2825, 8025, 6225, 4225, 2325, 0524, 83
229, 6029, 3829, 1728, 9528, 7328, 50
 633, 4333, 1832, 9532, 7232, 4532, 22
 1037, 3237, 0536, 7836, 5236, [...]535, 98
 1441, 2340, 9540, 6540, 3740, 0839, 78
 1845, 2244, 9044, 6044, 2843, 9843, 67
 2249, 2548, 9048, 5848, 2547, 9247, 58
 2653, 3052, 9552, 6252, 2751, 9051, 55
057, 4357, 0756, 7056, 3355, 9555, 58
 461, 6261, 2260, 8360, 4760, 0759, 68
 865, 8365, 4265, 0364, 6364, 2263, 83
 1270, 0869, 6769, 2768, 8568, 4368, 03
 1674, 3773, 9573, 5373, 1272, 6872, 27
 2078, 6878, 2777, 8377, 4076, 9876, 55
 2483, 0282, 6082, 1781, 7381, [...]080, 87
 2887, 3886, 9586, 5286, 0785, 6385, 20
291, 7591, 3290, 8890, 4590, 0389, 58
 696, 1295, 6895, 2594, 8094, 3893, 95
 10100, 45100, 0399, 6099, 1798, 7598, 32
 14104, 78104, 37103, 95103, 53103, 10102, 68
 18109, 10108, 68108, 28107, 87107, 45107, 05
 22113, 38112, 97112, 58112, 18111, 78111, 38
 26117, 63117, 2 [...]116, 85116, 47116, 08115, 70
 30121, 83121, 47121, 10120, 73120, 35119, 98

A Table of oblique Ascensions.
S.D123456
0121, 83121, 47121. 10120, 73120, 35119, 98
 4125, 98125, 63125. 30124, 93124, 58124, 23
 8130, 10129, 75129. 4 [...]129, 10128, 77128, 43
 12134, 17133, 85133. 53133, 23132, 92132, 60
 16138, 18137, 90137. 62137, 32137, 0 [...]136, 75
 20142, 15141, 88141. 62141, 35141, 08140, 82
 24146, 08145, 85145. 62145, 37145, 12144, 85
 28149, 97149, 77149. 53149, 32149, 10148, 87
2153, 82153, 63153. 43153, 25153, 05152, 85
 6157, 63157, 47157. 30157, [...]3156, 93156, 80
 10161, 42161, 27161. 13161, 00160, 87160, 72
 14165, 17165, 07164. 93164, 83164, 73164, 62
 18168, 90168, 82168. 72168, 63168, 57168, 48
 22172, 62172, 55172. 50172, 43172, 38172, 33
 26176, 32176, 28176. 27176, 23176, 20176, 17
0180, 00180, 00180. 00180, 00180, 00180, 00
 4183, 68183, 72183. 73183, 77183, 80183, 83
 8187, 38187, 45187. 50187, 57187, 62187, 67
 12191, 10191, 18191. 28191, 37191, 43191, 52
 16194, 83194, 93195. 07195, 17195, 27195, 38
 20198, 58198, 73198. 87199, 00199, 13199, 28
 24202, 37202, 53202. 70202, 8720 [...], 02203, 20
 28206, 18206. 37206. 57206, 75206, 95207, 15
2210, 03210. 23210. 47210, 68210, 90211, 13
 6213, 92214. 15214. 38214, 63214, 88215, 15
 10217, 85218. 12218. 38218, 58218, 92219, 18
 14221, 82222. 10222. 38222, 53222, 97223, 25
 18225, 83226. 15226. 47226, 38227, 08227, 40
 22229, 90230. 25230. 57230, 90231, 23231, 57
 26234, 02234. 37234. 70235, 07235, 42235, 77
 30238, 17238. 53238. 90239, 27239, 65240, 02

A Table of oblique Ascensions.
S.D.123456
0238, 17238, 53238, 90239, 27239, 65240. 02
 4242, 37242, 77243, 15243, 53243, 92244. 30
 8246, 62247, 03247, 42247, 82248, 22248. 62
 12250, 90251, 32251, 72252, 13252, 55252. 95
 16255, 22255, 63256, 05256, 47256, 90257. 32
 20259, 55259, 97260, 40260, 83261, 25261. 68
 24263, 88264, 32264, 75265, 20265, 62266. 05
 2826 [...], 25268, 68269, 12269, 55269, 97270. 42
2272, 62273, 05273, 48273, 93274, 37274. 80
 6276, 98277, 40277, 83278, 27278, 70279. 13
 10281, 32281, 73282, 17282, 60283, 02283. 45
 14285, 63286, 05286, 47286, 88287, 32287. 73
 18289, 92290, 33290, 73291, 15291, 57291. 97
 22294, 17294, 58294, 97295, 37295, 78296. 17
 26298, 38298, 78299, 17299, 53299, 93300. 32
0302, 57302, 93303, 30303, 67304, 05304. 42
 4306, 70307, 05307, 38307, 73308, 10308. 45
 8310, 75311, 10311, 42311, 75312, 08312. 42
 12314, 78315, 10315, 40315, 72316, 02316. 33
 16318, 77319, 05319, 35319, 63319, 92320. 22
 20322, 68322, 95323, 22323, 48323, 75324. 02
 24326, 57326, 82327, 05327, 28327, 55327. 78
 28330, 40330, 62330, 83331, 05331, 27331. 50
2334, 20334, 38334, 58334, 77334, 95335. 17
 6337, 95338, 13338, 30338, 45338, 62338. 78
 10341, 68341, 83341, 97342, 10342, 23342. 38
 14345, 38345, 50345, 62345, 72345, 83345. 93
 18349, 05349, 13349, 23349, 32349, 40349. 47
 22352, 72352, 77352, 83352, 88352, 93353. 00
 26356, 37356, 40356, 42356, 45356, 47356. 52
 30360, 00360, 00360, 00360, 00360, 00360. 00

A Table of oblique Ascensions.
S.D.789101112
0000, 00000. 00000, 00000, 00000, 00000, 00
 403, 4703. 4303, 4003, 3803, 3503, 33
 806, 9506. 8806, 8306, 7806, 7206, 67
 1 [...]10, 4 [...]10. 3510, 2710, 1810, 1010, 00
 1613, 9513. 8313, 7213, 6013, 5013, 37
 2017, 4817. 3317, 2017, 0516, 9216, 77
 2421, 0520. 8720, 7220, 5320, [...]820, 20
 2824, 6524. 4724, 2724, 0723, 8723, 67
228, 3028. 0727, 8527, 6327, 4027, 18
 631, 9831. 7231, 4831, 2330, 8230, 73
 1035, 7235. 4535, 1834, 9034, 6334, 35
 1439, 5039. 2038, 9238, 6238, 3238, 02
 1843, 3543. 0342, 7242, 4042, 0841, 75
 2247, [...]546. 9246, 5746, 2345, [...]045, 53
 2651, 2050. 8350, 4850, 1249, 7749, 38
055, 2054. 8354, 4754, 0853, 7053, 32
 459, 2858. 9058, 5258, 1257, 7257, 32
 863, 4263. 0362, 6262, [...]061, 8061, 37
 1267, 6067. 2066, 7866, 3565, 9365, 50
 1671, 8571. 4270, 9870, 5370, 1269, 68
 2076, 1275. 6875, 2274, 8074, 3573, 92
 2480, 4279. 9879, 5379, 0878, 6378, 18
 2884, 7584. 3283, 8783, 4282, 9782, 52
289, 1288. 6888, 2387, 7887, 3386, 88
 693, 4893. 0592, 6092, 1791, 7291, 27
 1097, 8897. 4597, 0096, 5796, 1295, 68
 14102, 27101. 83101, 40100, 95100, 52100, 10
 18106, 63106. 22105, 80105, 37104, 95104, 52
 22110, 97110. 58110, 17109, 77109, 35108, 92
 26115, 30114. 92114, 53114, 13113, 73113, 32
 30119, 60119, 23118, 87118, 48118, 10117, 72

A Table of oblique Ascensions.
S.D789101112
0119, 60119, 23118, 87118, 48118, 10117, 72
 4123, 87123, 52123, 17122, 80122, 43122, 07
 8128, 10127, 77127, 42127, 07126, 75126, 38
 12132, 30131, 97131, 65131, 33131, 02130, 68
 16136, 45136, 15135, 87135, 57135, 27134, 97
 20140, 55140, 28140, 02139, 75139, 47139, 18
 24144, 63144, 38144, 15143, 90143, 65143, 38
 28148, 67148, 45148, 22148, 02147, 78147, 55
2152, 67152, 47152, 28142, 08151, 88151, 68
 6156, 65156, 47156, 30156, 13155, 97155, 80
 10160, 58160, 43160, 30160, 15160, 02159, 87
 14164, 50164, 38164, 27164, 15164, 05163, 93
 18168, 40168, 30168, 22168, 13168, 05167, 97
 22172, 27172, 22172, 15172, 10172, 05171, 98
 26176, 13176, 12176, 08176, 07176, 03176, 00
0180, 00180, 00180, 00180, 00180, 00180, 00
 4183, 87183, 88183, 92183, 93183, 97184, 00
 8187, 73187, 78187, 85187, 90187, 95188, 02
 12191, 60191, 70191, 78191, 87191, 95192, 03
 16195, 50195, 62195, 73195, 85195, 95196, 07
 20199, 42199, 57199, 70199, 85199, 98200, 13
 24200, 35203, 53203, 70203, 87204, 03204, 20
 28207, 33207, 53207, 72207, 92208, 12208, 32
2211, 33211, 55211, 78211, 98212, 22212, 45
 6215, 37215, 62215, 85216, 10216, 35216, 62
 10219, 45219, 72219, 98220, 25220, 53220, 82
 14223, 55223, 85224, 13224, 43224, 73225, 03
 18227, 70228, 03228, 35228, 67228, 98229, 32
 22231, 90232, 23232, 58232, 93233, 25233, 62
 26236, 13236, 48236, 83237, 20237, 57237, 93
 30240, 40240, 77241, 13241, 52242, 90242, 28

A Table of oblique Ascensions.
S.D.789101112
0240, 40240, 77241, 13241. 52241. 90242. 28
 4244, 70245, 08245, 47245. 87246. 27246. 68
 8249, 03249, 42249, 83250. 23250. 65251. 08
 12253, 37253, 78254, 20254. 63255. 05255. 48
 16257, 73258, 17258, 60259. 05259. 48259. 90
 20262, 12262, 55263, 00263. 43263. 88264. 32
 24266, 52266, 95267, 40267. 83268. 28268. 73
 28270, 88271, 32271, 77272. 22272. 67273. 12
2275, 25275, 68276, 13276. 58277. 03277. 48
 6279, 58280, 02280, 47280. 92281. 37281. 82
 10283, 88284, 32284, 78285. 20285. 65286. 08
 14288, 15288, 58289, 02289. 47289. 88290. 32
 18292, 40292, 80293, 22293. 65294. 07294. 50
 22296, 58296, 97297, 38297. 80298. 20298. 63
 26300, 72301, 10301, 48301. 88302. 28302. 68
0304, 80305, 17305, 53305. 92306. 30306. 68
 4308, 80309, 17309, 52309. 88310. 23313. 62
 8312, 75313, 08313, 43313. 77314. 10314. 47
 12316, 65316, 97317, 28317. 60317. 92318. 25
 16320, 50320, 80321, 08321. 38321. 68321. 98
 20324, 28324, 55324▪82325. 10325. 37325. 65
 24328, 02328, 28328, 52328. 77329. 18329. 27
 28331, 70331, 93332, 15332. 37332. 60332. 82
2335, 35335, 53335, 73335. 93336. 13336. 33
 6338, 95339, 13339, 28339. 47339. 62339. 80
 10342, 52342, 67342, 80342. 95343. 08343. 23
 14346, 05346, 17346, 28346. 40346. 50346. 63
 18349, 57349, 65349, 73349. 82349. 90350. 00
 22353, 05353, 12353, 13353. 22353. 28353. 33
 26356, 53356, 57356, 60356. 62356. 65356. 67
 30360, 00360, 00360, 00360. 00360. 00360. 00

A Table of oblique Ascensions.
S.D.131415161718
0000, 00000, 00000, 00000, 00000, 00000, 00
 403, 2803, 2703, 2303, 2003, 1703, 13
 806, 6006, 5506, 4806, 4306, 3706, 30
 1209, 9309, 8309, 7509, 6709, 5709, 47
 1613, 2713, 1513, 0212, 9212▪7812, 67
 2016, 6316, 4816, 3316, 1816, 0315, 88
 2420, 0319, 8519, 6719, 5019, 3219, 15
 2823, 4723, 2723, 0722, 8522, 6522, 45
226, 9526, 7226, 4826, 2526, 0325, 78
 630, 4730, 2229, 9729, 7029, 4529, 17
 1034, 0733, 8033, 5233, 2232, 9832, 63
 1437, 7237, 4037, 1036, 7836, 4736, 15
 1841, 4341, 1040, 7740, 4340, 0839, 73
 2245, 2044, 8344, 4844, 1343, 7743, 40
 2649, 0248, 6548, 2847, 9047, 5247, 12
052, 9252, 5352, 1551, 7551, 3350, 93
 456, 9256, 5056, 0855, 6859, 2554, 83
 860, 9760, 5360, 1059, 6799, 2558, 80
 1265, 0764, 6364, 2063, 7563, 2862, 83
 1669, 2368, 8068, 3567, 8867, 9266, 95
 2073, 4773, 0072, 5572, 0871, 6271, 15
 2477, 7377, 2776, 8276, 3575, 8875, 40
 2882, 0781, 6081, 1380, 6780, 2079, 72
286, 4285, 9585, 5085, 0284, 5584, 07
 690, 8290, 3589, 9089, 4288, 9588, 47
 1095, 2394, 7794, 3293, 859 [...], 3892, 92
 1499, 6599, 2098, 7798, 3097, 8397, 37
 18104, 08103, 65103, 22102, 77102, 30101, 87
 22108, 52108, 08107, 67107, 23106, 80106, 35
 26112, 92112, 52112, 10111, 68111, 27110, 85
 30117, 32116, 93116, 55116, 15115, 73115, 33

A Table of oblique Ascensions.
S.D.131415161718
0117, 32116, 93116, 55116, 15115, 73115, 33
 4121, 70121, 33120, 95120, 58120, 20119, 80
 8126, 03125, 70125, 33124, 98124, 62124, 25
 12130, 37130, 03129, 70129, 37129, 03128, 68
 16134, 67134, 37134, 05133, 73133, 43133, 10
 20138, 90138, 63138, 35138, 05137, 77137, 47
 24143, 13142, 88142, 62142, 37142, 10141, 83
 28147, 32147, 08146, 87146, 63146, 40146, 17
2151, 48151, 28151, 07150, 87150, 67150, 47
 6155, 62155, 45155, 27155, 10154, 92154, 73
 10159, 73159, 58159, 43159, 28159, 13158, 98
 14163, 82163, 70163, 57163, 47163, 33163, 22
 18167, 88167, 80167, 70167, 62167, 52167, 42
 22171, 93171, 87171, 82171, 75171, 68171, 62
 26175, 97175, 93175, 92175, 88175, 85175, 82
0180, 00180, 00180, 00180, 00180, 00180, 00
 4184, 03184, 07184, 08184, 12184, 15184, 18
 8188, 07188, 13188, 18188, 25188, 32188, 38
 12192, 12192, 20192, 30192, 38192, 48192, 58
 16196, 18196, 30196, 43196, 53196, 67196, 78
 20200, 27200, 42200, 57200, 72200, 87201, 02
 24204, 38204, 55204, 73204, 90205, 08205, 27
 28208, 52208, 72208, 93209, 13209, 33209, 53
2212, 68212, 92213, 13213, 37213, 60213, 83
 6216, 87217, 12217, 38217, 63217, 90218, 17
 10221, 10221, 37221, 65221, 95222, 23222, 53
 14225, 33225, 63225, 95226, 27226, 57226, 90
 18229, 63229, 97230, 30230, 63230, 972 [...]1, 32
 22233, 97234, 30234, 67235, 02235, 38235, 75
 26238, 30238, 67239, 05239, 42239, 80240, [...]0
 30242, 68243, 07243, 45243, 85244, 27244, 67

A Table of oblique Ascensions.
S.D.131415161718
0242, 68243, 07243, 45243, 85244, 27244, 67
 4247, 08247, 48247, 90248, 32248, 73249, 19
 8251, 48251, 92252, 33252, 77253, 20253, 65
 12255, 92256, 35256, 78257, 27257, 70258, 13
 16260, 35260, 80261, 23261, 70262, 17262, 63
 20264, 77265, 23265, 68266, 15266, 62267, 08
 24269, 18269, 65270, 10270, 58271, 05271, 53
 28273, 58274, 05274, 50274, 98275, 45275, 93
2277, 93278, 40278, 87279, 33279, 80280, 28
 6282, 27282, 73283, 18283, 65284, 12284, 60
 10286, 53287, 00287, 45287, 92288, 38288, 85
 14290, 77291, 20291, 6529 [...], 12292, 08293, 05
 18 [...]94, 9 [...]295, 37295, 80296, 25296, 72297, 17
 22299, 03299, 47299, 90300, 33300, 75301, 20
 26303, 08303, 50303, 92304, 32304, 75305, 17
0307, 08307, 47307, 85308, 25308, 67309, 07
 4310, 98311, 35311, 72312, 10312, 48312, 88
 8314, 80315, 17315, 52315, 87316, 23316, 60
 12318, 57318, 90319, 23319, 57319, 92320, 27
 16322, 38322, 60322, 90323, 22323, 53323, 15
 20325, 93326, 20326, 48326, 78327, 07327, 37
 24329, 53329, 78330, 03330, 30330, 55330, 83
 28333, 05333, 28333, 5233 [...], 75333, 97334, 22
2336, 53336, 73336, 93337, 153 [...]7, 35337, 55
 6339, 07340, 15340, 33340, 50340, 68340, 85
 10343, 37343, 52343, 67343, 82343, 97344, 12
 14346, 73346, 85346, 98347, 0834 [...], 22347, 33
 18350, 07350, 17350, 25350, 33350, 43350, 53
 22353, 40353, 45353, 52353, 57353, 63353, 70
 26356, 72356, 73356, 77356, 80356, 83356, 87
 30360, 00360, 00360, 00360, 00360, 00360, 00

A Table of oblique Ascensions.
S.D.192021222324
0000, 00000, 00000. 00000, 00000, 00000, 00
 403, 1203, 0803. 0503, 0202, 9802, 95
 806, 250 [...], 1806. 1206, 0505, 9805, 92
 1209, 3809, 2809. 1809, 1009, 0008, 90
 1612, 5312, 4212. 2812, 1712, 0311, 90
 2015, 7315, 5815. 4215, 2715, 1014, 93
 2418, 9718, 7818. 5818, 4018, 2018, 00
 2822, 2322, 0221. 8021, 5821, 3521, 13
225, 3825, 3025. 0524, 8024, 5524, 30
 628, 9228, 6528. 3528, 0827, 8027, 52
 1032, 3532, 0531. 7331, 4331, 1230, 80
 1435, 8335, 5235. 1734, 8334, 5034, 15
 1839, 4039, 0538. 6838, 3337, 9537, 60
 2243, 0342, 6742. 2841, 9041, 5041, 10
 2646, 7346, 3345. 9345, 5345, 1244, 68
050, 5250, 1049. 6849, 2548, 8248, 37
 454, 4053, 9753. 5353, 0752, 6352, 15
 858, 3557, 9057. 4556, 9756, 5056, 02
 1262, 3861, 9261. 4560, 9760, 4759, 98
 1666, 4866, 0365. 5365, 0564, 5364, 02
 2070, 6770, 1869. 6869, 1868, 6768, 15
 2474, 9274, 4273. 9273, 4272, 9072, 38
 2879, 2278, 7378. 2277, 7077, 2076, 67
283, 5883, 0882. 5882, 0781, 5781, 03
 687, 9887, 4886. 9886, 4885, 9785, 45
 1092, 4391, 9591. 4590, 9590, 3389, 92
 1496, 9096, 4295. 9395, 4894, 9594, 47
 18101, 40100, 92100. 4799, 9899, 4898, 98
 22105, 92105, 43105. 00104, 52104, 05103, 57
 26110, 42109, 97109. 53109, 08108, 63108, 17
 30114, 92114, 50114. 08113, 65113, 50112, 77

A Table of oblique Ascensions.
S.D▪192021222324
0114, 92114, 50114. 08113, 65113, 50112, 77
 4119, 42119, 02118. 62118, 20117, 80117, 37
 8123, 88123, 51123. 13122, 73122, [...]5121. 95
 12128, 33128, 00127. 63127, 27126, 90126, 53
 16132, 78132, 47132. 12131, 80131, 45131. 10
 20137, 18136, 88136. 57136, 27135, 95135, 63
 24141, 58141, 30141. 01140, 73140, 47140, 17
 28145, 92145, 85145. 42145, 18144, 9 [...]144, 67
2150, 25150, 03149. 82149, 58149, 37149, 13
 6154, 57154, 37154. 18153, 98153, 80153, 60
 10158, 83158, 68158. 52158, 53158, 20158, 03
 14163, 10162, 97162. 85162, 72162, 60162, 45
 18167, 33167, 23167. 15167, 05166, 97166, 85
 22171, 57171, 50171. 43171, 38171, 32171, 25
 26175, 80175, 77175. 73175, 70175, 67175, 63
0180, 00180, 00180. 00180, 00180, 00180, 00
 4184, 20184, 23184. 27184, 30184, 33184, 37
 8188, 43188, 50188. 57188, 62188, 68188, 75
 12192, 67192, 77192. 85192, 95193, 03193, 15
 16196, 90197, 03197. 15197, 28197, 40197, 55
 20201, 17201, 32201. 48201, 47201, 80201, 97
 24205, 43205, 63205. 82206, 02206, 20206, 40
 28209, 75209, 97210. 18210, 42210, 63210, 87
2214, 08214, 15214. 58214, 82215, 07215, 33
 6218, 42218. 70218. 99219, 27219, 53219, 83
 10222, 82223. 12223. 43223, 73224, 05224, 37
 14227, 22227. 53227. 88228, 20228, 55228, 90
 18231, 67232, 00232. 37232, 73233, 10233, 47
 22236, 12236, 49236. 87237, 27237, 65238, 05
 26240, 58240, 98241. 38241, 80242, 20242, 63
 30245, 08245, 50245. 92246, 35246, 50247, 23

A Table of Oblique Ascensions.
S.D.192021222324
0245, 08245, 50245, 92246. 35246, 50247, 23
 4249, 58250, 03250, 47250. 92251, 37251, 83
 8254, 08254, 57255, [...]0255. 48255, 95256, 43
 12258, 60259, 08259, 53260. 02260, 52261, 02
 16263, 10263, 58264, 07264. 52265, 05265, 53
 20267, 57268, 05268, 55269. 05269, 67270, 08
 24272, 02272, 52273, 02273. 52274, 03274, 55
 28276, 42276, 92277, 42277. 93278, 43278, 97
2280, 78281, 27281, 78282. [...]0282, 80283, 33
 6285, 08285, 58286, 08286. 58287, 10287, 62
 10289, 33289, 82290, 32290. 82291, 33291, 85
 14293, 52293, 97294, 47294. 95295, 47295, 98
 18297, 62298▪0 [...]298, 55299. 03299, 53300, 02
 22301, 65302, 10302, 5530 [...]. 03303, 50303, 98
 26305, 60306, 03306, 47306. 93307, 33307, 85
0309, 48309, 90310, 32310. [...]5311, 18311, 63
 4313, 27313, 67314, 07314. 47314, 88315, 32
 8316, 97317, 33317, 72318. 10318, 50318, 90
 12320, 60320, 95321, 32321. 67322, 05322, 40
 16324, 17324, 48324, 83325. 17325, 50325, 85
 20327, 65327, 95328, 27328. 57328, 88329, 20
 24331, 08331, 35331, 65331. 92332, 20332, 48
 28334, 62334, 70334, 95335. 20335, 45335, 70
2337, 77337, 98338, 20338. 42338, 65338, 87
 6341, 03341, 22341, 42341. 60341, 80342, 00
 10344, 27344, 42344, 58344. 73344, 90345, 07
 14347, 47347, 58347, 72347. 83347, 97348, 10
 18350, 62350, 72350, 82350▪903 [...]1, 00351, 10
 22353, 75353, 82353. 88353. 95354, 02354, 08
 26356, 88356, 92356. 95356. 98357, 02357, 05
 30360, 00360, 00360. 00360. 00360, 00360, 00

A Table of oblique Ascensions.
S.D.252627282930
0000, 00000, 00000, 00010, 00000, 00000, 00
 402, 8802, 9502, 8502, 8022, 7802, 73
 805, 8505, 7805, 7005, 6305, 5805, 50
 1208, 8008, 7008, 5808, 4808, 3808, 27
 1611, 7711, 6311, 5011, 3511, 2011, 07
 2014, 7714, 6014, 4314, 2514, 0713, 90
 2417, 8217, 6017, 4017, 1816, 9816, 77
 2820, 9020, 6720, 4220, 1819, 9219, 68
224, 0123, 7723, 4823, 2222, 9222, 65
 627, 2226, 9226, 6226, 3026, 0025, 67
 1030, 4830, 1529, 8229, 4829, 1328, 78
 1433, 8233, 4533, 0732, 7232, 3231, 95
 1837, 2236, 8336, 4336, 0335, 6235, 22
 2240, 7040, 2839, 8839, 4539, 0038, 57
 2644, 2543, 8343, 3742, 9342, 4742, 00
047, 9047, 4747, 0046, 3246, 0345, 53
 451, 6851, 2050, 7250, 2249, 7249, 20
 855, 5355, 0354, 5354, 0053, 4852, 95
 1259, 4858, 9758, 4357, 9057, 3556, 82
 1663, 5262, 9862, 4561, 9261, 3360, 78
 2067, 6367, 1066, 5566, 0065, 4364, 85
 2471, 8371, 3070, 7570, 1869, 6269, 03
 2876, 1375, 5875, 0374, 4773, 8873, 30
280, 5079, 7579, 4078, 8378, 2577, 67
 684, 9284, 3883, 8383, 2782, 6882, 10
 1089, 4088, 8788, 3287, 7787, 2086, 62
 1493, 9393, 4092, 8592, 3291, 7591, 18
 1898, 4897, 9897, 4596, 9296, 3595, 82
 22103, 08102, 58102, 08101, 55101, 03100, 48
 26107, 68107, 20106, 73106, 22105, 72105, 20
 30112, 30111, 87111, 40110, 92110, 43109, 93

A Table of oblique Ascensions.
S.D252627282930
0112, 30111, 87111. 40110, 92110, 43109, 93
 4116, 93116, 53116. 07115, 62115, 15114, 67
 8121, 55121, 15120. 71120, 30119, 85119. 40
 12126, 17125, 78125. 38124, 98124, 57124, 15
 16130, 77130, 40130. 03129, 67129, 28128, 90
 20135, 32134, 98134. 65134, 32133, 97133. 62
 24139, 87139, 75139, 28138, 97138, 65138, 33
 28144, 40144, 13143. 87143, 6514 [...], 30143, 03
2148, 92148, 67148. 43148, 18147, 95147, 68
 6153, [...]0153, 20153. 00152, 78152, 57152, 35
 10157, 87157, 70157. 53157, 35157, 17157, 03
 14162, 33162, 18162. 05161, 90161, 77161, 62
 18166, 77166, 65166. 55166, 43166, 33166, 22
 22171, 18171, 12170. 03170, 97170, 90170, 82
 26175, 60175, 57175. 53175, 40175, 47175, 42
0180, 00180, 00180. 00180, 00180, 00180, 00
 4184, 40184, 43184. 47184, 52184, 53184, 58
 8188, 82188, 88188. 97189, 03189, 10189, 18
 12193, 23193, 35193. 45193, 57193, 67193, 78
 16197, 67197, 82197. 95198, 10198, 23198, 38
 20202, 13202, 30202. 47202, 65202, 83202, 97
 24206, 60206, 80207. 00207, 22207, 43207, 65
 28211, 08211, 33211. 57211, 82212, 05212, 32
2215, 60215, 87216. 13216, 35216, 70216, 97
 6220, 13220. 25220. 73221, 03221, 35221, 67
 10224, 68225. 02225. 35225, 68226, 03226, 38
 14229, 23229. 60229. 97230, 33230, 72231, 10
 18233, 83234, 22234. 62235, 02235, 42235, 85
 22238, 45238, 85239. 28239, 70240, 15240, 60
 26243, 07243, 47243. 93244, 38244, 85245, 33
 30247, 70248, 13248. 60249, 08249, 57250, 07

A Table of oblique Ascensions.
S.D.252627282930
0247, 70248, 13248, 60249, 08249, 57250, 07
 4252, 32252, 80253, 27253, 78254, 28254, 80
 8256, 92257, 42257, 92258, 45258, 97259, 52
 12261, 52262, 02262, 55263, 08263, 65264, 18
 16266, 07266, 60267, 15267, 68268, [...]5268, 82
 20270, 60271, 13271, 68272, 2 [...]27 [...], 80273, 38
 24275, 08275, 62276, 1727 [...], 73277, 32277, 90
 28279, 50280, 05280, 60281, [...]7281, 75282, 33
2283, 87284▪42284, 9728 [...], 53286, 122 [...]6, 70
 6288, 17288, 70289, 25289, 82290, 35290, 97
 10292, 37292, 90293, 45294, 00294, 57295, 15
 14296, 48297, 02297▪55298, 08298, 67299, 22
 18300, 52301, 03301, 57302, 10302, 65303, 18
 22304, 47304, 97305, 47306, 00306, 52307, 05
 26308, 32308, 80309, 28309, 78310, [...]8310, 80
0312, 10312, 53313, 00313, 6831 [...], 97313, 47
 4314, 75315, 17316, 63316, 07317, 53317, 00
 8319, 30319, 72320, 12320, 55321, 00321, 43
 12322, 78323, 17323, 57323, 97324, 38324, 78
 16326, 18326, 55326, 93327, 28327, 68328, 05
 20329, 52329, 85330, 18330, 52330, 87331, 22
 24332, 78333, 08333, 3533 [...], 70334, 00334, 33
 28335, 99336, 23336, 52336, 78337, 08337, 35
2339, 10339, 33339, 58339, 82340, 08340, 32
 6342, 18342, 40342, 60342, 82343, 02343, 23
 10345, 23345, 40345, 57345, 75345, 93346, 10
 14348, 23348, 3734 [...], 50348, 65348, 80348, 93
 18351, 20351, 30351, 42351, 52351, 62351, 73
 22354, 15354, 22354, 28354, 37354, 42354, 50
 26357, 12357, 05357, 15357, 20357, 22357, 27
 30360, 00360, 00360, 00360, 00360, 00360, 00

A Table of oblique Ascensions.
S.D.313232. 18333435
0000, 00000, 00000. 00000, 00000, 00000, 00
 402, 7002, 6702. 6602, 6202, 5802, 53
 805, 4305, 3505. 3405, 2705, 1805, 10
 1208, 1708, 0508. 0307, 9307, 8007, 68
 1610, 9210, 7810. 7510, 6010, 4510, 28
 2013, 7013, 5213. 4913, 3213, 0212, 92
 2416, 5316, 3216. 2816, 0715, 8515, 58
 2819, 4219, 1719. 1218, 8718, 6218, 32
222, 3522, 0721. 0121, 7321, 4321, 12
 625, 3325, 0224. 9624, 6724, 3223, 95
 1028, 4228, 0527. 9827, 6727, 2826, 88
 1431, 5531, 1531. 0830, 7330, 3229, 88
 1834, 7834, 3534. 2733, 9033, 4532, 98
 2238, 1037, 6537. 5737, 1736, 6836, 17
 2641, 5241, 0340. 9440, 5240, 0039, 87
045, 0344, 5244. 4243, 9843, 4342, 87
 448, 6748, 1247. 0247, 5547, 0046, 40
 852▪4051, 8351. 7351, 2550, 6750, 05
 1256, 2355, 6355. 5355, 0554, 4353, 82
 1660, 2059, 6059, 4958, 9858, 3557, 70
 2064, 2563, 6563. 5463, 0262, 3861, 72
 2468, 4 [...]67, 8067. 6967, 1766, 5265, 85
 2872, 6872, 0771. 9671, 4370, 7870, 08
277, 0376, 4 [...]76. 3175, 8075, 1574, 47
 681, 4880, 8880. 7780, 2579, 6078, 93
 1086, 0285, 4285. 3184, 7884▪1583, 48
 1490, 6290, 0189. 9089, 3888, 7788, 12
 189 [...], [...]794, 6794. 5794, [...]793, 4792, 83
 2299, 9599, 3899. 2898, 8098, 2297, 60
 26104, [...]7104, 12104. 02103, 57103, 00102, 40
 30109, 43108, 92108. 83108, 38107, 83107, 27

A Table of oblique Ascensions.
S.D313252 18333435
01 [...]9, 4 [...]108, 9 [...]108, 8310 [...], 38107, 83107, 27
 4114, 18113, 70113, 6111 [...], 18112, 67112, 13
 8118, 95118, 48118, 40118, 01117, 52117, 03
 12123, 72123, 28123, 20122, 85122, 38121, 92
 16128, 52128, 10128, 03127, 70127, 27126, 85
 20133, 25132, 88132, 81132, 5013 [...], 12131, 72
 24138, 00137, 68137, 62137, 32136, 98136, 62
 28142, 73142, 43142, 38142, 12141, 82141, 48
2147, 43147, 17147, 12146, 90146, 63146, 35
 6152, 13151, 90151, 86151, 67151, 43151, 18
 10156, 80156, 62156, 58156, 42156, 22156, 03
 14161, 47161, 32161, 29161, 15161, 00160, 83
 18166, 12166, 00165, 98165, 88165, 77165, 63
 22170, 80170, 67170, 66170, 60170, 52170, 43
 26175, 38175, 33175, 32175, 30175, 27175, 22
0180, 00180, 00180, 00180, 00180, 00180, 00
 4184, 62184, 67184, 68184, 70184, 73184, 78
 8189, 20189, 33189, 34189, 40189, 48189, 57
 12193, 88194, 00194, 02194, 12194, 23194, 37
 16198, 53198, 68198, 71198, 85199, 00199, 17
 20203, 20203, 38203, 42203, 58203, 78203, 97
 24207, 87208, 10208, 14208, 33208, 57208, 82
 28212, 57212, 83212, 88213, 10213, 37203, 65
2217, 27217, 57217, 62217, 88218, 18218, 52
 6222, 00222, 32222, 38222, 68223, 02223, 38
 10226, 75227, 12227, 19227, 50227, 88228, 28
 14231, 48231, 90231, 97232, 30232, 7323 [...], 15
 18236, 28236, 72236, 80237, 15237, 62238, 08
 22241, 05241, 52241, 60241, 99242, 48242, 97
 26245, 82246, 30246, 39246, 82247, 33247, 87
 30250, 57251, 08251, 17251, 62252, 17252, 73

A Table of oblique A scensions.
S.D.313252. 18333435
0250, 57251, 08251, 17251. 62252, 17252, 73
 4255, 33255, 88255, 98256. 4 [...]257, 00257, 60
 8260, 05260, 6 [...]260, 71261. 20261, 78262, 40
 12264, 73265, [...]3265, 43265. 9326 [...], 53267, 17
 16269, 38269, 99270, 10270. 62271, 23271, 88
 20273, 90274, 58274, 69275. 22275, 85276, 52
 24278, 52279, 12279, 23279. 75280, 40281, 07
 28282, 97283, 58283, 69284. 20284, 85285, 53
2287, 32287, 93288, 042 [...]8. 57289, 22289, 92
 6291, 58292, 20292, 31292. 83293. 48294, 15
 10295, 75296, 15296, 46296. 98297, 62298, 28
 14299, 80300, 40300, 51301. 02301, 65302, 30
 18303, 77304, 37304, 47304. 95305, 57306, 18
 22307, 60308, 17308, 27308. 75309, [...]3309, 95
 26311, 33311, 88312, 98312. 45313, 00313, 60
0314, 97315, 48315, 58316. 02316, 57317, 13
 4318, 48318, 97319, 06319. 48320, 00320, 13
 8321, 90322, 35322, 4 [...]322. 8 [...]323, 32323, 83
 12325, 22325, 65325, 73326. 10326, 55327, 02
 16328, 45328, 85328, 92329. 27329, 68330, 12
 20331, 58331, 95332, 02332. 33332, 82333, 12
 24334, 67334, 98335, 04335. 33335, 68336, 05
 28337, 65337, 93338, 99338. 27338, 57338, 88
2340, 58340, 83340, 88341. 13341, 38341, 68
 6343, 47343, 6834 [...], 72343. 93344, 15344, 42
 10346, [...]0346, 48346, 51346. 68346, [...]8347, 08
 14349, 08349, 22349, 25349. 40349, [...]5349, 72
 18351, 83351, 95351, 97352. 07352, 20352, 32
 22354, 57354, 65354. 66354. 73354, 82354, 90
 26357, 30357, 33357. 34357. 38357, 42357, 47
 30360, 00360, 00360. 00360. 00360, 00360, 00

A Table of oblique Ascensions.
S.D.363738394041
0000, 00000, 00000, 00000, 00000, 00000, 00
 402, 5002, 1302, 4202, 3702, 3302, 27
 805, 0304, 9304, 8504, 7704, 6704, 57
 1207, 5707, 4307, 3007, 1707, 0206, 88
 1610, 1209, 9509, 7709, 5809, 4009, 22
 2012, 7212, 5012, 2812, 0511, 8011, 58
 2415, 3515, 1014, 8214, 5714, 2713, 98
 2818, 0317, 7517, 4217, 1216, 8016, 47
220, 7720, 4520, 0819, 7319, 3718, 98
 623, 5823, 2022, 8222, 4222, 0021, 57
 1026, 4826, 0525, 6325, 1824, 7324, 25
 1429, 4328, 9728, 5228, 0327, 5327, 02
 1832, 5032, 0 [...]31, 50 [...]0, 9730, 4329, [...]8
 2235, 6735, 1334, 5834, 0333, 4532, 87
 2638, 9338, 3537, [...]837, 18 [...]6, 5735, 93
042, 3041, 7041, 1040, 4739, 82 [...]9, 15
 445, 8045, 1844, 534 [...], 9 [...]4 [...], 2042, 50
 849, 4248, 7848, 1047, 4346, 7246, 00
 1253, 1552, 5051, 8251, 1050, 3849, 63
 1657, 0556, 3755, 6554, 9354, 1853, 42
 2061, 0560, 355 [...], 6 [...]58, 8858, 1257, 33
 2465, 1764, 4763, 7362, 9962, 2061, 40
 2869, 4068, 7067, 9767, 2266, 4365, 63
273, 7873, 0772, 3371, 0870, 7869, 99
 678, [...]577, 5576, 8276, 0775, 2874, 48
 1082, 8282, 1281, 4080, 6579, 8879, 10
 1487, 4786, 7786, 0785, 3584, [...]883, 82
 1892, 1891, 5290, 8390, 1389, 4088, 65
 2296, 9796, 3295, 6794, 9894, 2893, 55
 26101, 82101, 18100, 5799, 9099, 2298, 52
 30106, 70106, 10105, 50104, 87104, 22103, 55

A Table of Oblique Ascensions.
S.D.363738394041
0106, 70106, 10105, 50104. 87104▪22103. 55
 4111, 60111, 03110, 45109. 87109. 25108. 62
 8116, 50115, 9 [...]115, 43114. 88114. 30113. 70
 12121, 43120, 95120, 45119. 92119. 37118. 82
 16126, [...]8125, 93125, 46124. 98124. 47123. 95
 20131, 32130, 88130, 47130. 02129. 57129. 08
 24136, 25135, 86135. 47135. 08134. 67134. 23
 28141, 15140, 82140, 46140. 12139. 73139. 37
2146, 05145, 75145, 45145. 13144. 80144. 48
 6150, 95150, 68150, 42150. 14149. 8714 [...]. 58
 10155, 82155, 60155, 38155. 15154. 90154. 68
 14160▪68160, 50160, 32160. 14159. 95159. 77
 18165, 52165, 38165, 25165. 12164. 98164. 83
 22170, 35170, 27170, 17170. 08170. 00169. 88
 26175, 18175, 13175, 10175. 05175. 00174. 95
0180, 00180, 00180, 00180. 00180. 00180. 00
 4184, 82184, 87184, 90184. 95185. 00185. 05
 8189, 65189, 73189, 83189. 92190. 00190. 12
 12194, 48194, 62194, 75194. 88194. 02195. 17
 16199, 32199, 50199, 68199. 86200. 05200. 23
 20204, 18204, 40204, 62204. 85205. 10205. 32
 24209, 05209, [...]2209, 58209. 86210. 13210. 42
 28213, 95214, 25214, 55214. 87215▪20215. 52
2218, [...]5219, 18219, 54219. 88220. 27220. 63
 6223, 75224, 14224, 5 [...]224. 92225. 33225. 77
 10228, 68229, 12229, 53229. 98230. 43230. 92
 14233, 62234, 07234, 54235. 02235. 53236. 05
 18238, 57239, 05239, 55240. 08240. 63241. 18
 22243, 50244, 02244, 57245. 12245. 70246. 30
 26248, 40248, 97249, 55250. 13250. 75251. 38
 30253, 30253, 90254, 50255. 13255. 78256. 45

A Table of oblique Ascensions.
S.D.363738394041
0253, 3025 [...], 90254, 50255, 13255, 78256, 45
 4258, 13258, 82259, 4 [...]260, 10260, 78261, 48
 8263, 03263, 68264, 33265, 02265, 72266, 45
 12267, 82268, 48269, 17269, 87270, 60271, 35
 16272, 53273, 23273, 93274, 65275, 42276, 18
 20277, 18277, 8827 [...], 60279, 35280, 12280, 90
 24281, 75282, 45283, 18283, 93284, 72285, 52
 28286, 22286, 93287, 67288, 92289, 22290, 01
2290, 60291, [...]0291, 03292, 78293, 57294, [...]7
 6294, 83295, 53296, [...]7297, 01279, 80298, 60
 10298, 95299, 65300, 37301, 12301, 88302, 67
 14302, 95303, 63304, 3530 [...], 07305, 82306, 58
 18306, 85307, 50308, 18308, 90309, 62310, 37
 22310, 58311, 22311, 90312, 57313, 28314, 00
 26314, 20314, 82315, 47316, 10316, 80317, 50
0317, 70318, 30318, 90319, 53320, 18320, 85
 4321, 07321, 65322, 22322, 82323, 43324, 07
 8324, 33324, 87325, 42325, 97326, 55327, 13
 12327, 50328, 00328, 50329, 03329, 57330, 12
 16330, 57331, 03331, 48331, 97332, 47332, 98
 20333, 52333, 95334, 37334, 82335, 27335, 75
 24336, 42336, 80337, 18337, 58338, 00338, 43
 28339, 23339, 55339, 92340, 27340, 63341, 02
2341, 97342, 25342, 58342, 88343, 20343, 53
 6344, 65344, 90345, 18345, 43345▪73346, 02
 10347, 28347, 50347, 72347, 95348, 20348, 42
 14349, 88350, 05350, 23350, 42350, 60350, 78
 18352, 43352, 57352, 70352, 83352, 98353, 12
 22354, 97355, 07355, 15355, 23355, 33355, 43
 26357, 50357, 87357, 58357, 63357, 67357, 73
 30360, 00360, 00360, 00360, 00360, 00360, 00

A Table of oblique Ascensions.
S.D.424344454647
0000, 0000, 00000, 00000, 00000, 00000, 00
 402, 2202, 1802, 1302, 0702, 0001, 92
 804, 4704, 3704, 2704, 1504, 0303, 92
 1206, 7306, 5706, 4206, 2506, 0805, 92
 1609, 0008, 8008, 6008, 3808, 1507, 92
 2011, 3311, 0710, 8210, 5310, 2509, 97
 2413, 7013, 4013, 0812, 7312, 4012, 05
 2816, 1215, 7715, 4015, 0214, 6224, 20
218, 6018, 2017, 7717, 3316, 8816, 42
 621, 1320, 6820, 2019, 7219, 2218, 68
 1023, 7723, 2722, 7522, 2021, 6521, 07
 1426, 4825, 9325, 3724, 7824, 1723, 52
 1829, 3028, 7328, 1027, 4726, 7826, 08
 2232, 2531, 6230, 9530, 2529, 5528, 80
 2635, 2734, 5833, 8833, 1732, 3831, 77
038, 45 [...]7, 7336, 9836, 2335, 4034, 57
 441, 7741, 0340, 2339, 4238, 5737, 68
 845, 2244, 4543, 6342, 7841, 8740, 97
 1248, 8548, 0347, 1846, 3045, 4044, 42
 1652, 6051, 7750, 8849, 9849, 0548, 05
 2056, 5055, 6554, 7853, 8352, 8851, 87
 2460, 5759, 7258, 8057, 8756, 8855▪87
 2864, 7063, 9263, 0162, 0761, 0760, 05
269, 0368, 2867, 3566, 4365, 4564, 42
 673, 6572, 7871, 8870, 9369, 9768, 95
 1078, 2777, 4276, 5375, 6074, 6573, 63
 1483, 0282, 1881, 3080, 4079, 4778, 47
 1887, 8787, 0786, 2085, 3384, 4 [...]83, 43
 2292, 7892, 0191, 1890, 3389, 4588, 52
 2697, 7897, 0396, 2595, 4394, 5893, 70
 30102, 85102, 13101, 38100, 6299, 8098, 97

A Table of oblique Ascensions.
S.D.424344454647
0102, [...]5102, 1310 [...], 38100. 6299, 8098▪97
 4107, 95107, 2710 [...], 57105. 83105▪07104. 28
 811 [...], 0 [...]112, 45111, 78111. 10110. 38109. 63
 121 [...]8, 25117, 65117, 0 [...]116. [...]8115. 73115. 03
 16123, 4 [...]122, 88122, 32121. 70121. 27120. 47
 20128, 60128, 10127, 58127. [...]126. 48125. 90
 24133, 90133, 35132, 87132. 42131. [...]7131. 33
 28138, 97138, 57138, 1 [...]137. 72137. 25136. 78
2144, 13143, 78143, 40143. 03142. 63142. 50
 6149, 30148, 9814 [...], 67148. 33148. 00147. 65
 10154, 43154, 17153, 92153. 63153. 35153. 07
 14159, 57159, 37159, 15158▪93158. 70158. 47
 18164▪68164, 52164, 37164. 20164. 03163. 87
 22169▪80169, 68169, 58169. 47169. [...]7169. 25
 26174, 90174, 85174, 80174. 73174. 67174. 63
0180, 00180, 00180, 00180. 00180. 00180. 00
 4185, 10185, 15185, 20185. 27185. 33185. 37
 8190, 20190, 32190, 42190. 53190. 63190. 75
 12195, 32195, 48195, 63195. 80195. 97196. 13
 16200, 43200, 63200, 85201. 07201. 30201. 53
 20205, 572 [...]5, 83206, 08206. 37206. 65206. 93
 24210, 70211, 02211, 33211. 67212. 00212. 35
 28215, 87216, 22216, 60216. 97217. 37217. 50
2221, 03221, 43221, 87222. 28222. 75223. 22
 6226, 20226, 652 [...]7, 13227. 58228. 13228. 67
 10231, 40231, 90232, 42232. 97233. 52234. 10
 14236, 58 [...]37, 12237, 68238. [...]0238. 73239. 53
 18241, 75242, 3524 [...], 97243. 62244. 27244. 97
 22246, 92247, 55248, 22248. 90249. 62250. 37
 26252, 05252, 73253, 43254. 17254. 93255. 72
 30257, 15257, 87258, 62259, 38260. 20261. 03

A Table of Oblique Ascensions.
S.D.424344454647
0257, 15257, 87258, 62259, 38260, 20261, 03
 4262, [...]2262, 97263, 75264, 57265, 42266, 20
 8267, 22267, 99268, 82209, 67 [...]70, 55271, 48
 12272, 13272, 93273, 80274, 67275, 58276, 57
 16276, 98277, 8 [...]278, [...]0279, 60280, 53281, 53
 20281, 73282, 58283, 47284, 40285, 35286, 37
 24286, [...]5287, 22288, 12289, 07290, 03291, 05
 28290, 97291, 72292, 65293, 57294, [...]5295, 58
2295, 30296, 08296, 99297, 93298, 93299, 95
 6299▪43300, 28301, 20302, 13303, 12304, 13
 1030 [...], 50304, 35305, 32306, [...]7307, 1 [...]308, 13
 14307, 40308, 23309, 12310, 02310, 95311, 95
 18311, 15311, 97312, 82313, 60314, 60315, 58
 22314, 78315, 55316, 37317, 22318, 13319, 03
 26318, 23318, 97319, 77320, 58321, 43322, 32
0321, 55322, 27323, 02323, 77324, 60325, 43
 4324, 73325, 42326, 12326, 83327, 62328, [...]3
 8327, 75328, 38329, 05329, 75330, 45331, 20
 12330, 70331, 27331, 90332, 53333, 22333, 92
 16333, 52334, 07334, 63335, 22335, 83336, 4 [...]
 20336, 23336, 73337, [...]5337, 80338, 35338, 93
 24338, 87339, 32339, 80340, 28340, 78341, 32
 28341, 40341, 8034 [...], 23342, 67343, 1234 [...], 58
2343, [...]8344, 23344, 60344, 98345, 38345, [...]0
 6346, 30346, 60346, 9 [...]347, 27347, 60347▪95
 10348, 6334 [...], 9 [...]349▪18349, 47349, 75350, 0 [...]
 14351, 00351, 20351, 40351, 62351, [...]5352, [...]8
 18353, 27353, 4 [...]353, 5835 [...], 7535 [...], 92354, [...]8
 22355, 53355, 63355, 73355, 8 [...]255, 97 [...]56, [...]8
 26357, 78357, 82357, 87357, 93358, 0035 [...], 08
 30360, 00360▪00360, 00360, 00360, 003 [...]0, 00

A Table of oblique Ascensions.
S.D.47. 474849505151. 53
000, 0000, 0000, 0000, 0000. 0000, 00
 401, 9001, 8801, 8301, 7701. 6801, 65
 803, 8703, 8003, 6 [...]03, 5303. 4003, 32
 1203, 8305, 7305, 5305, 3705. 1305, 02
 1607, 8107, 6707, 4207, 1506. 8706, 72
 2009, 8209, 6509, 3 [...]09, 0008. 6708, 48
 2411, 8811, 6811, 3010, 9210. 5010, 27
 2814, 0013, 7713, 3312, 8712. 3812, 12
216, 1915, 9315, 4214, 8814. 3314, 01
 618, 4318, 1517, 5716, 9716. 3516, 00
 1020, 7320, 3519, 8219, 1518. 4718, 08
 1423, 1822, 8522, 1721, 4320. 6720, 23
 1825, 7325, 3824, 4723, 8223. 0122, 55
 2228, 4028, 0327, 2226, 3525. 4724, 97
 2631, 2230, 7729, 8828, 9828. 0227, 50
034, 1333, 6832, 7531, 7830. 7730, 20
 437, 2336, 7535, 7834, 7733. 7033, 10
 840, 4840, 0138, 9837, 9236. 8036, 13
 1243, 9043, 4042, 3741, 2340. 0839, 43
 1647, 5347, 0245, 9344. 784 [...]. 5842, 92
 2051, 3850, 4049, 704 [...], 5347. 3246, 60
 2455, 3554, 8053, 6752, 4851. 2250, 50
 2859, 5058, 9757, 835 [...], 6355. 3754, 65
263, 8763, 3 [...]6 [...], 1861, 0059. 7359, 01
 668, 4267, 8766, 7365, 5564. 3063, 58
 1073, 1272, 5771, 4770, 3069. 0768, 37
 1477, 9777, 4376, 3375, 2073. 9873, 32
 1882, 9382, 4381, 4080, 2779. 137 [...], 47
 2288, 0587, 5786, 5385, 3584. 3583, 72
 2693, 2792, 7791, 8090, 7889. 7089, 10
 3098, 5398, 0897, 1596, 1895. 1794, 60

A Table of oblique Ascensions.
S.D47. 474849505151. 53
0098, 53098, 08097, 15096, 18095, 17094, 60
 4103, 88103, 4510 [...], 57101, 67100, 70100, 17
 8109, 27108, 87103, 05107, 20106, 30105, 80
 12114, 70114, 32113. 77112, 77111, 95111, [...]8
 16120, 15119, 80119. 12118, 38117, 62117, 18
 20125, 62125, 28124. 65123, 98123, 30122, 92
 24131, 08130, 82130. 2 [...]129, 62129, 02128, 67
 28136, 53136, 30135. 80135, 27134, 72134, 40
2142, 02141, 78141. 35140, 88140, 40140, 13
 6147, 43147, 28146. 90146, 50146, 10145, 87
 10152, 92152, 75152. 43152, 10151, 77151, 57
 14158, 33158, 22157. 97157, 70157, 43157, 27
 18163, 75163, 68163. 48163, 28163, 08162, [...]7
 22169, 18169, 13169. 00168, 87168, 73168, 65
 2617 [...], 60174, 57174. 51174, 45174, 37174, 33
0180, 00180, 00180. 00180, 00180, 00180, 00
 4185, 40185, 43185. 49185, 55185, 63185, 67
 8190, 82190, 87191. 00191, 13191, 27191, 35
 12196, 25196, 32196. 52196, 72196, 92197, 03
 16201, 67201, 78202. 03202, 30202, 57202, 73
 20207, 08207, 25207. 57207, 90208, 23208, 43
 24212, 57212, 72213. 10213, 50213, 90214, 13
 28217, [...]8218, 22218. 65219, 12219, 60219, 87
2223, 47223. 70224. 20224, 73225, 28225, 60
 6228, 92229. 18229. 78230, 38230, 98231, [...]3
 10234, 38234, 72235. 35236, 02236, 70237, 08
 14239, 85240. 20240. 20241, 6 [...]242, 38242, 82
 18245, 30245, 68246, 62247, 23248, 05248, 52
 22250, 73251, 13251. 9 [...]252, 70253, 70254, 20
 26256, 12256, 55257. 43258, 33259, 30259, [...]3
 30261, 47261, 92262. 8526 [...], 82264, 83265, 40

A Table of oblique Ascensions.
S.D.474849505151. 53
0261, 47261, 92262, 85263, 12264, 83265, 40
 4266, 23267, 23268, 20269, 20270, 30270, 90
 8272, 95272, 43273, 47274, 65275, 65276, 28
 12277, 07277, 57278, 60279, 72280, 87281, 53
 16282, 03282, 57283, 67284, 80286, 02286, 68
 20286, 88287, 43288, 53289, 70290, 93291, 63
 24291, 58292, 13293, 27294, 45295, 70296, 42
 28296, 13296, 67297, 82299, 00300, 27300, 99
2300, 50301, 0330 [...], 17303, 37304, 63305, 35
 6304, 65305, 20306, 33307, 52308, 78309, 50
 10308, 62309, 60310, 30311, 47312, 68313, 40
 14312, 47312, 98314, 07315, 22316, 42317, 08
 18316, 10316, 60317, 63318, 77319, 92320, 57
 22319, 52319, 99321, 02322, 08313, 20343, 17
 26322, 77323, 25324, 22325, 23326, 30326, 90
0325, 87326, 32327, 25328, 22329, 23329, 80
 4328, 78329, 23330, 12331, 02331, 98332, 50
 8331, 60331, 973 [...]2, 78333, 65334, 53335, 03
 12334, 27334, 62335, 53336, 18336, 99337, 45
 16336, 82337, 15337, 83338, 57339, 33339, 77
 20339, 27339, 65340, 18340, 85341, 53341, 92
 24341, 57341, 85342, 43343, 03343, 65344, 00
 28343, 81344, 07344, 58345, 12345, 67345, 99
2346, 00346, 23346, 67347, 13347, 62347, 88
 634 [...], 12348, 32<