CHAP. I. Of Letters and Syllables.

GRammer is an ART which Teacheth how to Speak and Write truly.

The Parts thereof are Four, Letters, Syllables, Words, and Sentences.

A Letter is a Character, or Index, of a simple sound. And in the English Tongue there are Twenty four.

The which Letters are distinguished from one another, partly by their shapes and partly by their sounds.

[Page 2]In reference to their shapes, they are di­stinguished by three different Characters, the Roman, Italick, and black English.

And in each of these Characters there is the great and the small Letter.

In the Roman Character, the Great Letter is thus formed,

A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z.

The small thus,

a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, s, t, u, v, w, x, y, z.

The great and small Italick Letters are made thus,

A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z,

a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, s, t, u, v, w, x, y, z.

The great and small black English thus,

A, B, C, D, E, F, G, H, I, K, L, M, N, O, P, Q, R, S, T, V, W, X, Y, Z.

a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, r, s, s, t, u, v, w, x, y, z.

The great Letters are used in the begin­ning of proper Names, Emphatical words, Sentences, and Verses. The Letter I when it stands alone, is always written with a great Character.

[Page 3]These Twenty and four Letters are divi­ded into Vowels and Consonants.

A Vowel is a letter which maketh a full and perfect sound of it self, and they are five, a, e, i, o, u, besides the Greek Vowel y.

A Consonant is a letter which maketh a sound by help of a Vowel, and these are Eighteen, besides the letters j, v, and y, which sometimes are Consonants also.

Of the eighteen Consonants, some are mutes, as these eight, b, c, d, g, k, p, q, and t. Some semi-Vowels, as these eight, f, l, m, n, r, s, x, and z, of which these four, l, m, n, r, are also called Liquids, x, and z, double Consonants, and the other two, h, and w, irregular Letters.

Some of these Letters, as well Vowels as Consonants, have sounds very different from their common names. Thus the let­ter c, before e, and i, is sounded like f, but before a, o, u, it is sounded like k, as in cat, cot, cut.

The Letter f, is sometimes sounded ac­cording to its usual name, as when it fol­lows a Vowel, as in if, of, effeminate, but when it begins a Word or Syllable, it is sounded fee, as in feet, foolish.

The Letter g, before a, o, and u, is soun­ded hard, thus, ghee, as in gad, God, gut, but before e and i it is sometimes, but not always, sounded according to its usual name gee, as in danger, ginger.

[Page 4]The Letter h, is never sounded according to its name ach, but thus, hee, as in hand, help, him.

The letters j and v, when they come be­fore themselves, or any other Vowel in the same Syllable, become Consonants, and have different sounds from their usual names, j is pronounced like g soft, thus ji is pronounced like gi, in ginger, v is pronounced vee, or vu, as in vanish, vine; and when they are thus sounded, their shape is also changed, and hence some would have them to be distinct letters, and would have the number of our letters to be not 24 but 26.

The Liquids l, m, n, and r, when they be­gin a Word or Syllable, are sounded thus, lee, mee, ree, as in light, mind, need, read.

The letter q, hath always u after it, to help its sound, but is not to be sounded accor­ding to its name eu, but que, as in question.

The letter s, when it begins a word or Syllable is to be sounded thus; see, as in sad, secret, but in the end of a word, or between two Vowels or Dipthongs, it hath for the most part the sound of z, as in easie, bosom.

The letter t before i, if another Vowel fol­loweth, hath the sound of si, as in Egyptian, patience; but when it followeth s or x, it hath its own proper sound, as in bestial, mixtion.

The letter w, hath its name from its shape, being composed of twice u, it is called dou­ble u; but is in no case so sounded, but we, as in wall, well, will.

[Page 5]The letter x, when it begins a word or Syllable, is sounded thus, xee, as in Xerxes; in other cases thus, ex, or ecs.

The letter y hath by no means its sound according to its usual name wi, but when it begins a word or Syllable, and so becomes a Consonant, it is sounded yee; when it comes in the middle or end of a word, it is sounded like i Vowel, as in my, thy.

The letter z is to be sounded zee, as in Zeal.

A Syllable is a literal or articulate Voice of one individual sound.

Syllables are of two sorts, improper and proper.

An improper Syllyble is made of one or more Vowels without a Consonant; as a-ny, e-vil, Ae-neas, Oe-dipus.

A Proper Syllable is the comprehension of one or more Consonants, with one or more Vowels, in one sound or breath; as Ge-ne-ra-ti-on, Moun-tain, and in our English Tongue doth sometimes consist of eight let­ters, as strength.

When two Vowels are joyned together in one sound or breath, they are called Dip­thongs; of which there are two sorts, Proper and Improper.

Of proper Dipthongs, there are these eight, ai, ei, oi, au, eu, ou, ee, and oo.

The first six are sometimes written thus, ay, ey, oy, aw, ew, ow.

[Page 6]Of improper Dipthongs there are but these three, ea, oa, and ie.

The two Vowels which make a Dipthong, are for the most part to be sounded together, as in Faith, neither, Eunuch, but in these words, Laity, Mosaick work, Deity, Atheist, moity, doing, reenter, reiterate, and such like; and in most Proper Names in the Bible they are to be sounded severally.

The Improper Dipthongs ea, and o [...], are sounded together, except in these words, beatitude, Creator, creation, real, theatre, and most proper names of Women, Cities, and Countries; but the two Vowels in this Dip­thong ei, are usually parted, except in these two words, friend, grief, and when they come in the end of a word, as in mer­cie, charitie, and such like.

An English syllable, though it may consist of eight letters, yet doth it never begin with more than two Vowels before a Con­sonant, of three Consonants before a Vowel or Dipthong.

The two Consonants which may begin an English word or syllable, are these thirty, Bl, br, ch, cl, cr, dr, dw, fl, fr, gl, gn, gr, kn, pl, pr, sc, sh, sk, sp, sl, sm, sn, sq, sw, th, tr, tw, wh, and wr.

And the three Consonants that may begin an English word, are these nine, Sch, scr, shr, skr, spl, spr, str, thr, thw.

In the sounding of the Consonants, which [Page 7] are joyned together in the beginning of a word, there is no difficulty, but in these few, ch, gh, and th.

The letters ch, when they come before a Vowel in a pure English word, they are to be sounded as in chance, cheap; and when they come after a Vowel, they are to be sounded, as in ach, reach, rich. But in words derived from the Greek and Hebrew, they are to be sounded like k, as in character, these few only excepted, Rachel, Cherubin, Tychicus, Arch-Bishop, Arch-Duke, Architect, Arch-enemy, Arch-pirat.

The letters gh, in the beginning of a word, are to be sounded like g hard, as in ghost, ghess, in the midd1e of a word, they are ei­ther not sounded at all, or but softly, as in might, light, and in the end of a word they have the sound of ff, as cough, tough.

These letters th, in words of one syllable, and in words of more than one, ending in ther, thed, theth, thest, thing, they have the sound of d, in other words the sound of t, or the Greek Theta.

The letters ph, never begin a pure English word, but such only as are derived from the Greek and Hebrew, as Pharisee, Pharez, Epi­taph, and in these they are sounded like f.

The Liquids, l, m, n, r, when another Consonant doth precede them in the begin­ning or middle of a word, do retain their own sound, but in the end of a word, though [Page 8] the Vowel e, ought to be written, yet in the pronounciation, you must stop at the two Consonants, and omit the Vowel; for Ex­ample, fable, acre, uncle, must be pronoun­ced as though they were written thus, fabl, acr, uncl.

CHHP. II. Of Words.

A Word, is such a comprehension of letters and syllables, as helpeth Man-kind to express their minds to one another.

There are eight kinds of Words, or parts of Speech, Noun, Pronoun, Verb, Participle, Adverb, Conjunction, Preposition, Interjection.

A Noun, is the name of a Person or Thing; as, an Author, a Book, learned, guilded.

Of Nouns, some be Substantives, and some be Adjectives.

A Noun Substantive, is a Word, that sig­nifieth something, and may have the sign (a) or (the) before it; as a Man, the Book.

A Noun Adjective, is a Word, that can­not signifie a thing of it self; as, good, bad.

There are two sorts of Nouns Substantives.

A Noun Substantive proper, and a Noun substantive common.

A Noun Substantive proper, is a Noun that is proper to the person or thing, that it be­tokeneth; as, Henry, England.

[Page 9]A Noun substantive common, is a Noun common to all things of the same kind; as, a Man, a Land, an Angel.

To a Noun there doth belong two things, number and comparison.

There be two Numbers, the singular and the plural; the Singular number speaketh but of One; as a Man, a Book, a Stone. The Plural number speaketh of more than One, as Men, Books, Stones.

Nouns Substantive of the singular number, are turned into the plural, by adding unto them s or es, as web, webs, robe, robes, Church, Churches, hedge, hedges. Some Nouns of the singular number ending in f, being plurals, do change f into v, as beef, beeves, calf, calves. And some are made plurals, by adding of en or ren; as, Ox, oxen, chick, chicken, brother, brotheren, or by contraction brethren, child, children; of Man is formed mannen, or men, house, housen, hose, hosen; to which may be added, mouse, mice, louse, lice, die, dise, sow, swine, cow, kine, peney, pence, goose, geese, tooth, teeth, foot, feet; these two; Sheep and Mile, are both singular and plural; as, one sheep, ten sheep, one mile, ten mile or miles.

Other variation of Nouns we have none in the English Tongue; all other distinctions are made by these Articles and Prepositions; a, of, to, the, o, and in, or from, &c.

Nouns that signifie the Male-kind, we call hees; such as signifie the Female, we call [Page 10] shees; and of such as signifie neither, we say it; as, Esau could not obtain his Fathers blessing, though he sought it, with tears: Jezabel was a wicked woman, for she slew the Lord's Prophets.

Comparison belongeth only to Nouns Adje­ctives, whose significatoin may be increased, or diminished.

There be three degrees of Comparison, the Positive, Comparative, and the Superlative.

The Positive degree setteth down the qua­lity of a thing absolutely without excess, as hard, soft, swift.

The Comparitive degree raiseth the signi­fication of the Positive, in comparison of some other, as harder, softer, swifter.

The Superlative exceedeth his positive in the highest degree, as hardest , softest, swiftest.

Adjectives are compared in the English tongue, either by the signs more and most, or by the terminations er, and est, as hard, ha [...]der, or more hard, hardest, or most hard.

Some Adjectives are compared irregular­ly; as, Good, better, best; bad, worse, worst, little, less, least.

CHAP. III Of a Pronoun.

A Pronoun is a part of Speech, much like to a Noun, implying a Person, and not ad­mitting the sign a or the, before it.

[Page 11]There are twelve Pronouns, I, Thou, He, who, which, that, the same, my, thy, this, his, whose.

Of Pronouns, some be primitives, and some derivatives.

Pronoun primatives are of three sorts, Per­sonal, Relative, and Demonstrative.

There are three Pronoun personals, I, Thou, and He.

Pronoun Relatives, are likewise three, who, which, and that.

Pronoun Demonstratives, are these two, this, the same.

Pronoun Derivatives, are these four, my, thy, his, whose. All which with their va­riations, are expressed in the following Type.

• 1. Person. Sing. I, me, my, mine.
• 1. Person. Plur. we, us, our, ours.
• 2. Person. Sing. thou, thee, thy, thine.
• 2. Person. Plur. ye, you, your, yours.
• 3. Person. Sing. Mal. he, him, his. Fem. she, her, hers. neith, it, its.
• 3. Person. Plur. they, them, their, theirs
• Relatives. To pers. who, whom, whose.
• Relatives. To thing. what, whereof.

[Page 12] Own is a Noun adjective, and self, or selves, a Substantive, but are sometimes joyned to, or compounded with the Pro­nouns; as, my self, thy self, themselves, his own self, their own selves.

This word where, with certain Preposi­tions following it; as, about, at, by, in, of, unto, with, hath the signification of which as, wherein, or in which. And these words, here, there, and in like manner used for, this, that; as, herewith, therewith, for with this, with that.

CHAP. IV Of a Verb and Participle.

A Verb is a part of Speech, that joyneth the Signification of other words to­gether.

There are three kinds of Verbs, Active, Passive, and Neuter.

A Verb Active, is a Verb that betokeneth doing, as, I love.

A Verb Passive, is a Verb which betoken­eth suffering, as I am loved.

A Verb Neuter, is a Verb which betoken­eth being, as I am.

Four things belong to a Verb, Mood, Tense, Number and Person.

There are four Moods, the Indicative, the [Page 13] Imperative, the Potential, and the Infinitive.

The Indicative either sheweth a reason true or false, as I love, or asketh a Questi­on, as, dost thou love.

There Imperative Mood, intreateth, per­mitteth, or commandeth, as love he, or let him love.

The Potential Mood, signifieth a power, duty, or desire, and hath one of these Signs, may, can, might, would, should, could, or ought, as I may or can love.

The Infinitive Mood, notes no certain Number or Person, but followeth another Verb, or an Adjective, and hath commonly this Sign (to) before it, as I desire to learn, worthy to be praised.

The Tenses or distinctions of Time, are five, The Present Tense, the Preterimperfect Tense, the Preterperfect Tense, the Preter­pluperfect Tense, and the Future Tense.

These Tenses in respect of signification, are thus distinguished; in the Indicative Mood, do is the sign of the Present Tense, did of the preterimperfect Tense, have of the Preterperfect, had of the Preterpluper­fect, shall and will of the Future,

In the Potential Mood, by the signs alrea­dy given, the Present Tense by the signs may or can, the Preterimperfect would, should, could, or ought, and the Preterperfect, by annexing the sign have to the former Signs, and the Future, by adding hereafter to the [Page 14] signs of may or can, the Signs of the Present, as, I may or can hereafter, the Preterpluper­fect in this Mood is wanting in the English Tongue.

But in respect of Termination, there are no Moods but one, no Tenses but two, namely, the Present, and Preterimperfect Tenses.

And the Preterimperfect Tense is formed from the Present, by adding thereto the ter­mination (ed) and in some few the termina­tion (en) as of love is formed loved, of fall, fallen.

The Persons in every Tense are distin­guished by the personal Pronouns, I, Thou, and He, in the Singular Number, and We, Ye, They, in the Plural; only the Second Per­son Singular in the Present and Preterimper­fect Tenses is formed from the first, by ad­ding thereto the Termination est, as of love, lovest, of loved, lovedst; and the Third Per­son Singular in the Present Tense is formed from the First, by adding thereto the Ter­mination (eth) as of love is formed loveth. other variations of Persons or Tenses there is none, but what is done by Signs, as was said before.

A Verb Active then is thus formed in the Indicative Mood.

CHAP. V. Of Adverbs, Conjunctions, Prepositions, and Interjections.

AN Adverb is a Word joyned to a Verb or Noun, to declare their Signification.

Some of Time, as when, now, then, to day.

Some of Number, as, how oft, once, twice.

Some of Order, as, first, next, afterward.

Some of Place, as where, here, there.

Some of Affirming, as, yea, perhaps.

Some of Denying, as, no, not.

Some of Shewing, as, lo, behold.

Some of Similitude, as, so, how much, more.

A Conjunction is a part of Speech, which joyneth Words and Sentences together, of which these are some, And, also, likewise, nor, neither, whether, or, either, but, for, &c.

A Preposition, is a Word commonly set before other parts of Speech, either in ap­position, as before the Master, or in composi­tion, as overwise.

An Interjection is a Word, expressing some suddain passion of the Mind, oh, alass, O strange, ho, hark, sirrah.

CHAP. VI. Of Dividing of Words into Syllables.

FOr the dividing of Words into Syllables there are four Rules.

1. Two Vowels which make no Dipthong, must be divided; as, ie, iu, ua; as in qui-et, tri-umph, mutu-al.

2. Those Consonants which are doubled in the middle of a Word, must be divided; as in Abba, accord, adder.

Except they be needlesly doubled, as in words of the Plural Number; as in crabbs, rodds.

Except such words in which they are dou­bled for distinction sake; as in the words, Ann, Cann, Inn.

3. Rule. When a Consonant cometh be­tween two Vowels, it is to be joyned to the latter; as in a-vail, a-ni-mate.

But to this Rule there are four Exceptions

1. Except Words ending in es, as in Nouns, of the Plural Number, and Verbs of the third person Singular, in which this particle is for the most part swallowed up, in the for­mer Syllable; but in all proper Names, ex­cept Charles and James, it makes a distinct Syllable.

2. Except Words that are compounded of such Simple Words, as are significant a­part, [Page 19] in which each Simple Word must re­tain its own letters; as, Trades-man, safe-guard, hence-forth.

3. Except Derivative Words, whose ad­dition to the Primitive, doth signifie nothing of it self, in which the Primitive must be sounded by it self, and the addition by it self; as, hope-less, lov-ing, joyn-ing, and such like.

4. Except such Words in which x cometh between two Vowels, in which it must be joyned to the first Vowel; as, ox-en, ex­ercise.

5. Rule. Any two or three Consonants, which may be joyned together in the begin­ning of a word, are not to be seperated in the middle; as in a-gree, bestow, en-thrall; destruction; but in compounded words, each simple word must retain its own Letters.

When you are to write any hard long word, mark how many sounds or Syllables it hath, as if you were to write disdainfullness, universalitie, or the like, before you write it, say thus to your self; dis-dain-full-ness, u-ni-ver-sa-li-tie, and you shall hardly miss in the writing thereof.

CHAP. VII. Of Sentences, and such Distinctions, or Points as are to be used in Writing, and ob­served in Reading.

A Sentence, is a number of words, joy­ned together in perfect Sense.

The Stops or Points to be observed in Sen­tences, are of two sorts, Primary, and Secun­dary.

The Primary Points are these Eight.

1. A Comma, made with a little stroke thus (,)

2. A Colon, made with two points thus (:)

3. A Semi-colon, made with a point, and a little stroke under it thus (;)

4. A Period, made with a single point thus (.)

5. An Erotesis or Interrogation, made in this manner (?)

6. An Ecphonesis, or note of Admiration, whose note is a perpendicular right line, with a point under it thus (!)

7. A Parenthesis, is a note, like two half Moons, inclosing a sentence, which may be used or omitted, and yet the sense remain in­tire, thus ()

[Page 21]8. A Parathesis, is a note, which doth in­clude a word which is opposed to another word, and is made with two Semiquadrats, thus []

The Secondary Points are these six.

1. An Apostrophe, which is a note, set on the top or side of a Letter, whereby two Syllables are contracted into one, and is made like a Comma, thus (') as it's for it is.

2. An Eclipsis, which is a note cutting off one or more words in the beginning or end­ing of a Verse or Sentence, cited in our Writing, and is made with a long stroke thus — as

3. A Dieresis, which is a note for the par­ting of two Vowels, which otherwise might seem to make a Dipthong, and is made with two pricks over the two Vowels, thus, (") as in Laïs.

4. An Hyphen, which is a note of con­tinuation, made thus (-) and is to be used when one part of a word conclud­eth the former line, and the other part beginneth the next; or else, when two words are, by way of Elegancy, as it were [Page 22] joyned into one; as self-love, for the love of ones self.

5. An Accent which is a small stroak drawn slopewise towards the left-hand, thus, (') and is to be set over that Syllable in a word, which is to be pronounced long.

6. A Circumflex, which is the joyning to­gether of two oblique stroaks into one figure, one of them being made towards the right hand, and the other towards the left, and is to be set over a Vowel, thus, (â) which is to be pronounced long, as in bîte, wîle, stîle, not in bit, will, still.

The Accent in words of many syllables is commonly placed on the third Vowel from the last; as in tolerátion, índustry.

But words ending in (ary) have the accent on the first syllable; as témporary; words that have many Consonants in the last syllable save one, have their accent on that syllable, as in etérnal; words ending in ire and ure, have their accent in that syllable; as inúre.

A Noun hath its accent in the first, a Verb in the last syllable; as ábsent, to absènt.

So Húmane, when it comes before a Sub­stantive, as húmane-learning; but in the last syllable, when it comes aftér a Substantive, as Christ had two natures, the one divìne, the other humàne.

CHAP. I. Of single Arithmetick in whole Numbers.

ARithmetick is the art of accompting by Numbers; it is either positive or negative.

2. Positive Arithmetick, is that which is wrought by certain and infallible Numbers at first propounded; and this is either single or comparative.

3. Single, which is wrought by Numbers, considered alone, without relation to one a­nother, and this either in whole Numbers; or in Fractions.

[Page 24]4. The parts of single Arithmetick, are two, Notation and Numeration.

5. Notation hath two parts; the first shew­eth the value of the Notes, by which all num­bers are expressed; the second sheweth how to read the Numbers which are expressed by those notes.

6. The Notes or Characters, by which all Numbers are usually expressed are these, 1. one, 2. two, 3. three, 4. four, 5. five, 6. six, 7. seven, 8. eight, 9. nine, 0. nothing.

7. These notes are either significant Fi­gures, or a Cypher.

8. The significant Figures, are the first nine, viz. 1, 2, 3, 4, 5, 6, 7, 8, 9. The first whereof is more particularly termed an u­nite or unitie, the rest are said to be compo­sed of unities; so 2, is composed of two unites 3, of three unites, &c.

9. The Cypher, though it signifie nothing of it self, yet being set before or after any of the rest, increaseth or decreaseth their va­lue, as shall be farther shewed hereafter.

10. The second part of Notation, is the reading of the Number expressed by these notes; and this is done by distinguising the Number given into Degrees and Periods.

11. The degrees are three, the first is that first place of a number towards the right hand, and is the place of Unity. The second is the second Figure towards the right hand, and this is the place of Tens. The third is the [Page 25] third Figure towards the right hand, and is the place of Hundreds; so this Character 9, doth signifie Nine; these Notes 27, Twenty seven; and these 235, Two hundred thirty five.

12. A Period, is when a number consisting of more notes than three, hath each three notes thereof (beginning at the right hand) distin­guished by Points or Commas: The several parts of the Numbers so distinguished, are called Periods; so the Number 38156249, being distinguished into Periods, will stand thus, 38.156.249. of which the first Period is read thus, Two hundred forty nine; the first Figure in the second Period is the place of Thousands, the second Tens of Thousands, and the third Hundreds of Thousands. In the third Period, the Figure is in the place of Mil­lions, the second Tens of Millions, and so this Number is thus to be read. Thirty Eight Millions, One Hundred Fifty Six Thousand, Two Hundred Forty Nine.

13. Numeration, is that which by certain known Numbers propounded, doth discover another Number unknown.

14. Numeration hath four Species; Additi­on, Subtraction, Multiplication, and Division.

15. Addition, is that by which divers num­bers are added together, to the end that the Sum or Total may be discovered. For which purpose, having placed the numbers as in the following Example, begin with those in the [Page 26] Unity place first, then with these in the place of Tens then of Hundreds, and so forward, according as the Numbers given do consist of places, carrying the Tens, if there be any, to the place of the next greater rank, as here you see.

• 472961
• 341608
• 74325
• 6739
• 895633

• 3814527
• 4567890
• 6549238
• 816365
• 15748020

16. Subtraction is that, by which one num­ber is taken out of another, so that the Resi­due or remainder may be known. To per­form this, you must rank your Numbers, and begin as in Addition; and in case any of the figures of the Number to be subtracted shall be greater than that, from whence the Sub­traction is to be made, you must borrow one from the next place above it; as in the Ex­amples following.

17.

• 895633
• 341695
• 553938

• 6549238
• 3814527
• 2734711

Multiplication, is that by which we Mul­tiply two numbers, the one by the other, to the end, that their Product maybe discovered.

18. Multiplication hath three Parts, the Multiplicand, the Multiplicator, and the Pro­duct.

[Page 27]19. Multiplication, is single or compound.

20. Single Multiplication, is when the Mul­tiplicand, and Multiplicator, do each of them consist of one only Figure; as if 9 were given to be Multiplied by 6, 9 is the Multiplicand, 6 is the Multiplicator, and 54 is the Product.

21. Compound Multiplication, is when the Multiplicator and Multiplicand do either, or both consist of more Figures than one.

22. When the Product of any of the par­ticular Figures shall exceed ten, place the Ex­cess under the Line, and for every ten that it so exceeds, keep in mind one to be added to the next rank: Example; 76147, being to be Multiplied by 5, the Product is 180735, and 39634 being gi­ven [...] to be Multiplied by 47, the work will stand as in the Mar­gin, where the Product by 7 is 277438, and the Product thereof by 4, is 158536, and the Sum of these two Products is 1862798.

23. Division is that by which we discover how often one Number is contained in ano­ther, that we may find out the Quotient.

24. Division hath three parts, the Dividend, the Divisor, and the Quotient; thus, if 35 were given to be Divided by 5, 35 is the Dividend, 5 the Divisor, and 7 will be found to be the Quotient.

[Page 28]25. In Division, make a crooked line at each end of your Dividend, that on the left hand serving for your Divisor, and that on the right for the Quotient; then see how oft your Divi­sor is contained in the first Figure or Figures of your Dividend, and put the answer in the Quotient, then Multiply your Divisor by the Figure in the Quotient, and the Product sub­tract from your Dividend, then draw down the next Figure of your Dividend, and ask how oft your Divisor may be found in the re­mainer so increased, & the answer put in the Quotient, and proved as before, till there be no Figures left in your Dividend, and so oft as the Question is repeated, so many places must be in the Quotient, as in manifest by the following Example. [...]

[Page 29]Let 1862798, be given to be divided by 47, I ask how often 47 may be had in 186? the Answer is 3, which I place in the Quotient, then I Multiply 47 by 3, the Product is 141, which being Subtracted from 186, the Re­mainer is 45, to which draw down 2 the next Figure in the Dividend, and then it will be 452, now then I ask how often 47 may be had in 452? the which by the Table made by the continual Addition of 47 unto it self, is 9 times, therefore I place 9 in the Quotient, and the Product of 47 is 423, which being Subtracted from 452, the Remainer is 29, to which I draw 7 the next Figure, and then proceed as before, and so at last I find the Quotient to be 39634.

26. Multiplication and Division, prove one another, for if you Multiply the Quotient by the Divisor, the Product will be equal to the Dividend: so 39634, being Multiplied by 47, the Product is 1862798, and this Pro­duct being Divided by 47, the Quotient is 39634.

CHAP. II. Of Single-Arithmetick in Fractions.

SIngle Arithmetick in a whole Numbers, hath been shewed in the last Chapter; Single Arithmetick in Fractions now followeth.

2. A Fraction is a part of an Integer.

3. Single Arithmetick in Fractions, doth al­so consist of two Parts, Notation, and Nume­ration.

4. Notation of Fractions, is that which sheweth how the Fraction part of any Inte­ger may be expressed in numbers; that is, an Integer on one whole thing being Divi­ded into any Number of equal parts, Notati­on sheweth how these parts may be expres­sed; as if a Yard were Divided into four parts, and it were desired, that I should set down three of these parts; the usual manner is thus, draw a line, & set the Number of parts into which the Integer is supposed to be di­vided, under the line, and the Number of parts you would express set above the line; thus to express three of four parts, I write 4 under a line, and 3 above it, thus, ¾; and so may you do with any other number pro­pounded: Where note, that the number a­bove the line is called the Numerator, and the number under the line the Denominator.

5. A Fraction is either Proper or Improper.

[Page 31]6. A Proper Fraction is that whole Nume­rator is less than the Denominator, such as are these ¾ 6/12 25/100.

7. A Proper Fraction is either single or com­pound.

8. A Single Fraction is that which consists of one Numerator and one Denominator, such as are ¾ 6/12 25/100.

9. A Compound Fraction (otherwise called a Fraction of a Fraction) is that which hath more Numerators and more Denominators than one, which kind of Fractions are disco­verable by this word (of) which is interpo­sed between their parts; as, ⅔ of ¾ is a Fra­ction of a Fraction, or a Compound Fracti­on, and expresseth two thirds of three fourths of an Integer.

10. The things expressed by broken num­bers or Fractions, are principally the Parts or Fractions of Money, Weight, Measure, Time, and things accounted by the Dozen.

11. The least part or Fraction of Money used in England is a Farthing; and four Far­things makes a Peny; twelve Pence, a Shil­ling; and twenty Shillings, one Pound Ster­ling.

12. The least Fraction of weight used in England, is a Grain; that is, the weight of a Grain of Wheat, well dryed and gather'd out of the middle of the Ear, whereof 32 make a peny weight, and twenty peny weight an ounce Troy, and twelve ounces a Pound; but [Page 32] a peny weight being thus ascertained, it is now subdivided into twenty four Grains.

13. The weights used by Apothecaries are de­rived from a Pound Troy, which is subdivi­ded in this manner.

14. Besides Troy weight, there is another kind of weight used in England, called Aver­dupois weight, a Pound whereof is equal to fourteen Ounces, twelve peny weight Troy, the which is subdivided into 16 Ounces, each Ounce into 16 Drams, and each Dram into 4 Quarters. Of this weight 112 makes a Hundred.

15. The Measures used in England are of Capacity or Length.

16. The Measures of Capacity are Liquid or dry; Liquid Measures are according to this Table.

17. Dry Measures are those in which all kind of dry substances are Meted; as Grain, Sea-coal, Salt, and the like; their Table is this that followeth.

[Page 34]18. Long Measures are expressed in the Table following.

Note that a Yard, as also an Ell is usually subdivided into four quarters, and each quarter into four Nails.

19. A Table of Time is this that followeth.

Fifty two Weeks, one Day, and six hours make one Year.

And these Fractions of Money, Weight, Measure, &c. are usually written under their several Denominations, instead of having their Denominators written under them thus;

[Page 35]And as their Notation is two-fold, so is their Numeration also, First, then I will shew you the Numeration of parts when written, as Integers, and then as vulgar fra­ctions.

20. Numeration of parts when written, as Integers, is Accidental or Essential.

21. Accidental Numeration, otherwise cal­led Reduction, is either descending or ascen­ding.

22. Reduction Descending, is when a num­ber of greater Denomination being given, it is required, to find how many of a lesser de­nomination, are equal in value to that gi­ven Number of the greater. And this is performed by Multiplication; as if it were required to Reduce 329 Shillings into Pence, if you Multiply 329 by 20, the number of shillings in a pound, the Product will be 6580 shillings, and 6580 shillings being mul­tiplied by 12, the number of pence in a shil­ling, the Product will be 78960 pence.

23. Reduction Ascending, is when a num­ber of a lesser Denomination being given, it is required, to find how many of a greater Denomination, are equal to that given num­ber of the lesser: And this is done by Divi­sion; as if it were required to find how ma­ny Pounds there were in 78960 pence; if 78960 pence be divided by 12, the number of pence in a shilling, the Quotient will be 6580 Shillings, and if 6580 shillings be divi­ded [Page 36] by 20, the number of shillings in a pound, the Quotient will be 329 Pounds, and so for any other.

24. Essential Numeration, doth consist of four Species, Addition, Subtraction, Multipli­cation, and Division.

25. In Addition of Numbers of several Denominations, you must begin with the least first, and when the sum of any of the Denominations amounts to an Integer, add it to the next Denomination that is greater.

CHAP III. Of Comparative Arithmetick.

THus much hath been said concerning Single Arithmetick, Comparative fol­lows, which is wrought by Numbers, as they are considered to have relation to one ano­ther.

2. This Relation consists either in quan­tity or in quality.

3. Relation in quantity is the reference that the Numbers themselves have one to another; as when the comparison is made be­tween 8 and 2, or 2 and 8; 7 and 3, or 3 and 7.

[Page 45]And here the Numbers propounded are always two, whereof the first is called the Antecedent, the other the Consequent.

4. Relation in quantity, consists either in the difference, or in the rate or reason found between the Numbers propounded; the one is found by Subtracting the less from the greater; so 6 is the difference between 8 and 2; but the other, to wit, the rate or reason, is found by dividing the greater by the less, and thus the rate between 8 and 2 is four-fold, because 2 is found four times in 8; Or the rate may be also found by di­viding the less by the greater, or setting the Numbers given in manner of a Fraction, and thus the rate between 2 and 8 is 4 also, or 2/8 that is ¼.

5. This rate or reason of Numbers is ei­ther equal or unequal; equal reason, is the relation that equal Numbers have one to another, as 5 to 5, 6 to 6. Unequal Rea­son is the relation that Unequal Numbers have one to another, and this is either of the greater to the less, or of the less unto the greater.

In the one the greater Number is the An­tecedent, and the less the Consequent; and in the other the lesser Number is the Ante­cedent, and the greater is the Consequent.

6. Relation in quality, (otherwise called Proportion) is the reference or respect that the reasons of Numbers have one to ano­ther, [Page 46] and therefore the Numbers must be more than two, or else three cannot be the comparing of reasons in the Plural Number.

7. Proportion is two-fold, Arithmetical and Geometrical.

8. Arithmetical Proportion, is when num­bers differ according to equal reason; that is, have equal differences; as 2, 4, 6, 8, 10, or 3, 6, 9, 12, in the first rank the common dif­ference is 2, and in the second 3.

9. Arithmetical Proportion, is either con­tinued, or interrupted.

10. Arithmetical Proportion continued, is when divers numbers are linked together by a continued Progression of equal differ­ence; and in such a Progression, the sum of the first and last Terms being Multiplied by half the number of the Terms, the Product will be the sum of all the Terms; as in this Progression, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, the sum of the first and last is 13, which be­ing Multiplied by 6, half the number of the Terms the Product is 78, the sum of all the terms in that Progression.

11. Three Numbers being given in A­rithmetical Proportion, the mean number be­ing doubled is equal to the sum of the Ex­treams; so 3, 6, 9, being given, the double of 6, the mean number is equal to the sum of 3 and 9, the two Extreams.

12. Arithmetical Proportion Interrupted, is when the Progression is discontinued, [Page 47] as in these numbers, 2, 4, 8.10.

13. In Arithmetical Proportion continued, or discontinued, the sum of the Means is e­qual to the sum of the Extreams, as in 3, 6, 9, 12, being given, the sum of 6 and 9 is e­qual to the sum of 3 and 12; or 3, 6, 12, 15, being given, the sum of 6 and 12, is e­qual to the sum of 3 and 15.

14. Geometrical Proportion is, when di­vers numbers differ by the like reason; as, 1, 2, 4, 8, 16, which differ one from ano­ther by double reason; for as 1 is the half of 2, so 2 is the half of 4, 4 of 8, 8 of 16.

15. Geometrical Proportion is either con­tinued or interrupted, Geometrical Proportion continued, is when divers numbers are lin­ked together, by a continued Progression of the like reason; as 1, 2, 4, 8, 16, or 3, 6, 12, 24, 48.

16. In numbers Geometrically proporti­onal, If you Multiply the last Term by the common rate by which they differ, and from the Product deduct the first Term, and di­vide the Remainer by the former rate less by an Unite, the Quotient shall be the sum of all the Progressions; So 2, 6, 18, 54, 162, 486, 1458, being propounded the last term 1460, being multiplied by 3 the rate, the Product is 4374 out of which deducting 2 the first Term, the Remainer is 4372, which being divided by 2 the rate less one, the quotient 2186 is the sum of that Progression.

[Page 48]17. Three Proportionals being given, the square of the Mean is equal to the Pro­duct of the Extreams; so 4, 8, 16, being given, the square of 8 is equal to four times 16.

18. Geometrical Proportion interrupted, is when the Progression of like reason is dis­continued; as, 2, 4, 16, 32, where the Term between 4 and 16 is wanting, and therefore the rate between 4 and 16 is not the same that is between 2 and 4, or 16 and 32.

19. Four Proportional Numbers what­soever being given, the Product of the two Means is equal to the Product of the two Extreams; so 2, 4, 16, 32, being propound­ed, 4 times 16 is equal to 2 times 32, which is 64.

CHAP IV. Of the Rule of Proportion, or Rule of Three.

FRom the last Rule of the former Chap­ter ariseth that precious Gem in Arith­metick, the Rule of three, which for its ex­cellency, deserves the name that is given to it, The Golden Rule.

[Page 49]2. The Golden Rule, is that by which cer­tain numbers being given, another number Geometrically proportional to them may be found out.

3. The Golden Rule is either single or compound.

4. The single Rule, is when three terms or numbers are propounded, and a fourth in proportion to them is desired.

5. The Terms of the Rule of Three con­sist of two Denominations; two of the Terms propounded have one Denominati­on, the third propounded and fourth requi­red, have another.

6. Of those two numbers given which are of one Denomination, that which moves the Question must possess the third place, the other number of the same Denominati­on, must be put in the first place, and con­sequently, the other known Term, which is of the same Denomination with the fourth required, must possess the second place.

7. The three Terms propounded being thus placed, consider whether your third doth require more or less; if it requires more, Multiply the middle number by the greater of the two Extreams, and divide the Product by the lesser, the Quotient is the fourth Number or Term desired.

But if the third Term in the Question re­quire less, Multiply the middle Term by the lesser of the two Extreams, and the Pro­duct [Page 50] Divide by the greater, the Quotient shall be the fourth Term desired; An Exam­ple in each Case will sufficiently explain the Rule.

If 7 Pound of Sugar cost 2 s. 7 d. What shall 28 Pound of Sugar cost? The Terms must stand thus,

Where it is plain, that 28 pound of Su­gar must needs cost more than 7, therefore I Multiply 2 s. 7 d. or 31 pence, by 28, the Product 868 being Divided by 7, and the Quotient is 124 d. or 10 s. 4 d.

2. Example: If 7 Men will digg a Gar­den in 31 Dayes, In how many Dayes will 28 Men digg the same Garden? Here the Terms must stand thus,

And by the state of the Question it plain­ly appears, that the third Term requireth less: therefore I Multiply 31, the middle Term, by 7, the lesser Extream, and the Product 217 being Divided by 28, the Quo­tient 7 21/28 is the fourth Term desired.

CHAP. V. Of the Compound Rule of Three.

THe Compound Rule of Three, is when more than three Terms are propoun­ded.

2. Under the Compound Rule of Three is comprehended the Double Rule of Three, and divers Rules of plural proportion.

3. The Double Rule of Three, is when five Terms are propounded, and a sixth in pro­portion to them is required.

4. In this Rule the five Terms given do consist of two parts; first a Supposition, and then a Demand; the Supposition is expres­sed by three of the Terms propounded, and the demand by the other two.

5. And here the greatest difficulty is in placing of the Terms; for which observe amongst the Terms of Supposition, which of them hath the same Denomination with the Term required, reserve that for the se­cond place, and write the other two Terms in the Supposition one above another in the first place; and lastly, the Terms of De­mand one above another, likewise in the third place, in such sort, that the upper­most may have the same denomination with the uppermost of those in the first place.

CHAP. VI. Of the Rule of Fellowship.

THe Rules of plural proportion are those, by which we Resolved Questions that are discoverable by more Rules of Three than one, and cannot be performed by the double Rule of Three mentioned in the last chapter.

Of these Rules there are divers kinds and varieties, according to the nature of the Question propounded; I will only mention one, and refer the rest to my larger treatise of this Subject.

2. The Rule of plural proportion that I mean to mention, is the Rule of Fellowship.

3. And the Rule of Fellowship is that by which in Accompts amongst divers Men, (their several stocks together) the whole Loss or Gain being propounded, the Loss or Gain of each particular man may be disco­vered.

4. The Rule of Fellowship is either single or double.

5. The Single Rule of Fellowship is, when the stocks propounded are single numbers; As in this Example: A and B were Partners in an Adventure to Sea, A put in 25. l. B 56, and upon return of the Ship, they sold the [Page 55] Fraight for 50 l. profit; the question is, What part of this 50 l. is due to A, and what to B? to resolve this and the like Que­stions, the sum of the stocks must be the first term in the Rule of Three, the whole gain the second, and each particular stock the third; this done repeating the Rule of Three, as often as there are particular stocks in the Question, the fourth term pro­duced by these several operations are the respective Gains or Losses of those particu­lar stocks propounded; so in the present question, the Resolution will be as here you see. [...]

6. The Double Rule of Fellowship is, when the stocks propounded are double numbers, that is, when each stock hath relation to a particular time. A, B, and C, hire a piece of Ground for 45 l. per Annum, in which A had 24 Oxen 32 days, B 12, for 48 days, C 16, for 24 days; now the question to be resolved is, What part of the Rent each person must pay?

For this purpose you must first Multiply each particular stock by its respective time, and take the total of their Products for the first term, the Gain or Loss for the second, and every man's particular stock and time [Page 56] for the third; this done repeating the Rule of Three so often as there are Products of the double Numbers; the fourth terms pro­duced upon those several operations are the numbers sought. So then in the question propounded, the Product of 24 and 32 is 768; the Product of 12 and 48 is 576, and the Product of 16 and 24 is 384, the sum of these Products is 1728, which is the first term, 45 l. the Rent is the second, and each particular Product the third; [...]

By which three Operations the question is Resolved.

CHAP. I. Of the Definition and Division of Geometry.

GEOMETRY is the Art of Measu­ring well.

2. The Subject of Geometry is Magnitude, or continued Quantity, whose parts are joyned together by a common term or limit.

3. Magnitude is either a Line, or some­thing made of a Line or Lines.

4. A Line is a Magnitude, consisting on­ly of length, without either breadth or thick­ness, the term or limit whereof is a Point.

[Page 58]5. A Point is an indivisible sign in Magni­tude. A Point therefore is no quantity, but the beginning of all continued quantities, which are divisible in power infinitely.

6. A Line is either considered simply by it self, or else comparatively with another Line.

7. A Line considered simply of it self, is either Right or Oblique.

8. A Right line, is that which lyeth equal­ly between his Points.

9. An Oblique line, is either circular or mixt.

10. A Periphery, or Circular Line, is that which is equally distant from the middle of the comprehended space, which middle is called the Centre, and the distance between that Centre and the Circumference, is cal­led the Radius.

11. Lines compared to one another are or the same or different Species.

12. Lines compared together of the same Species, are either Parallel or Angular.

13. Parallel lines, are such as are equally distant in all places, and are either Right lined Parallels, or Circular.

14. Right lined Parallels, are such as being in one and the self same plane, and infinite­ly produced on both sides, do never meet in any part.

15. A Circular Parallel is a Circle drawn within or without another Circle.

[Page 59]16. Angular lines are such as inclining, or bowing to one another, touch one another, but not in a direct line.

17. An Angle is either Right or Oblique.

18. A Right Angle, is that whose legs or sides are Perpendicular to one another.

19. An Oblique Angle, is that whose legs or sides do incline to one another upon one side more than upon another.

20. An Oblique Angle is either Acute, or Obtuse.

21. An Acute Oblique Angle, is that which is less than a Right.

22. An Obtuse Oblique Angle, is that which is greater than a Right Angle.

23. The Measure of an Angle, is the Arch of a Circle described upon the Angular Point, and intersected between the sides of the Angle sufficiently prolonged; but of this Measure there can be no certain know­ledge, unless the quantity of that Arch be ex­pressed in Numbers.

24. Every Circle therefore is supposed to be divided into 360 equal parts, called De­grees, and every Degree into 60 Minutes, and every Minute into 60 Seconds, and so forward; others suppose every Degree to be subdivided into 10 parts, and every one of those into 10 more, and so forward, as far as you please.

25. A Semi-circle is the half of a whole Circle, and containeth 180 Degrees.

[Page 60]26. A Quadrant, or fourth part of a Cir­cle, is 90 Degrees; and seeing that a Right Line falling Perpendiculary upon a Right Line, doth make the Angles on both sides e­qual, and cutteth a Semi-circle into two e­qual parts, the fourth part of a Circle, or 90 Degrees, must needs be the Measure of a Right Angle.

27. Thus are Lines compared with Lines of the same Species, the comparing of Lines of different Species, is the comparing of Right Lines with those that are Oblique or Circular.

28. And Right Lines, as they have refer­ence to, or are compared with the circum­ference of a Circle, are either such as are in­scribed within it, or applyed to it.

29. A Right Line, inscribed in a Circle, either passeth through the Centre, as the Diameter and Radius, or is drawn besides the Centre, as Chords and Sines.

30. A Diameter, is a Right Line inscrib­ed through the Centre of the Circle, divi­ding the Circle into two equal parts.

31. The Radius of a Circle is the one half of the Diameter, or a Right Line drawn from the Centre to the Circumference; thus the Right Line GBD, in Fig. 1. is a Dia­meter, GB, or BD, the Radius.

32. A Chord or Subtense, is an inscribed Right Line drawn through or besides the Centre bounded at both ends with the Cir­cumference.

[Page 61]33. A Chord or Subtense, drawn through the Centre is the same with the Diameter.

34. A Chord or Subtense, drawn besides the Centre, is a Right Line bounded at both ends with the Circumference, but always less than the Diameter.

35. Sines are either Right or Versed.

36. A Right Sine is half the Chord of the Double Arch and it is either the whole Sine, and Sine of 90 Deg. or Sine less than the whole.

37. The whole Sine is equal to the Semi­diameter or Radius of a Circle, as the right Line BE.

38. A Sine less than whole, is half the Chord of any Arch less than a Semi-circle; as CA is the sine of CD.

39. A Versed Sine, is a part of the Diame­ter lying between the right sine and the cir­cumference, as the Right Line AD, which is one part of the Diameter, is the versed sine of the Arch C D, and the right line AG, which is the other part of the Dia­meter, is the versed sine of the Arch CEG.

40. A Right line applied to a Circle, is either a Tangent or Secant.

41. A Tangent, is a right line without but touching the Circle, drawn Perpendicular to the end of the Radius or Diameter, conti­nued to the Secant.

42. A Secant, is a right line drawn from the Centre of the Circle, through the term [Page 62] of an Arch, and continued to the Tengant; thus the right line FD, is the Tangent, and the right line BF, is the Secant of the Arch CD, or of the Arch CEG, the Comple­ment thereof to a Semi-circle.

43. These Lines thus inscribed in, or ap­plyed to a Circle, may to any limited Radi­us be drawn or made upon a Rule of Wood, Brass, or other Metal; or, a Table may be made, expressing the length of these lines in numbers, answering to every Degree and part of a Degree in the Quadrant or Semi-circle; That is, the lines of Chords and Ver­sed Sines may be made to any part of a Semi-circle, and the lines of Sines, Tangents and Secants, to any part of a Quadrant: The use of such Scales and Tables is such, that no Student in Geometrie can well be without them; here therefore I will lay down such Propositions as will sufficiently demonstrate the way of making these lines upon a Scale or Ruler, but as to the construction of the Tables by which the lengths of these lines are expressed in Numbers: I refer them to my Trigonometria Britannica, and other Books of the like nature.

CHAP. II. Of Right Lined Triangles.

HItherto we have spoken of the first kind of Magnitude, that is, of Lines, as they are considered of themselves, or among themselves.

2. The second kind of Magnitude, is that which is made of Lines, that is a Fi­gure.

3. A Figure is that which is every where bounded, whether it be with one only limit as a Circle; or with more, as a Triangle, Quadrangle, Pyramis, or Cube, &c.

4. The terms or limits of every Figure, are either Lines or Superficies.

5. A Figure, which is terminated by Lines is a Superficies.

6. A Figure, which is bounded or limited with several Superficies, is a Body or Solid.

7. A Superficies is a Magnitude, consisting of length and breadth, and is either right lined, curved lined, or composed of both.

8. A Right Lined Plane or Superficies, is that which is Terminated with right lines; and it is either a Triangle, or a Triangu­late.

9. A Triangle, or the first right lined Fi­gure, is that which is comprehended by [Page 68] three right lines. It is distinguished from the sides, or from the Angles.

10. In respect of the sides, a Triangle is either Isopleuron, Isosceles, or Scalenum.

An Isopleuron Triangle, is that which hath three equal sides. An Isosceles, which hath two equal sides. And a Scalenum, whose three sides are all unequal.

11. In respect of the Angles, a Triangle is either Right or Oblique.

12. A Right Angled Triangle, is that which hath one right line.

13. An Oblique Angled plane Triangle, is either Acute or Obtuse

14. An Oblique and Obtuse Angled plane Triangle, hath two Acute Angles and one Obtuse; an Acute angled Triangle hath all the three Angles Acute.

15. The second sort of right lined planes is called a Triangulate, or a Plane, composed of Triangles.

16. The sides of a Triangulate, are in number more by two than the Triangles, of which it is composed.

17. A Triangulate, is either a Quadrangle, or a Multangle.

18. A Quadrangle, is a Plane comprehen­ded, by four right lines, and is either a Pa­rallelogram or a Trapezium.

19. A Parallelogram, is a Quadrangle, whose opposite sides are Parallel or Equidi­stant, and it is either Right Angled or O­blique.

[Page 69]20. A Right Angled Parallelogram, is that which hath every Angle Right; and it is ei­ther a Square or an Oblong.

21. A Square is a Right Angled Parallelo­gram, whose four sides are equal, and the Angles Right.

22. An Oblong, is a Right Angled Paral­lelogram, whose Angles are all right, but the sides unequal.

23. An Oblique angled Parallelogram, is that whose Angles are all Oblique, and is either a Rhombus, or a Rhomboides.

24. A Rhombus, is an Oblique Angled Pa­rallelogram, of equal sides.

25. A Rhomboides, is an Oblique angled Parallelogram of unequal sides.

26. A Trapezium, is a Quadrangle, but not a Parallelogram, and it is either Right angled, or Oblique.

27. A Right Angled Trapezium, hath two opposite sides, parallel, but unequal, and the sides between them perpendicular.

28. An Oblique Angled Trapezium, is a Quadrangle, but not a Parallelogram, hav­ing at least two Angles thereof Oblique, and none of the lines Parallel.

29. A Right angled Multangled Plane, is that which is comprehended by more than four lines.

30. A Multangled Right lined Plane, or Polygon, is either Ordinate and Regular, or Inordinate and irregular.

[Page 70]31. Ordinate and Regulate Polygons, are such as are contained by equal sides and an­gles, as a Pentagon, Hexagon, &c.

32. Inordinate or Irregular Polygons, are such as are contained by unequal sides and angles.

32. Having thus shewed what a right lin­ed Figure is, with the several sorts of them, we will now shew, how they may be measur­ed, both in respect of the lines by which they are bounded, and also of their Area or Superficial Content.

33. And first we will shew how the lines, and angles of all plane Figures, especially Triangles, may be measured, as being the first and chiefest of them, and into which all other may be reduced.

34. The sides of all plane Triangles, and other plane Figures, are to be Measured by the scale or line of equal Parts.

35. The Angles may be measured by the lin [...]s of Sines, Tangents, or Secants, as well as by the line of chords; but here it shall suffice to shew how any Angle may be pro­tracted, or being protracted, be Measured by the line of Chords only.

CHAP. III. Of the Solution or Mensuration of plane Triangles.

IN the Solution of plane Triangles, the an­gles only being given, the sides cannot be found, but the reason of the sides only; it is therefore necessary, that one of the sides be known.

2. In all plane Triangles, the three angles are equal to two Right: two Angles therefore being given, the third is also gi­ven; and one of them being given, the sum of the other two is also given.

3. In a Right angled plane Triangle, one of the Acute Angles being given, the other is also given, it being the Complement of the other to a Quadrant or 90 degrees.

4. In a Right Angled plane Triangle, there are seven Cases, whose Solution shall be shewed in the Problems following.

[Page 73]5. The sides comprehending the Right angle we call the legs, and the side subtend­ing the Right angle, we call the Hypothenuse.

CHAP. IV. Of Bodies or Solids.

AFter the description of lines and planes, the Doctrine of Bodies is to be consi­dered.

2. A Solid or Body, is that which hath Length, Breadth and Thickness, whose bounds or limits are Superficies.

3. A Solid is either Plane or Gibbous.

4. A Plane Solid, is that which is compre­hended of Plane Superfices, and is either a Pyramide or Pyramidate.

5. A Pyramide, is a solid Figure, which is contained by Planes, set upon one Plane or Base, and meeting in one point.

6. A Pyramidate, is a solid Figure, com­posed of Pyramides, and is either a Prisme or a mixt Polyhedron.

7. A Prisme, is a Pyramidate or solid Fi­gure, by Planes, of which these two which are opposite, are equal, like, and parallel and all the other Planes are parallelograms.

8. A Prisme, is either a Pentahedron, a Hexahedron, or a Polyhedron.

9. A Pentahedron Prisme, is that, which comprehended of five sides, and the Base Triangle.

[Page 87]10. An Hexahedren Prisme, is that which is comprehended of six sides, and the Base a Quadrangle.

11. An Hexahedron Prisme, is either a Parallelipipedon, or a Trapezium.

12. A Parallelipipedon, is that whose sides or opposite planes are parallelograms.

13. A Prisme, called otherwise a Trapezi­um, is that solid, whose opposite planes or sides are neither parallel nor equal.

14. A Parallelipipedon, is either Right an­gled or Oblique.

15. A Right angled Parallelipipedon, is that which is comprehended of right angled sides and it is either a Cube or an Oblong.

16. A Cube, is a Right angled parallelipi­pedon of equal sides.

17. An Oblong, is a right angled paralleli­pipedon of unequal sides.

18. An Oblique angled Parallelipipedon, is that which is comprehended of oblique sides

19. A Polyhedron, is that which is compre­hended of more than five sides, and the Base a Multangle.

20. A mixt Polyhedron, is that whose Ver­tex is in the Centre, and the several sides exposed to view, and of this sort, there are only three; the Octahedron, the Icosohedron, and the Dodecahedron.

21. An Octahedron, is a solid Figure, which is contained by eight Equal and Equilateral Triangles.

[Page 88]22. An Icosohedron, is a solid Figure, which is contained by twenty Equal and Equilate­ral Triangles.

23. A Dodecahedron, is a solid Figure, which is contained by twelve Pentagons, E­quilateral and Equiangled.

24. A Gibbous solid, is that which is com­prehended of Gibbous Superficies, and it is either a Sphere or Various.

25. A Sphere, is a Gibbous body, abso­lutely Round and Globular.

26. A Various Gibbous Body, is that which is comprehended by various superficies and a circular base; and is either a Cone, or a Cylinder.

27. A Cone, is a Pyramidical Body, whose Base is a Circle.

28. A Cylinder, is a solid Body of equal thickness, having a Circle for its Base. The solid content of these several Bodies may be measured by the Problems following.

CHAP. I. Of SINGING.

MVSICK is the Art of modulating Notes in Voice or Instrument.

2. It doth consist in Singing or Setting.

3. In Singing there are five things to be considered: 1. The Number of the Notes. 2. Their Names. 3. Their Tunes. 4. Their Times. And 5. Their Adjuncts.

4. The number of Musical Notes are three times seven, or twenty one, that is from the lowest Note of a Man's Base, to the high­est of a Boy's Treble, we usually reckon twenty one Notes; though there are some [Page 92] Bases that reach below, and some Trebles that arise above this ordinary compass.

The number of Musical Notes is there­fore divided by Septenaries, because there are in Nature, but seven distinct sounds ex­prest in Musick, by seven distinct Notes, in the several Cliffs or Cleaves of the Scale; for the eighth & fifteenth have the same sound or tune, and therefore the name and cliff of the first; the 9th and 16th of the second; the 10th and 17th of the third; the 11th and 18th of the fourth; the 12th and 19th of the fifth; the 13th and 20th, of the sixth; the 14th and 21th, of the seventh.

6. These thrice seven Notes are descern­ed by their places. A place is either a Rule or space, and therefore in eleven rules with their spaces, is comprehended the whole scale.

7. At the beginning of each rule and space is placed one of the first seven Letters in the Alphabet, and these Letters are thrice re­peated one above another, the letter G be­ing put upon the first or lowest place of each sepentary being the first letter in the word Greece, and in the first sepentary, retained the Name and Form of the Greek Gamma, in remembrance, that the Art of Musick, as other learned Arts came to us from that seat of the Muses.

8. By these seven letters of the Alphabet, otherwise called seven cliffs or cleaves, the [Page 93] scale is divided into three several parts of Musick; the first and lowest is called the base; the 2d. or middle part, the Mean; the third or highest part, the Treble. As for the Notes, which do exceed this compass, ei­ther in the base or treble, they are signed with double letters in the same manner, that the ordinary Notes are with single.

9. The second thing to be considered in Singing, is the Name by which each of these Notes is called.

10. And for these seven notes, signed by the first seven letters in the Alphabet, there are but six several names invented to help the lear­ner in the tuning of them; ut, re, Mi, fa, sol, la, and for the seventh note, because it is but half a tone above la, as the fourth is above Mi, (whereas the rest are all whole tone) it is fitly called by the same name with the fourth, and so the next will be an eight, or Diapason to the first, and consequently placed in the same let­ter or cliff, and called by the same name.

And thus they were wont to be placed in the scale, in which the first name ut being placed upon the same line with the Greek Gamma, hath caused the whole scale to be called the Gamut; but modern Musicians in these latter times, have rejected the names of ut and re, as finding the other four to be sufficient for the expressing of the several sounds, and less bur­thensome to the Memories of Practisioners.

11. This scale or Gamut then is divided into [Page 94] four Columns. In the first you have the Al­phabetical letters or cliffs, the other three shew the names of the notes, ascending and de­scending, according to their several names & keys ▪

In the second column is set the names of the notes as they be called, where is B duralis, or B sharp, as having no flat in B mi, and then your notes are called as they are set there on the rules and spaces ascending.

In the third Column is B proper, or B na­turalis, which hath a B flat in B mi only, which is put at the beginning of the line with the Cliff, and there you have also the names as they are called on Rule and Space.

In the fourth Column is B fa, or B molla­ris, having two B flats, the one in B mi, the other in E la mi, placed as the other; by [...]serving of which you have a certain rule for the Names of the Notes in any part.

12. In these three columns observe this for a ge­neral rule, that what name any note hath, the same name properly hath his eight above or below.

13. Although the whole ordinary scale of Musick doth contain three septenaries of lines and spaces; yet when any of the parts which it is divided into, shall come to be Prick'd out by it self in Songs or Lessons, five Lines is only usual, for one of those Parts as being sufficient to contain the compass of notes thereunto belonging: And if there be any Notes that extend higher or lower, it is usual to add a Line in that place with a Pen.

[Page]

[Page 96]14. Though the seven Letters set at the beginning of each Rule and Space, are se­ven Cleaves, yet four of them are only usual: The first is called the F fa ut Cleave or Cliff, thus marked 𝄢 this is proper to the Base or lowest Part, and is set upon the fourth line, at the beginning of Songs or Lessons. The second is the C sol fa ut, which is proper to the middle or inner parts, and is thus mar­ked. 𝄡. The third is the G sol re ut Cleave or Cliff, which is only proper to the Treble or highest, and is signed thus, 𝄞 on the second line of the Songs or Lessons; and these are called the three signed Cliffs.

The fourth is the B Cliff, which is proper to all Parts, as being of two natures and pro­perties; that is to say, Flat and Sharp, and doth only serve for the Flatting and Sharp­ing of Notes; it is called by two Names, and signed by two Marks, the one is B fa, or B flat, and is known on Rule or Space by this mark, (♭), The other is called B mi or B sharp, and is known by this mark ♯

15. Concerning this fourth Cliff, you are to observe: 1. That the B fa, or B flat doth alter both the Name and Property of the Notes before which it is placed; changing mi into fa, and making that Note to which he is joyned, a Semi-tone, or half a note low­er. 2. That the B mi or B sharp alters the pro­perty of the Notes before which he is pla­ced, but not the Name; for he is usually pla­ced [Page 97] either before fa or sol, and they retain their name still, but their sound is raised half a Tone or Sound higher. Lastly, note, that these two B Cliffs are placed not only at the beginning of the Lines with the other Cliff, but is usually put to several Notes in the middle of any Song or Lesson, for the flatting and sharping of Notes, as the Har­mony of the Musick doth require.

16. Of these four Notes now in use, Mi is the principle or master Note, for that be­ing found, the rest are known by this dire­ction; after Mi, sing fa sol la, twice upward and la sol fa, twice downward, and so you come to Mi again in the same Cliff both wayes.

17. This Note Mi, hath his being in four several places, but he is but in one of them at a time. Its proper place is in B mi, as in the second Column of the Gamut; but if a B fa, or B flat, be in its place, then he is in E la mi, as in the third Column of the Gamut, which is its second place. But if a B flat be placed there also, then its in A la mi re, which is its third place. If a B flat come there also, then it is remov'd into its fourth place, which is D la sol re, according to these Examples.

1. Example. Mi in B mi. [...]Sol la mi fa sol la fa sol.

[Page 98]II. Example. Mi in E la. [...]Sol la fa sol la mi fa sol.

III. Example. Mi in Ala mi re. [...]La mi fa sol la fa sol la.

IV. Example. Mi in D la sol. [...]La fa so la mi fa sol la.

CHAP. II. Of the Tunes of Notes.

THe next thing to be considered in Sing­ing, is the Tunes of Notes, which can­not be declared by Precept, but must be lear­ned either by the lively Voice of the Tea­cher, or by some Instrument rightly Tuned. Only observe that from mi to fa, and so from la to fa, is but half a Tone; but between a­ny other two Notes is a whole Tone, as from fa to sol, or sol to la. And in the first guiding of the Voice, it will much help, if at the first Tuning, you sound by degrees all these Notes, as sol la mi, and at the second Tuning, leave out la the middle Note: this will not only help you to Tune a Third, as from sol to mi, but it will also help you in the raising of Fourths and Fifths, &c.

Of which there are some Examples in the plain Songs following.

First. [...]Sol la mi fa sol la fa sol sol fa la sol fa mi la sol.

Second. [...]Sol mi la fa mi sol fa la la fa sol mi fa la mi sol la so

[Page 100]Third. [...]Sol la mi sol mi sol la mi fa sol fa sol la mi fa sol

[...]sol sol sol la mi fa sol la sol la sol la mi fa sol la fa

[...]sol fa sol la mi fa sol la fa sol sol sol sol fa la

[...]sol la sol fa la sol sol sol sol fa la sol fa

[...]sol fa sol fa la sol fa mi sol mi sol fa la sol

[...]fa mi la sol la sol fa la sol fa mi la sol sol sol

[...]fa sol la sol sol sol fa sol mi sol la sol.

CHAP. III. Of the Time of Notes.

THe Notes in Musick have two Names, one for Tune, the other for Time or Pro­portion. The Names of Notes in reference to their Tunes, are, as hath been said, these four, Sol La Mi Fa; And their Names in Proportion of Time, are Eight; A Large, a Long, a Breve, a Semi-breve, a Minum, a Crotchet, a Quaver, a Semi quaver.

The four first are of Augmentation, or Increase; the four latter are of Diminuti­on or Decrease, and are thus proportioned. The Large being the first of Augmentation, and longest in Sound; the Semi-breve is the last of Augmentation, and the shortest in Sound, and in Time is called the Master-Note, being of one Measure by himself, all the other Notes are reckoned by his value, both in Augmentation and Diminution.

In Augmentation, the Large is Eight Se­mi-breves, the Long four, the Breve two, the Semi-breve is one Time or Note.

In Diminution, the latter four do decrease in this proportion; two Minums make a Semi-breve, two Crotchets make a Minum, two Quavers make a Crotchet, and two Se­mi-quavers make a Quaver. As in the Ta­ble following may be seen.

[Page 102]

CHAP. IV. Of the Adjuncts belonging to Musical Notes.

THere belong to Notes, thus described by their Number, Names, Tunes, and Time, these seven things. A Tye, a Repeat, a Pause, a Direct, a Close, and single and double Bars, and several Moods.

2. A Tye is a Semi-circle, whose two ends point to the two Notes conjoyned, as when two Minums, or one Minum and a Crotchet are tyed together; as also, when two or more Notes are to be Sung to one Syllable, or two Notes or more to be plaid with one drawing of the Bow on the Viol or Violin.

3. The middle and principal Note is the Se­mibreve: And when any Note & his half note in the same place are conjoyned for one Syl­lable, the mark of the half Note, and of the Ligature too, is a point set by the Note, as 𝆹· 톹텥· and it is as much, as if with the Note his half Note were exprest, and conjoyned by Ligature, and prolongeth the sound of that Note it follows, to half as much more; thus a Semi-breve, which is of it self but two Minums, having a prick after it, is made three Minums, in one continued sound, and so in other Notes.

[Page 104]4. A Repeat is either of the same Notes and Ditty together, or of Ditty with other Notes, and is marked thus, (vocal join) and is used to signifie, that such a part of a Song or Lesson must be Play'd or Sung over again from that Note over which it is placed.

5. A Pause is a mark of rest or silence in a Song for the time of some Note, whereof it hath its name. A line discending from a superiour Rule, and not touching the Rule below, is a Semibreve Rest: the like line ri­sing from an inferiour Rule, and not tou­ching the Rule above, is a Minum Rest: the same with a crook to the Right hand, is a Crotchet Rest, and to the left hand, a Qua­ver Rest: Also a line reaching from Rule to Rule, is a Breve Rest, or a Pause of two Semibreves; a line from a Rule to a third Rule, is a Long pause, or of four Semibreves, and two of them together make a Large pause, or a Rest of Eight Semibreves.

6. A Direct in the end of a line, sheweth where the Note stands in the beginning of the next line, and is marked thus, [...]

7. A Close is either Perfect or Imperfect; A Perfect Close is the end of Song, no­ted thus, 𝄐 or thus, 𝄑 or with two Bars thwart all the Rules, or both ways. An Imperfect Close, is the end of a Strain, or a­ny place in a Song, where all the Parts do [Page 105] meet and Close before the end, and it is marked with a single Bar. [...]

8. The usual Moods are two, the Imper­fect of the more, when all goes by two, ex­cept the Minims, which goes by three, as two Longs to a Large, two Breves to a Long, two Semibreves to a Breve, three Minums to the Semibreve, with a prick of perfection; this Mood is thus signed, 𝇊3 and is usually called the Triple Time.

The other usual Mood is the Imperfect of the less; when all goes by two, as two Longs to a Large, two Breves to a Long, two Semi­breves to a Breve, &c. this is called the Com­mon Time, because most used, and is marked thus, (timeimperf-prolatperf-str).

Thus much, concerning singing; I leave setting to the larger Treatises of this subject.

CHAP. I. Of the General Subject of Astronomie.

AStronomy, is an Art, by which we are Taught the Measure and Moti­on of the heavenly Orbs and Stars that are in them.

2. The Heavenly Orbs are either [...], without Stars, as the Primum Mobile, or [...], such as have Stars in them, as the eight inferiour Orbs.

3. The Stars are either fixed or movea­ble: The fixed Stars are those which always keep the same distance from one another; but the moveable Stars, otherwise called [Page 107] Planets, are such as do not always keep the same distance.

4. All the Stars, as well fixed as moveable have a double motion; the one occasioned by the Primum Mobile, from East to West, the other natural or proper to themselves, by which they move from West, to East.

5. According to this double motion of the Stars, this Art of Astronomy is divided in­to two Parts; the first sheweth the motion of the Primum Mobile, and how the several Heavenly Orbs are by that carried round the World, from East to West, which is called the Diurnal motion of the Stars.

The second part of Astronomy, sheweth the Periodical motion of the Stars, in which the inferiour Orbs, according to their own proper and natural motion, do move from West to East.

6. For the better understanding of these several motions, the Primum Mobile, or tenth Orb, is usually represented by a Sphere or Globe, with such lines drawn about it as the Stars in their motions are supposed to make, or may help to discover unto us, the quantity of their motions, and shew the time of their Risings and Settings, and such like.

7. This Sphere or Globe, is a round bo­dy, containing one Superficies, in the mid­dle whereof there is a Point, from whence all Right Lines drawn to the Superficies are equal.

[Page 108]8. In the Sphere or Globe, there are ten imaginary Lines or Circles, of which six are great, and four are small.

9. The great Circles are these which di­vide the Sphere or Globe into two equal Hemispheres, and such are the Horizon, Ae­quinoctial, Zodiack and the two Colures; the two first of which are called external and mu­table, the other internal and immutable.

10. The Lesser Circles, are those which divide the Sphere or Globe, into two une­qual Hemispheres, whereof one is more, and the other less than the half of the Sphere or Globe; such are the two Tropicks of Can­cer and Capricorn, and the Artick and An­tartick Circles, all which are represented in Fig. 9.

11. The Horizon, which is also called the Finitor, is a Circle, which divideth the visible part of the Heavens from the not vi­sible; that is, the lower Hemisphere from the upper, as the line AB; one of whose Poles is in the Point directly over our heads, and is called the Zenith, the other Diame­trically opposite, called the Nadir, and no­ted with the Letters Z. N.

12. The Horizon, is either Sensible or Ra­tional.

13. That is called the Sensible Horizon, which bounds our sight, and seemeth to di­vide the Heavens into two equal Hemis­pheres.

[Page 109]14. And that is called the Rational or In­telligable Horizon, which doth indeed bisect the Heavens; and this is Right, when it passeth through the Poles of the World; or Oblique, when one of the Poles is some­what elevated, and the other depressed; or Parallel, when one Pole is in the Verti­cal Point or Zenith, for then the Horizon is Parallel to the Aequator; it otherwise makes therewith either Right or Oblique Angles.

15. Hence there is a threefold position of Sphere. 1. A Right, where the Horizon is Right; that is, where the Aequator pas­seth through the Zenith and Nadir, 2. Ob­lique, when the Horizon is Oblique; that is, when one Pole is somewhat elevated and the other depressed. 3. Parallel, when one of the Poles of the world is in the Zenith.

16. In a Right Sphere, all the Stars do Rise and Set, but in an Oblique Sphere, some are hid from our sight, and some are always above the Horizon.

17. The Meridian is a great Circle pe­culiar and proper to every place, and drawn through the Vertical point and the Poles of the World, to which when the Sun comes in his Diurnal motion, in the Day-time he mak­eth the Mid-day, and in the Night time, he maketh Midnight. There may be as many Meridians as there are Vertical points, but upon the Globe they are usually drawn thro' every tenth or fifteenth Degree of the Ae­quator.

CHAP. II. Of the Internal and Immutable great Circles.

HItherto of the two External and Muta­ble Circles, the Horizon and Meridi­an, I come now to the Internal and Immu­table.

2. The first Internal and Immutable Cir­cle is called the Aequator, or Equinoctial Circle, which divideth the whole Sphere òr Globe into two equal parts between the Poles, to which when the Sun cometh, which is twice in the Year, the days and nights are equal in all places but in a Parallel Sphere: this Circle is noted with the letters EF.

3. This Circle is also the measure of Time; for as oft as 15 Degrees of this Cir­cle do ascend above the Horizon, so many hours are compleated in its going round.

4. The second Immutable Circle is called the Zodiak, which is a great Oblique broad Circle, under which the Planets do always move; the Poles of this Circle are distant, from the Poles of the world 23 Degrees, 31 Minutes, and 30 Seconds, or 23.53 Cen­tesms.

5. This Circle doth differ from other Circles in the Heavens, in that other Circles to speak properly, have Longitude or [Page 111] Length, but no Breadth, whereas this Cir­cle is allowed to have both.

6. In respect of Longitude, this Circle is divided as other Circles commonly are into 360 Degrees, but more peculiarly into 12 parts, constituting, as it were, the 12 Parts or Months of the Year, or 12 Constellati­ons of Stars, called Signs, each Sign being subdivided into 30 Degrees or Parts. The Names and Characters of these 12 Constel­lations, or Signs, are as followeth. A­ries ♈, Taurus ♉, Gemini ♊, Cancer ♋, Leo ♌, Virgo ♍, Libra ♎, Scorpio ♏, Sagit­tarius ♐, Capricornus ♑, Aquarius ♒, Pis­ces ♓.

7. The Zodiack, in respect of Latitude, is divided into 16 Degrees, that is, into 8 Degrees North-ward, and 8 Degrees South-ward, because all the Planets, except the Sun, do in their Motions vary from the middle Line, sometimes one way, and some­times another; to the quantity of 8 De­grees; and the middle Line in which the Sun moves, is the Ecliptick Line, because when the Sun and Moon are in Conjunction, the Sun is Eclipsed, but when they are in Opposition, the Moon is Eclipsed.

8. Of these 12 Signs, 4 are called Cardi­nals, viz. Aries and Libra, in which do happen the Vernal and the Autumnal Ae­quinoctials; Cancer and Capricorn, in which do happen the Summer and the Winter Sol­stices.

[Page 112]9. Again these Signs are distinguished in­to Northern and Southern; the Northern signs are those which decline from the Ae­quator towards the North Pole, as ♈, ♉, ♊, ♋, ♌, ♍; And the Southers signs are those which decline from the Aequator to­wards the South Pole, as ♎, ♏, ♐, ♑, ♒, ♓.

10. All other Constellations or fixed stars are referred to some one or other of the 12 signs, whether they be the 21 Northern con­stellations, called Vrsa Minor, Vrsa Major, Draco, Cepheus, Arctephylax, Corona Bore alis, Engonasus, Lyra, Avis, Cassiopeia, Persius, Heniochus, Serpentarius, Serpens, Sagitta, Aqui­la, Delphinus, Equisectio, Pegasus, Andromeda, Triangulus. Or whether they be the 15 Sou­thern constellations, called Cetus, Orion, Eri­danus, Lupus, Canis Major, Precyon, Argo, Hy­dra, Crater, Corvus, Centaurus, [...]ra, Ara, Corona Austr. Pisces Austra.

11. The two other great Circles called the Colures, are the two Circles which pass through the Poles of the World, and the four Cardinal points in the Zodiack.

12. That circle which passeth thro' the Poles of the world, and the two Solstitial points in the Zodiack, which are the beginnings of ♋ and ♑, and is called the Solstitial Colure.

13. That Circle, which passeth through the poles of the world and the two Aequino­ctial points, or first entrance into ♈ and ♎, is called the Aequinoctial Colure, and in Fig. 9. represented by the line D. C.

[Page 113]14. The Lesser Circles of the Sphere are the two Tropicks of ♋ and ♑ with the Ar­tick and Antartick Circles.

15. The Tropick of ♋ is a Circle joyned to the Zodiack in the beginning of ♋, and is de­scribed by the Suns Diurnal Motion, when he is in the Summers Solstitial point, and is di­stant from the Aequinoctial towards the North Pole 23 deg. 31' 30" or in Decimal Numbers, 23 deg. 5.25. to which when the Sun cometh, he causeth the longest day and shortest night to all Northern; the shortest day and longest night to all Southern Inha­bitants; and is noted with G ♋.

16. The Tropick of ♑, is a Circle joyned to the Zodiack in the beginning of ♑, and de­scribed by the Suns Diurnal Motion, being in the winters Solstitial point, and is distant from the Aequinoctial towards the South Po [...] [...]3 deg. 31' 30", or in Decimal Num­bers, 23 deg. 5.25 parts, to which, when the Sun cometh, he maketh the longest day and shortest night, to all Southern; the shortest day and 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 the Circles, he is at his greatest distance from the Aequator, and returneth thither again.

17. The Artick Circle, is distant from the North Pole of the world, as much as [Page 114] the Tropick of ♋ is distant from the Aequi­noctial and is noted with KL.

The Antartick Circle is distant from the South Pole as much as the Tropick of ♑ is di­stant from the Aequator, & is noted with OM.

18. By the Intersection of any three of the greatest Circles of a Sphere is made a Spherical Triangle.

19. A Spherical Triangle, is either Right Angled or Oblique.

20. A Right Angled Spherical Triangle, hath one Right Angle at the least.

21. An Oblique Angled Spherical Triangle, is either Acute or Obtuse.

22. An Acute Angled Spherical Triangle, hath all its Angles Acute.

23. An Obtuse Angled Spherical Triangle, hath all his Angles, either Obtuse or mixt, that is one Angle at the least Obtuse, and the other Acute.

24. In Spherical Triangles, there are 28 Varieties or Cases, 16 in Rectangular, and 12 in Oblique Angular, whereof all the Rectan­gular and 10 of the Oblique Angular, may be resolved by one Catholick, and Universal Proposition; for the understanding where­of, some things must be premised.

1. That in a Right Angled Spherical Triangle, the Hypotenuse and both the Acute Angles are supposed to be noted with their Complements.

2. That the Right Angle is not reckoned a­mongst the Circular parts, and therefore one of the other five will be always a middle part, and the other four extreams Conjunct or Disjunct.

CHAP. III. Of the Ascensions and Descensions of the Parts of the Zodiack.

HItherto we have spoken of the general Principles of Astronomy, from whence the motion of the Primum Mobile is explai­ned; come we now to these affections which properly belong to the motion there­of, and these are the Ascension and Descension [Page 120] of the Parts of the Zodiack, or Astronomi­cal Rising and Setting.

2. Astronomical Rising and Setting, is the Elevation of the parts of the Zodiack or E­cliptick above the Horizon, and Depressed under it, compared to the Ascension and de­scension of the parts of the Aequator; and this comparison is in reference to diverse Elevations of the Poles.

3. But this Astronomical Rising and Set­ting, takes his Denomination from the parts of the Zodiack; which are above the Horizon or beneath it, and are measured with respect unto the Aequator; for Astro­nomers do not refer the Aequator to the Zodiack, but the Zodiack to the Aequator, for it is Zodiack, and not the Aequator which stands in need of measuring.

4. And an Arch of the Ecliptick or Zodi­ack, is to be understood two manner of ways; namely, Continued or Discreet; A Continued Arch, is when it is reckoned in the Aequator in a Continued Series, from the beginning of Aries, and so forward into the consequent Signs.

5. A Discreet Arch, is so called, because it is not reckoned from the first Degree of Aries, but from any other point; as from the fourteenth of Gemini, to the fourteenth of Taurus.

6. Any part of the Zodiack is then said to Ascend Right, when a greater part of the [Page 121] Aequator riseth above the Horizon than of the Zodiack. And that is said to be a grea­ter Arch of the Aequator, which is more than 90 Degrees.

7. Any part of the Zodiack is then said to Descend Right, when a greater part of the Aequator than of the Zodiack is beneath the Horizon.

8. Any part of the Zodiack therefore is said to Ascend Obliquely, when a less part of the Aequator than of the Zodiack doth As­cend; as also, to Descend Obliquely, when less of the Aequator than of the Zodiack is below the Horizon.

9. Ascension, is either Right or Oblique.

10. Right Ascension or Descension, is that which is in a Right Sphere.

11. In a Right Sphere, the four Quadrants of the Zodiack beginning from the Aequino­ctial and Solstitial Points, do equally Ascend and Descend, so that in these whole Qua­drants, as many Degrees of the Aequator as of the Zodiack do Ascend; but the interme­diate parts of those Quadrants in the Zodi­ack do vary, and have not equal Ascension and Descension with the parts of the Aequa­tor.

12. Those Signs that are equally distant from any of those Points, have also equal As­cension, as Gemini and Cancer. And the As­cension of a Sign is always equal to the Des­cension of the same.

[Page 122]13. In a Right Sphere therefore, four Signs only do rise Right, all the rest do rise Obliquely.

14. In an Oblique Sphere, the two halves that begin at the two Aequinoctial Points, do rise together, but the parts of those halves do rise Obliquely. And those Signs that rise Rightly, do Descend Obliquely, and the contrary.

15. The Ascension of opposite Signs in an Oblique Sphere, taken together, are equal to the Ascension of the same in a Right Sphere. And those signs that are equall di­stant from either of the Aequinoctial Points, have equal Ascensions, because they equally Decline from the Aequator.

16. Besides the Astronomical Rising and setting of the stars, or their rising and set­ting, in respect of the Horizon and Aequa­tor, there are other affections of the stars to be considered, namely, those which they have in respect of the sun.

17. In respect of the Celestial Circles, that is in respect of the Zodiack, Aequator, and Horizon, there is a fourfold affection of the stars. 1. Longitude. 2. Of Altitude. 3. Of Latitude. 4. Of Declination.

18. The Longitude of a star is his distance from the first Degree or Point of Aries, ac­counting from West to East.

19. The Altitude of a star is to be conside­red generally or specially. Generally con­sidered, [Page 123] the Altitude of a star is the height thereof above the Circle of the Horizon.

20. Specially considered, the Elevation of the Pole star above the Horizon, is called the Altitude.

21. The Latitude of a star is his dDstance from the Ecliptick, that is from the very mid­dle of the Zodiack towards either Pole, whe­ther North or South.

22. The Declination of a star, is his Di­stance from the Aequator, and as he declines from thence either Northward or South­ward, so is his Declination nominated ei­ther North or South.

23. Thus much of these affections of the stars, which they have in respect of the Ce­lestial Circles; come we now to those which they have in respect of the sun; usually cal­led the Poetical rising and setting; and this is threefold. The first of these in Latin, is called Ortus Matutinus sive Cosmicus, The Morning or Cosmical Rising. The second, Vespertinus five Achronicus, The Evening or Achronical; and the last, Heliacus vel Sola­ris, Heliacal or Solary.

24. The Cosmical or Morning Rising of a star, is when it Riseth above the Horizon, together with the sun. And the Cosmical or Morning setting of a star is, when it-set­teth at the opposite part of Heaven, when the sun riseth.

25. The Achronical, or Evening Rising of [Page 124] a Star, is when it Riseth on the opposite part, when the Sun setteth; And the Achro­nical Evening setting of a Star, is when it setteth at the same time with the Sun.

26. The Heliacal Rising of a Star, which you may properly call the Emersion of it, is when a Star that was hid by the Sun beams, beginneth to recover it self out, and to ap­pear. And so likewise, the setting of such a star, which may be also called the Occultati­on of the same, is when the Sun by his own proper motion overtaketh any star, and by the brightness of his beams doth make it invisible unto us.

And thus having briefly shewed the chief affections of the Primum Mobile; how the quantity of these affections may be compu­ted, by the Doctrine of Spherical Triangles, shall be declared in the Problems following.

CHAP. IV. Of the Secondary or Periodical Motion of the Stars.

Having done with the first part of Astro­nomy, the motion of the Primum Mobile, and the affections of the stars, occasioned by that motion; we are now to speak of their [Page 131] own Proper or Periodical motion; in which contrary to the motion of the Primum Mo­bile, they are carried from West to East.

2. This motion of the fixed stars is very slow; for they alter their places but little in many Years, but are not immoveable as some thought; the quantity of their annual moti­on, according to Tycho Brahe is 50 seconds, and 37 thirds of a degree, and others since him do conceive that 50 seconds only is the quantity of their annual motion, that is most agreeable unto truth and observation.

3. This motion in the Planets is more swift, and although they never move out of the Zodiack, yet they do move sometimes in one part of Heaven, sometimes in another, sometimes towards the south Pole, sometimes towards the North, sometimes near one fix­ed star, sometimes near another, and some­times nearer, sometimes farther from one a­nother also, whereas the fixed stars do al­ways keep the same distance from one another.

4. The Planets do not move in one Orb, but every Planet hath a several Orb, where­as the infinite number of fixed stars do all move in one only sphere or Orb.

5. The Names and Characters of the pla­nets are these:

1. Saturn, whose mark is ♄, finisheth his re­volution in 29 Years, 174 Days, 4 Hours.

2. Jupiter, whose mark is ♃, finisheth his Revolution in 11 Years, 317 Days, 15 Hours.

[Page 132]3. Mars, whose mark is ♂, finisheth his Revolution in 1 Year, 321 Days, 23 Hours.

4. The Earth or Sun, marked thus ☉, finisheth his Course in 365 Days, 5 Hours, 49 Minutes, 4 seconds, and 21 thirds.

5. The Moon, marked thus ☽, finisheth her Course in 27 Days, 7 Hours, 43 Minutes, and 6 seconds, but returneth not into Conjuncti­on with the Sun, under 29 Days, 12 Hours, 44 minutes, and 3 seconds.

6. Venus, marked thus ♀, finisheth her Course in 224 Days, 16 Hours, 40' and 30".

7. Mercury, marked thus ☿, finisheth his Course in 87 Days, 23 Hours, 00' and 15".

6. The Civil Year, though it doth not ex­actly agree, yet hath it some proportion with the Motions of the sun and Moon in every Nation; Romulus the founder of Rome, ap­pointed the year at first to consist of 10 Moons, or Months, and called the first March, 2. April, 3. May, 4. June, the rest Quin­tilis, Sextilis, S [...]ptember, October, November, December, because they were 5, 6, 7, 8, 9, and 10 Months distant from March.

After whom, Numa Pompilius added two Months more, and called them January and February, and appointed each Month to con­tain 29 and 30 Days, whereby the Year, did consist of 354 Days, in which time the Moon returneth into Conjunction with the Sun, and this is the quantity of the Year in Turky [Page 133] at this day; only in every third Year, they reckon 355 days. The Persians and Aegypti­ans do also count 12 Moons or Months to their Year, but their Months are proporti­oned to the time of the Suns continuance in every of the 12 signs: In their Year there­fore, which is solar, there are always 365 days, that is, 11 days more than the Lunar Year.

And the Julian Year, which is the accompt of all Christendom, doth differ from the o­ther only in this, that by reason of the suns excess in motion above 365 days, which is about 5 Hours, 49 Minutes, it hath a day in­tercalated once in four Years, and by reason of this Intercalation, it is more agreeable with the motion of the Sun, the former dif­fering from the Numan Year, 11 days and 6 Hours, the which 11 days, Julius Caesar di­stributed amongst the Months, and the month Quintilis, was by him called July, ac­cording to his own name; and Augustus Cae­sar called the Month Sextilis, by the name of August, and altered the Position of days in each month to that which we now use, in which there are 52 Weeks, and one odd day, and this one day supernumerary, maketh an alteration in all the rest, so that the days of the Week, which used to be assigned by the Letters of the Alphabet, fall not alike in se­veral Years, but Sunday this Year, must fall out upon the next years Monday, & so forward, till [Page 134] seven years; and because the six odd Hours do make a day in four years, every fourth year hath a day added to its accompt, and such a year doth consist of 366 days, which doth occasion the Sunday letter still to alter till four times 7, that is, 28 Years be gone about. This Revolution is called the Cycle of the Sun, taking name from ☉, Sunday, the Letter whereof it doth appoint for every year, as by the Table may be seen.

To find which of 28 the present is, add 9 to the Year of Our Lord, because this Cir­cle was so far gone about at that the time of Christ's birth, divide the whole by 28, what remains, is the present year; if nothing re­main, the Cycle is out, and that year you must call the last, or 28.

This Intercalation of a day, placed in Fe­bruary, doth occasion the Letter F to be twice repeated in the latter end of that Month, viz. upon the 24 and 25 days, and in such a year St. Matthias day is to be observed upon the 25 of that month, and the very next Sunday doth change and alter this letter, from which Leaping or Changing, such a year is called the Leap Year, and the Number of days in each Month is well expressed in these Distichs.

[Page 135] Thirty Days hath September,

April, June, and November;

February hath Twenty Eight alone,

All the rest hath Thirty and One:

—But when of Leap Year cometh the time,

Then Days hath February Twenty & Nine.

That this Accompt is somewhat too long, is acknowledged and confess [...]d by the most skilful Astronomers, as for the Number of days in a year, the Emperours Mathemati­cians were in the right, for it is certain, no Year can consist of more than 365 days, but for the odd Hours, it is a certain that they cannot be fewer than five, nor so many as six, so that the doubt is upon the minutes, sixty whereof goeth to the making of an Hour; a small matter one would think, and how great in the recess and consequence we shall see.

Julius Caesar alotted 365 days, 6 hours, to his Revolution; but the Sun goeth about in less time, that is, (according to the most exact accompt,) in 365 days, 5 hours, 49 Minutes, and a little more; so that the Em­perours year must of necessity breed a diffe­rence in so many Minutes every year, be­twixt the year which the Sun it self describes in the Zodiack, and that which is reckoned upon in the Calender, which though for a year or two may pass insensibly, yet in the space of 134 years it will rise to a whole day [Page 136] that is, the beginning of the year in the Calender must be set one day back.

CHAP. I. Of the Definition and Parts of RHETORICK.

RHETORICK, is the Art or facul­ty of Eloquent and delightful Spea­king.

The Parts of Rhetorick are Five; Invention, Disposition, Elocution, Memory, and Pronounciation.

In Invention, we are to consider three things:

1. What we are to Invent. 2. By what Arguments we may confirm the Matter In­vented. 3. From what Topicks or gene­ral [Page 148] Heads those Arguments may be raised.

And first, the thing or matter which we are to invent, is the scope and purpose of the intended Oration: That is, we must propound some certain Proposition to which we mean to direct our Speech; and of those several Propositions which may be raised from the subject propounded, we should still make choice of that which is most agreea­ble to the Sentence given.

Secondly, When we have resolved upon a Proposition, we are to bethink our selves of some Arguments or probable Reasons, by which that Proposition may be confirmed.

Thirdly, We are to consider the several Topicks or common places from whence these probable Arguments may be invented and raised, and these are of two sorts; In­trinsecal and Extrinsecal; those that are called Intrinsecal, which are comprised in the matter which is propounded, and the Topicks or Heads, from whence such Argu­ments may be invented, are these following.

1. Definition. 2. Division. 3. Notation. 4. Conjugation. 5. Genus. 6. Species. 7. Semilitude. 8. Dissimilitude. 9. Contraries. 10. Opposites. 11. Comparison. 12. Causes. 13. Effects. 14. Adjuncts. 15. Antece­dents. 16. Consequents. All other Topicks, from whence Intrinsecal or Artificial Argu­ments may be raised, are contained in these, or may be derived from them.

[Page 149]1. Definition, is a Speech explaining or declaring what a thing is; The parts where­of, according to Logicians are two; 1. The Genus, or general name agreeing with the thing defined, and with several other things besides. 2. The difference or particular name, which doth only agree with that which is defined:

CHAP. II. Of Disposition.

DIsposition, is the orderly placing of those things which are invented: It is two-fold.

First, Natural, in which things are dis­coursed in that order in which they were done, or in which according to Nature, they should be done; as if you were to commend a Person, you should begin with his Child­hood, next his Youth, and so to the other degrees of his Age.

The second way is Artificial, which doth either for delight or profit diversly mingle and confound the matter, putting that in the end, which should be in the beginning, and the beginning in the end, that so he may both delight the Auditors, and hold them in suspense; which in an unexpected e­vent doth not a little please and delight the Hearers.

The Orator then having resolved of his Proposition, must first consider of what na­ture it is, whether single, or consisting of se­veral parts; and which of the parts should be first handled, which next.

Secondly, he must choose some few of the best Arguments he hath invented, and place [Page 157] some solid Argument in the beginning, those that are less forcible in the midst, re­serving still the best and most convincing for the conclusion; because the Auditor at the first being greedy of knowing, must be prepos­sessed and convinced; but in the end he must be strongly confirmed and forced.

And the most perswasive Arguments are those which proceed from the Definition, Distribution, Genus, Causes, and Effects of the thing discoursed of, for these explain the nature thereof; and less forcible Argu­ments are such as are collected from some trivial Adjuncts and Conjectures.

Thirdly, he must Logically dispose of these Reasons and Arguments; First, into Syllogisms; and then consider how to enlarge them in an Oratorical manner.

Fourthly, he must consider into what parts his Oration should be divided, and the parts of an Oration are usually reckoned to be these five.

• 1. Exordium.
• 2. Proposition.
• 3. Narration.
• 4. Confirmation.
• 5. Peroration, or Conclusion.

As for Confutation, it is comprised in Confirmation: But all these parts are not always necessary; for the ingenious Orator, may as he shall see it convenient, sometimes omit the Narration, sometimes the Exordi­um, [Page 158] sometimes the Peroration or Conclusion, yea, and the Confirmation is many times scarce discernable; as when the things pro­pounded are certain, there is more need of Ornament than Proof, as in Gratulatory O­rations, and the like. As for the placing of these parts, their natural Order is that in which we have named them. 1. The Exordium. 2. The Proposition. 3. The Narration, if it be not thought fit to omit it. 4. The Confirmation; and Lastly, The Pe­roration.

An Exordium, is as it were the door of the Oration, in which the Orator doth pre­pare the minds of the Auditor for that which is to follow: And this is commonly done by one of these three ways; By bespeaking their favour; by making them Docible; or by begging their Attention. The Favour of the Auditors is bespoke either from the person of the Orator, from the persons of the Auditors, from the persons of the Ad­versaries, or from the subject matter of the Discourse. The Orator may bespeak the Favour of the Auditors, in respect of him­self, if his gesture and deportment be suita­ble unto theirs that are his Auditors, and express himself modestly. And in respect of the Auditors, if he shew how well they have deserved of the Common-wealth, of him, and other men. And in respect of the Adversaries, if he modestly shew wherein [Page 159] they are faulty, and render them to the Au­ditors inexcusable. And lastly, in respect of the matter in hand, if he say, that it is some excellent, necessary, and profitable thing.

Secondly, the Orator may be said to make the Auditors Docible, if he clearly explain the thing of which he is to speak, and how he purposeth to enlarge upon it.

Thirdly, the Attention will be quickened, if he saith, that he intends to speak of some great and wonderful thing, and something that is delightful; necessary, and very much concerns his Auditors, &c.

The second part of an Oration is the Pro­position; and the Proposition is that part of the Oration, in which the Orator doth briefly deliver the sum of the whole Matter, of which he intends to speak, and bespeaks the Hearers Attention, if need be. Some­times it doth immediately follow the Exor­dium; sometimes it follows the Narration; in what place soever it be put, it must be short and clear, and fit for Confirma­tion.

The third part of an Oration is Narrati­on, by which a relation is made of the mat­ter or thing done. And this is either a di­stinct part of the Oration, and then for the most part it doth immediately follow the Exordium, that the Proposition with the Con­firmation, which is to be done in such Ora­tions which assume the explaination of [Page 160] the thing done to prove the matter in hand.

CHAP, III Of Elocution.

ELocution, or the garnishing of Speech, is an Art by which the Speech is beautified with the Elegancy of Words and Sentences.

And this is performed two ways; by the fine manners of Words, called a Trope; or by the fine frame of Speech, called a Figure.

A Trope is such an Elocution or manner of Speech, as doth change the signification of a word into a different signification from the natural.

In a Trope two things are to be considered. 1. The Affections. 2. The Kinds.

The Affections of a Trope are four,

• Catachresis.
• Hyperbole.
• Matalepsis.
• Allegoria.

Catachresis, is a harsh and unpleasant change of a Word; as namely, when one word or name is put to another, not by any proper relation, but by a kind of force. He threatens me a good turn.

Hyperbole, is a very high relation of a thing, or a more bold excess of a Trope, which doth exceed belief, either by Augmen­tation [Page 163] or by Diminution. Note that though an Hyperbole doth vary from the truth, yet doth it not deceive us through-Fiction, or such variation.

An Hyperbole is two-fold; Auxesis or Meio­sis.

An Auxesis is, when for Argumentation sake or Amplification, we interpose a more vehement expression, in his proper place; as when we say, magnificent for liberal.

A Meiosis, or a Tapinosis, is when for ex­tenuation sake, we use a milder or more fa­vourable expression, than the matter requi­reth; as when we say a flatterer is a courteous and an affable person.

A Matalepsis, is that which containeth ma­ny Tropes in one expression; as, when we by an improper Speech, signifie, first, that which is improper, and by that improper Speech perhaps another, and so forward, till we come to that which is proper, making way for Transition, by interposing a mean degree; as All the City was moved. Mat. 21.10. where the City is put for Jerusalem, by a Synechdoche Generis: and Jerusalem for its In­habitants, by a Metonymy of the Subject.

An Allegory, is the continuation of a Trope as where many Tropes of the same kind are joyned together; as, Put on the whole Armor of God, Ephesians 6.11.

In an Allegory, observe to end with the same kind of Trope with which you begin, or [Page 164] else the Consequence will be abused.

The several kinds of Tropes are these four:

• 1. A Metonomy.
• 2. An Irony.
• 3. A Metaphor: and
• 4. A Synechdoche.

A Metonomy, is a Trope of the Cause to the Effect, of the Subject to the Adjunct: and the contrary, of the Effect to the Cause, or of the Adjunct to the Subject.

There are four kinds of Causes.

• 1. The Efficient Cause, by which a thing is.
• 2. The Material Cause, of which a thing is made.
• 3. The Formal Cause, by which a thing is what it is.
• 4. The Final Cause, for which a thing is; of which the two first only belong to our pre­sent purpose.

A Metonymy of the Cause, is of the Effici­ent, or of the Matter.

A Metonymy of the Efficient Cause, is when the Author or Inventor of any thing is put for those things which he hath invented; as Virgil, for the Poem or Works composed by Virgil.

A Metonymy of the Material Cause, is when the name of the Matter is put for the Effect; as Brass, for Brass Money.

A Metonymy of the Effect, is when the Ef­ficient Cause is signified by the Effect; as, Pale Death, which maketh Pale.

[Page 165]A Metonymy of the Subject, is when the proper name of any Subject is made to sig­nifie the Adjunct; as, the Cup, for the Drink in the Cup.

A Metonymy of the Adjunct, is when the Adjunct is put for the Subject; as Gen. 31.53. Jacob swear by the fear of his Father Isaac, i. e. by God, whom Isaac feared.

An Irony, is a Trope from one opposite to another, or in which we speak by con­traries.

Opposites; are either unlike or contrary; all things of different natures are said to be unlike, as a Man, a Stone; and all things of contrary natures are said to be contrary to one another; as light and darkness.

An Irony of a thing unlike, is when any thing is spoken of one person, and under­stood of another.

An Irony from the contrary, is when one contrary is signified by another; as O thou hast done very well; meaning that he had done very ill.

Paralepsis, is a kind of Irony, by which we seem to pass by, or take no notice of such things which yet we strictly observe and re­member.

Apophasis, is a kind of Irony, by which we deny to say or do what yet we speak with greatest earnestness, and do with all our might.

A Metaphor, is a Trope, by which we [Page 166] express our selves by a word, which is of the like signification with that we mean; as, the King is the Head of the Common-wealth.

Synecdoche, is a Trope, by which a part is put for the whole, or the whole for a part.

A Part, is either a Member or Species.

A Synecdoche of a Member, when by a Member the whole is signified; as, the Roof for the House.

A Synecdoche of the Species, is when the Species is put for the Genus; as, Croesus, for a Rich man.

The whole is either an Integer or Genus.

A Synecdoche of an Integer, is when an In­teger is put for a Member; as, His Army was so great, that it drank the Rivers dry; mean­ing a great part of the Water in the River.

A Synecdoche of the Genus is, when the general is put for the special; as, Preach the Gospel to every Creature, meaning Mankind only, and not to every Creature.

Hitherto of Tropes, the first kind of elocu­tion, the second kind of Elocution by Fi­gure.

CHAP. IV. Of a Figure.

A Figure, is a kind of Elocution, by which the form of a Speech is changed from its right and plain use.

A Figure, is either of a Word, or of a Sentence.

A Figure of a Word, is that by which an Oration or Speech is composed of words aptly and sweetly suitable to one another, and this consists in the Dimension or Repe­tition of Sounds or VVords.

A Figure, in the Dimension of Sounds, is the sweet number of Sounds in a Sentence.

Number, is either Poetical or Oratorical.

A Poetical Number, is that which is con­fined to a perpetual observation of certain Spaces.

A Number Poetical, is either Rhyme or Meter.

Rhyme is a Poetical Number, containing a certain number of Feet, without any regard to the quantity of the Syllables; whether long or short, As,

A Meter, is a Poetical Number, consisting [Page 168] of certain Feet, of which the last Foot hath the last Syllable indifferent or common; that is, long or short.

Oratorical Number doth indeed consist of Feet, but not of any certain number of Feet, but of as many or as few as the Orator plea­seth.

The Figure of a word in respect of the re­petition thereof, is either of like or unlike Sounds.

A Figure of a word in the repitition of the like Sound, is either with, or without Inter­mission.

Repetition of the like Sound without inter­mission, is either an Epizeuxis, or an Ana­diplosis.

An Epizeuxis, is when a like Sound is re­peated in the same Sentence without Inter­mission; as, a sword, a sword is sharpened.

An Anadiplosis, is when a like sound with­out Intermission is repeated in divers senten­ces, i. e. when it ends one and begins ano­ther; as,

Repetition of like sound with intermission in the same place, is either an Anaphora or Epistrophe.

An Anaphora, is when a like sound is re­peated [Page 169] in the beginning of Sentences; as,

An Epistrophe, is when a like sound is re­peated, in the close of sentences; as, Are they Hebrews? so am I: Are they, Israelites? so am I: Are they of the seed of Abraham? so am I.

Repetition of like sound with intermission in divers parts or places, is either an Epa­nalepsis, or an Epanados.

An Epanalepsis, is when a like sound is re­peated in the beginning and ending of the same Sentence; as, In sorrow was I born, and I must dye in sorrow.

An Epanados, is when the like sound is in the beginning and ending of divers senten­ces, an Anadiplosis coming between; as Par­thenia desired above all things to have Arga­lus; Argalus feared nothing but to miss Par­thenia.

A Figure of a Word made by the repeti­tion of sounds somewhat unlike, is either Pa­ronomafia, or Polyptoton.

Paronomafia, is when a Word being chan­ged in a Letter or Syllable, it is also chan­ged in sense and signification; as, Though you advise me to repent, I have not Grace to follow your advise.

A Polyptoton, is when words of the same [Page 170] Original are reiterated, but with some variati­on; as, Deceiving, and being Deceived.

A Figure in reference to a sentence, is a Figure which affecteth the whole sentence with some motion of the Mind, either in absolute reasoning, or in reasoning Dia­logue-wise.

Logismus, or absolute Reasoning, is when a sentence is composed without any talk­ing with other supposed; this is either Ec­phonesis, a recalling of ones self, Apostrophe, or Prosopopeia.

Ecphonesis, is a Figure in reasoning, by way of Exclamation, by an Adverb expres­sed, or understood; as, O wretched man that I am!

Recalling of ones self, is when something is called back; and it is as it were a Dimi­nution of the over-hastiness or heat of speech; and this is either Epanorthosis, or Aposiopesis.

An Eparnorthosis, is when something pre­cedeing is called back, by correcting it; as, I had one only Young Man to my son; ah! what have I said! I had! yea I had! It is now un­certain whether I have or not.

An Aposiopesis, is when the close of a sen­tence begun is stopped, by keeping in a part, which yet is understood; as, You Rogue if I Live!

An Apostrophe, is when a speech is dire­cted to another, than was by the speech it [Page 171] self at first intended; as, God knows I lye not.

A Prosopopoeia, is when in our Oration, we suppose another person to be speaking; as, Josh. 24.27. Behold this shall be a witness un­to us; for it hath heard all the Words of the Lord, which he hath spoken unto us.

A Figure, in reasoning Dialogue-wise, is when a sentence is composed in form of a Conference; this consisteth in Question and Answer, in Consenting or dissenting Dialogism.

A Figure of consenting Dialogism, is when ones Answer doth admit of the Obje­ction expressed or understood; yet so, as that from thence the inconsequence of the Objection may be shewed if need be.

Dissenting Dialogism, is when ones an­swer doth impugn or cross the Objection.

And thus much concerning Elocution, as for Memory and Pronounciation, which are the other two parts of Rhetorick, I purpose­ly omit them, as being natural Endowments, which may be better improved by constant practice, than by any Precepts which can be given.

CHAP. I Of Simple Themes.

LOgick, is an Art which conducteth the Mind in the knowledge of Things.

2. The Parts of Logick are two, Thematical and Organical.

3. The Thematical part is that, which Treateth of Themes, with their various af­fections, and second Notions, as of the mat­ter of which Logical Instruments are com­posed.

4. The Organical part, is that which trea­teth of these Instruments, and their Com­position.

5. A Theme, is any thing propounded to [Page 174] the understanding, that it may be known.

6. A Theme, is either simple or compound.

7. A Simple Theme, is one Voice, signifi­ing one thing as, a Man, a Horse.

8. A Compound Theme, is a Theme made of several simple themes rightly Joyned to­gether; signifying many or several things; such are all Orations.

9. A Simple Theme or Voice, is,

• 1. Concrete, which expresseth a thing Concretely or Joyntly; as, Learned.
• 2. Abstract, which noteth something Ab­stracted from all others; as, Learning.

10. An Abstract Voice, or simple theme, is Singular or Universal.

11. A singular theme, is that which in its own nature can be spoken of no more than one, and is called an Individual.

12. Individuals are of two sorts.

• 1. Such as are Certain and Determinate; as, this man, Paul, Alexander, the Apostle of the Gentiles, &c.
• 2. Such as are uncertain and indetermi­nate, as some man.

13. An Vniversal simple Theme, otherwise called a Predicable, is that which may be spoken of many; as, a Body; and this is either of the first or second Intention.

14. A simple Theme of the first intention, is that which expresseth the thing it self; as, Gold, Stone, &c. so called, because they are the names by which the things themselves are first made known.

[Page 175]15. A simple Theme of the second Intention, is that which doth not express the things it self, but certain affections agreeing to the thing, and such are all Words of Art; as, a Noun, a Metaphor, &c.

16. An Vniversal simple Theme, may be spoken of many, two ways.

1. In Quid? or by declaring what a thing is; and thus it is spoken of such as do dif­fer in the species, and is called Genus; as, a li­ving Creature, colour, &c. or else of such as do differ in number only, and is called spe­cies; as, a Man.

2. In Quale, or by declaring what a kind of thing it is, of which it is spoken; & that Essentially or Accidentally, Essentially, and then it is called Difference, the which is,

1. Divisive, by which a Genus is divided in­to its several species, as by rational and irra­tional a Living Creature is divided into a Man or a Beast.

2. Constitution, which doth Essentially constitute some species, and this is,

1. Generical, which doth constitute some remote species, but not the next, for the next is the Genus, thus sensibility in respect of Man, is a generical difference, constituting first a living Creature, and then a man. And this is always spoken of many differing in species, or number.

2. Specifical, which doth constitute the nearest species; as, rationalibility doth constitute man.

2. Accidentally, and that either of neces­sity, [Page 176] and then it is called a proper Accident, which is convertable with its Species, per­petually inherent in every of them, and in no other, as the visible faculty in a Man.

Or not of necessity, and then it is called a common or simple Accident, not converti­ble with its Species; as white.

17. All simple Themes, may be reduced to ten ranks or orders, called Predicaments, of which some are more principal, some less.

18. The more principal Predicaments are the first six, the less principal, are the other four.

19. The Predicamental Ranks or Orders, are of two sorts, the one of Substance, and the other of Accidents.

20. Of Substance, there is only one, and it is called by that name Substance, which is a thing subsisting of it self, and it is ei­ther first or second.

21. The first substance, is a Singular sub­stance, or a substance that cannot be predi­cated of its subject; as, Alexander.

22. The second Substance is an Universal substance, or a substance which may be pre­dicated of its subject; as, a Man, a Horse. The first substance is chiefly and properly a substance, and among the second substan­ces, every one is by so much more a substance, by how much it is nearer to the first.

23. The Predicamental Ranks or Orders of Accidents, are of two sorts.

1. Absolute, as the Predicaments of quan­tity, [Page 177] Quality, Action, and Passion.

2. Relative, as the Predicament of Relation.

24. Quantity, is an absolute accident, by which a thing is said to be great in bulk or number.

25. Quality, is an absolute Accident, by which it is simply and determinately decla­red what kind of thing, that subject is, of which it is the Quality.

26. Action, is an Accident, by which a subject is said to be doing.

27. Passion, is an Accident, by which the subject is called Patient; or it is the recep­tion of Action.

28. Relation, is a respective accident, by which one thing is predicated of another, or may by some way be referred unto another.

29. The less principal Predicaments are these four, When, Where, Scituation, and Habit.

30. The Predicament When, is an acci­dent, by which finite things are said to be in time, past, present, or to come.

31. The Predicament Where, is an acci­dent, by which things finite, are said to be in some place.

32. The Predicament of Scituation, is a certain Ordination, or placing of parts in Generation.

33. The Predicament of Habit, is an ac­cident, by which some garment or something like a Garment, is put about, hanged upon, or some way or other joyned to a Body.

CHAP. II. Of Compounded Themes.

HItherto of Simple Themes: Compounded Themes, or such as are made of several Simple Themes are next to be considered; otherwise called Enunciations, or Propositions.

2. An Enunciation, or Proposition, is an Indi­cative, Congruent and perfect Oration, signi­fying true or false without any Ambiguity.

3. The parts of a Proposition are two, the parts Signing or Signed.

4. The parts Signing are simple terms, whose parts can signifie nothing, being se­parated from the whole, or no such thing as they did signifie being joyned all together.

5. These simple terms are of two sorts, Categorematical, or Syncategorematical.

6. Categorematical, or Significative terms, or such simple terms, as do by themselves signifie something perfectly; and these are either Nouns or Verbs.

7. A Noun, is a simple term or word, which doth signifie some certain thing with­out destinction of time; as, a man, a horse.

8. A Verb, is a simple term, which doth sig­nifie something, with some destinction of time past, present, or to come; as, he runneth.

9. Syncategorematical, or Consignificative terms, are simple terms, which of them­selves do not signifie any certain thing, or [Page 179] constitute a Proposition, but being joyned with other Words, are significative, to ex­press the manner of such a thing; and such are all Words which serve to express the quantity of a proposition; as, all, none, some, &c. with all Adverbs, Conjunctions, Pre­positions, and Interjections.

10. The parts signed are three; the Sub­ject, the predicate, and the Copula.

11. The subject is all that which precedes the Copula in the Proposition.

12. The Predicate, is all that which is spoken of the subject.

13. The Copula, is the principal Verb, joyning the Predicate to the subject, and in e­very Proposition is some person of this Verb Substantive, as in this Proposition, A Man is a living Creature; a Man is the sub­ject; a living Creature is the Predicate; and the Verb is the Copula; sometimes the Co­pula is some Person of a Verb Adjective; as in this Proposition, Socrates lived at Athens.

Here note, that the subject doth not always precede, and the predicate follow the Copula, in order of the parts or terms, but in sense and construction; and also, that in some Pro­positions, the three terms are not always ex­prest, but implyed; as, I walk, for I am walking.

14. Propositions are distinguish'd three ways, according to Substance, Quantity, and Quality.

15. A Proposition, in respect of the substance or parts of which it doth consist, is either Categorical or Hypothetical.

[Page 180]16. A Categorical Proposition, is that which doth consist of one subject, one Predicate, and one Copula; as, a man is a Living Creature, and this is either Pure or Modal.

17. A Pure Categorical Proposition, is when the Predicate is purely affirmed or de­nyed of the subject, without expressing the manner of affirming or denying.

18. A Modal Categorical Proposition, is when besides the subject, predicate, and Copu­la, we add some modification, to shew how the Predicate is in the Subject, as, it is neces­sary; it is contingent, it is possible; it is impos­sible that a man should be without reason.

19. An Hypothetial Proposition, is that which doth consist of two Categorical Propositions, joyned together by some Conjunction, as, if a man be a living Creature, then a man is a Body.

20. A Proposition, in respect of Quality, is distinguished two ways; first, according to the Quality of the sign, and so it is Affirmative or Negative; secondly, according to the quantity of the thing; & so it is either True or False.

21. A Proposition, in respect of Quantity, is universal, particular, indefinite, or singular.

22. An Vniversal proposition, is that which hath a note of Universality added to a com­mon or universal Subject; as, every man is a Living Creature.

23. A particular proposition, is that in which a note of particularity is added to an universal [Page 181] Subject; as, some man is a Living Creature.

24. An Indefinite proposition, is that, in which no note, whether Universal or Par­ticular is put before the universal Subject; as, a man is a Living Creature.

25. A Singular proposition, is that in which the subject is singular, whether it be a proper Name; as, Secrates is a Philosopher; or whether it be a common name, with a note of singulari­ty set before it; as, this man is Learned.

26. Pure Categorical propositions, as they have reference to one another, have three affections; Opposition, Aequipollency, and Conversion.

27. Opposition, is the repugnancy of two ca­tegorical propositions, either in quantity alone, or in quality alone, or else in quantity and qua­lity both, in which there is the same subject, the same predicate, and the same Copula, as, every man is just, no man is just.

28. The categorical propositions, may be said to be opposite four ways; Contrarily, Subcon­trarily, Subalternately, and Contradictorily.

29. Two propositions, that are contrarily, and subcontrarily opposite, are opposite only in quality; and such as are subalternately oppo­site, are opposite only in quantity; and such as are contradictorily opposite, are opposite both in quantity and quality.

30. Opposition, by way of contrariety is the repugnancy of two Universal Propositions in quality; as, every man doth run, no man doth run; [Page 182] and these in a contingent matter, may be both False, but cannot be both together true.

31. Subcontrary Opposition, is the repugnan­cy of two particular Propositions in quality; as, some man doth run, some man doth not run; and these in a contingent matter may be both true, but cannot be both together False.

32. Sabalternate Opposition, is the repug­nancy of two Affirmative, or two Negative Propositions in their quantity; as, every man doth run, some man doth run.

33. Contradictory Opposition, is the repug­nancy of two Propositions, both in quality and in quantity, so that if one of them be Affirmative, the other shall be Negative; if one be Universal, the other shall be particu­lar; as, Every man is Learned, some man is not learned: All which may be easily appre­hended by the following Scheme.

[Page 183]34. Aequipollency, is the equivalency of two Propositions, in sense and signification, though they differ in Words, by virtue of this Word of Negation (not) being set be­fore the Sign and Subject, after the Sign and Subject, or both before and after, in which there is the same Subject, and the same Pre­dicate; as, some man is Learned; not every man is Learned: The several varieties where­of are fully expressed in these Distichs.

35. Conversion, is an apt mutation of the whole subject, into the place of the whole Predicate, and of the whole Predicate, into the place of the whole subject, keeping the same Quality, but sometimes changing the Quantity; as, Every man is a Living Crea­ture; some Living Creature is a man.

36. This Conversion is three-fold;

1. Simple, in which the predicate is chan­ged into the place of the whole Subject, and the Contrary, keeping the same both qua­lity and quantity; as, No man is a Stone, therefore no stone is a man.

2. By Accident, in which the whole pre­dicate is changed into the place of the whole Subject, and the Contrary, keeping the same [Page 184] Quality, but changing of the Quantity; as, Every man is a living Creature, therefore some Living Creature is a man.

3. By Contraposition, in which the whole Subject is changed into the place of the whole predicate; and the contrary, keep­ing both the same Quality and Quantity, but changing the terms from Finite to Infi­nite; as, Every-Man is a Living Creature, therefore every thing that is a Living Creature, is not a man: What Propositions may be con­verted this or that way, these Verses do express.

And what these Letters A, E, I, O, do signifie there Distichs do declare:

CHAP. III. Of Difinition and Division.

HAving done with the first part of Logick, namely, that which treateth of Themes.

I come now unto the second, called the Organical, or that which treateth of Logical Instruments, and their Composition.

2. Logical Instruments are four; Definiti­on, Division, Argumentation, and Method.

3. Definition, is the explication of the thing which is defined; and this is either Nominal, or Real.

4. A Nominal Difinition, is that which sheweth the Signification of the Name; whe­ther it be by giving the Etymology thereof, or by expressing it by some other Synony­mous word more generally known.

5. A Real Definition, is that which shew­eth what the thing is; and this is either perfect or imperfect.

6. A Real and a Perfect Difinition, is that which doth explain the thing by Essential Attributes.

7. A Real, but Imperfect Definition, other­wise called a Description, is that which ex­plains the Nature of a thing, by certain Ac­cidental Attributes.

8. Division, is the Deduction of something [Page 186] that is large, into a straighter and narrower comprehension; and this is either of some ambiguous word, into its several significations, and then it is called Distincti­on, or of the whole into its parts.

9. The whole is either Simple, or Aggre­gate; Division of the whole, simply and pro­perly so called is three-fold.

1. Vniversal into its subjective parts, or of the General into the Specials; as, to di­vide Animal into Man and Beast.

2. Essential, which resolves the whole in­to essential parts, and this either of a Species into its Genus and Difference, or of some spe­cial nature into its matter and form; as, A Man into Soul and Body.

3. Integral, which resolveth the whole in­to Integral parts, and this is the Division of some individual, either into its sensible or material parts.

4. Division of the aggregated whole into its parts, and by Accident is five-fold.

1. When the Subject may be divided by its Accidents; as, Men are Learned or Vn­learned.

2. When an Accident may be divided by its Subjects; as, Feavers are in the Spirits or in the Humours, or in the solid parts.

3. When an Accident may be divided by Accidents; as, Good is either profitable, ho­nest, or pleasant.

4. When things may be divided by their [Page 187] Objects; as, Sight by Colours, Hearing by Sound.

5. When Causes may be divided by their Effects; and the Contrary; as, Heavenly heat is from the Sun, and Elementary from Fire.

CHAP. IV. Of Argumentation.

ARgumentation is an Oration by which some Problem is proved by inference.

1. A Problem, is the proposition or Que­stion to be proved; the which Problem, when it is so proved is the Conclusion, and follows the Illative note, or note of infe­rence: All that which precedes is the Ante­cedent, that which follows is the Consequent or Conclusion; the Illative is commonly this word (therefore,) and in this doth the tye or force of the Argument consist.

2. Argumentation, may be considered ei­ther in reference to the form and manner of Arguing, which is the more general con­sideration; or as it is restrained to certain matter, as shall be shewed in his place.

3. The kinds of Argumentation are usual­ly reckoned to be four; Syllogism, Induction, [Page 188] Enthymeme, and Example, but may be redu­ced to two; for an Enthymeme is nothing but an imperfect Syllogism; an Example, an imperfect Induction; Other less principal kinds of Argumentation there are, which either are of no use, or may be reduced to a Syllogism; as, Sorites and Dilemma, which are indeed redundant Syllogisms; Sorites Ca­tegorical, and Dilemma Hypothetical.

4. A Syllogism, is an Oration, in which something being taken for granted, some­thing else not granted before, is proved or inferred from them.

5. A Syllogism is two-fold, Categorical, in which all the propositions are Categori­cal: or Hypothetical, in which one or more of the propositions are Hypothetical; in both which we are to consider the Matter and the Form.

6. The Matter of a Syllogism, is either Remote or Next.

7. The Remote matter, is that of which it is remotely made, as the Simple Terms which in the propositions of the Syllogism are made Subject and predicate.

8. The Simple Terms of a Syllogism are three, of which one is called the Middle Term, the other two are the M [...]jor and the Minor Extreams, The Major and Minor Extreams are the Predicate, and the other the Subject of the question, and the Middle Term or Argument, is the Term not ex­pressed [Page 189] in the question, but is united once to the Major Extream, and once to the Minor.

9. The next or immediate matter of a Syllogism, is that of which the Syllogism is immediately made, as the three propositi­ons, which are made of the simple terms, of which the first is called the Major, the second the Minor, & the third is call'd the Conclusion.

10. The form of a Syllogism is the right disposing of the two-fold Matter, Next and Remote, and this comprehendeth two things, Figure, and Mood; the one, to wit Figure, hath respect to the Remote Matter or Simple Terms, and Moods respects the next Matter or the propositions.

11. A Figure, is the fit disposing of the middle Terms with the Extreams, in refe­rence to subjection and Predication; this is three-fold.

12. The first Figure maketh that which is the middle simple term to be the subject in the major proposition and the Predicate in the minor.

13. The second Figure, maketh the middle simple term to be the Predicate, both in the major and the minor propositions.

14. The third Figure maketh the middle simple term to be the subject both in the major and the minor propositions; according to these Distichs.

[Page 190]15. A Mood is the disposing of the pro­positions according to quantity and quality.

16. There are 19 Moods, of which there are nine in the first Figure; four in the se­cond; and six in the third, according to these Verses.

• 1. Barbara, Celarent, Darii, Ferio, Baralipton.
• Celamtes, Dabitis, Fapesmo, Fricesomorum.
• 2. Cesare, Camestres, Festino, Baroco.
• 3. Darapti:
• Felapton, Disamis, Datisi, Bocardo, Ferison.

17. These moods are so many words of Art, which serve only to denote the quali­ty and quantity of every proposition, by help of the Vowels, A, E, I, O, as hath been shewed already; and are some of them per­fect, as the four first Moods in the first Fi­gure, and all the moods in the second and third Figures; the rest are imperfect.

18. And the question propounded is pro­ved by or inferred from the premises, by help of these moods two ways, viz. Directly, and Indirectly.

1. Directly, when the Minor Extream is the subject in the Conclusion, and the Major in the Predicate.

2. Indirectly, when the Major Extream is the subject in the Conclusion, and the Minor the Predicate, and this is in the five last moods of the first Figure only, according to these Distichs.

19. These things premised, a Syllogism, may be made in any Mood and Figure in this manner.

The question propounded is always the conclusion of the Syllogism, and by the quan­tity thereof doth plainly shew in what mood or moods it may be framed, and by conse­quence, in what Figure also.

20. If the Syllogism be to be made in such a mood as doth directly infer the Conclusion from the Premises; then the subject in the Proposition is the Minor Extream, and the Predicate the Major; as in the four first moods of the first Figure, and in all the Moods of the second and third Figures; but in the five last Moods of the first Figure, the subject in the Proposition is the Major Extream and the Predicate the Minor; and the mid­dle term is the Cause or Argument by which the truth or falsitie of the proposition is to be proved.

21. The Middle Term or Argument be­ing joyned to the Major Extream, doth make the Major proposition, and being joyned to the Minor Extream, it maketh the minor propositi­on.

CHAP. V. Of A Material Syllogism.

I Come now to speak of a Special or Mate­rial syllogism, as it is constrained to cer­tain Conditions of Matter.

2. A special or material syllogism, is of [Page 195] three sorts; Apodictical, Dialectical and So­phistical.

3. An Apodictical syllogism, otherwise cal­led a Demonstration, may be defined two ways; either from the end, or from the mat­ter of Demonstration.

4. From the end of Demonstration, an Apo­dictical syllogism, is a syllogism begetting knowledge, or making to know. And we are then said to know a thing, when we know the cause for which it is so, and can­not be otherwise.

5. All Knowledge is of such Conclusions, to which we assent, for our preceding know­ledge of the Premises; and the Praecognita in every Science are these three: The Sub­ject, the Affection, and the Cause. And the means by which these are foreknown, are called Praecognitions, and they are two; That a thing is, and what a thing is.

6. The subject, is the less Extream, in a Demonstration, concerning which some acci­dent is Demonstrated by its next Cause; as, a man, concerning whom we must know both that he is, and what he is.

7. Affection or Passion, is a proper acci­dent, which is Demonstrated of the subject, by a proper Cause, it is always the greater Extream, which is Predicated in the Conclu­sion; as, Risibility, the which is necessary to be foreknown, in respect of its name, What it is, but not, that it is; for that is the thing [Page 196] to be enquired after, the thing we are to find by Denomination.

8. A Cause, is that by which the Affection is Demonstrated of its subject, and is always the Major Proposition in the Demonstrati­on; as, Every rational Animal is risible; what the Cause is cannot be foreknown, be­cause it is a compounded Proposition, but it ought to be known, That it is, or else the Conclusion cannot be inferr'd from it.

9. An Apodictical syllogism, being defined from the matter of Demonstration, is a syl­logism, which proveth its Conclusion from such Premises, as are of themselves suffici­ently known.

10. A Demonstration, is to be considered, either in respect of the Matter or in respect of the Form.

11. In respect of the Matter, one kind of Demonstration, sheweth why the Predicate is inherent in the subject, and another sheweth that it is inherent in the subject.

12. In the first of these kinds of Demon­stration, called the Demonstration causal, why a thing is; the Conditions to be observed, do partly belong to the Question, partly to the Cause or Medium of the Demonstration, and partly to the Premises.

13. Every Question doth not admit of the first and most perfect kind of Demon­stration, called, Why a thing is? but such a Question only as is true, and hath a certain [Page 197] and immutable Cause of its own Truth.

14. The Medium of a Demonstration, ought to be the next Cause of the Predicate; and that either Efficient or Final, and the Ef­ficient either Internal or External.

15. The Conditions to be observed in the Premises of a Demonstration, are Absolute or Relative.

16. The Absolute Conditions are two; the first is, that the Propositions be necessarily true and reciprocal; The second, is that they be immediate or first, in respect of the subject; as, A man is Rational, and in re­spect of the Causes; as, That which is ratio­nal, is visible, a man is rational, Ergo.

17. The Relative Conditions to be obser­ved in reference to the Conclusion, are three. 1. That the Premises be the Cause of the Conclusion. 2. That they be before it: and 3. That they be more known than the Con­clusion.

18. The other less principal kind of De­monstration in respect of the Matter, or the Demonstration what, is two-fold, the one is from some sensible Effect, and the o­ther from a remote Cause.

19. The form of these Demonstrations, is descerned partly from the Quantity, and so it is Vniversal or Particular; Partly from the Quality, and so it is Affirmative or Ne­gative; partly from the manner of the proof, and so it is Ostensive, or by Reduction to Im­possibility.

CHAP. VI. Of a Topical Syllogism.

HItherto we have spoken of a Demon­strative syllogism, whose matter is ne­cessary, and the end a perfect Knowledge; come we now to a Dialectical or Topical syl­logism, whose matter is Probable and Con­tingent, and the end Opinion.

2. In a Dialectical, or Topical Syllogism, we are to consider of Problems, Propositions, and Invention of Arguments.

3. A Problem or Question, is the thing of which it is probably discoursed, and the Conclusion of a syllogism already made.

4. Dialectical Propositions, ought to be certain, at least probable, and not Paradox­es; now that is said to be Probable, which not being absolutely true, doth seem to be true rather than false: And that is said to be a Paradox, which is true, though contra­ry to the vulgar opinion.

5. For the Invention of Arguments, we are to consider Common places and Rules.

6. A Place, is common Note, by whose help an Argument is found.

7. A Rule or Canon is a Proposition, con­taining [Page 199] the Reason of the Consequence, in a Dialectical syllogism.

8. Arguments are of two sorts, Artificial and Inartificial.

9. Artificial Arguments, are such as from the consideration of the parts of a Problem, are not found but by Rules of Art.

10. Inartificial Arguments, are such as are found without any help of Art, and these are nothing but Testimonies.

11. Artificial Arguments, may be raised from these seven Topicks or Heads. 1. From the Cause and the Effect. 2. From the sub­ject and the Accident. 3. From Dissentany and Comparison. 4. From Conjugates and Notation. 5. From the Whole and its Parts. 6. From Genus and Species. 7. From Defi­nition and Division.

12. A Cause in General, may be defined to be that, by whose power a thing is.

An Argument therefore from the Cause, is when in a probable syllogism, the middle term is the cause of the Major Extream.

13. There are two kinds of Causes; In­ternal as the material, or matter, of which a thing is made; and the Formal, by which a thing is; as, The shape and form of a statue.

External, as the Efficient, which doth bring the thing to pass; and the Final or End, for which a thing is done.

14. An Argument from the Efficient Cause, is when in a probable syllogism, the [Page 200] middle Term is the Efficient of the Major Ex­tream: as, The Earth is Diametricaly inter­posed between the Sun and the Moon, therefore the Moon shall be eclipsed.

15. An Argument from the Final Cause, is when in a probable syllogism, the middle Term is the Final Cause of the major Ex­tream.

16. An Argument from the material cause, is when in a probable syllogism, the middle Term is the material cause of the Major Ex­tream, or the Genus or Species thereof.

17. An Argument from the Formal Cause, is when in a Probable syllogism, the middle Term is the Form, Definition, Description, or Difference of the major Extream.

18. In the Topicks of the subject and the Accident, we do not take the subject for the substance, in which the Accident is inherent, or the Accident for that which doth precise­ly and adiquately adhere to the substance; but subject is here taken for all that, to which any thing not belonging to its essence is at­tributed: And Accident is here taken for a­ny such attribute, as, Number is the subject of Equality, that is, it is an Accident of an Accident.

19. An Argument from the subject, is as oft as the middle Term in a Probable syllo­gism, is the subject of the major Extream.

21. The third General Topick for the In­vention of Arguments, is from Dessentainies and Comparison.

[Page 201]22. Dessentanes, are either Opposites or Disparates; as, a Horse, and a Bull: There are four kinds of Opposites; Relative, Contra­ry, Privative, and Contradictory. Compari­sons are either in respect of quality; as, like and unlike, or in respect of quantity, or also of degrees; as, equal and unequal; and what ever may be said to be more or less or equal.

23. An Argument from Dissentanies, is when in a Probable Syllogism, the middle Term is opposed to the Major Extream, whether it be by way of a Disparate, or a Contrary, or otherwise.

24. An Argument from Comparison, is as oft as in a probable syllogism, one part of the Major Proposition is compared with the other, in reference to their agreement or their disagreement.

25. The fourth general Topick, for the Invention of Arguments, is from Conjugates and Notation. And they are properly cal­led Conjugates, which for the affinity of signification, have also an affinity in the Voice or Sound; as, Just, Justice, and Just­ly; some Conjugates are only Nominal, and some Real, and some both, and do compre­hend Denominatives under them, and are either substantives where one is a Noun sub­stantive abstracted from the Subject; as, Justice, Just; or Adjectives, where they be both Denominatives, or Concretes, which [Page 202] shew the form in the Abstract; as, Just, Justly. Notation or Etymology, is the Ex­plication of a Word by the Original there­of; as, a Consul, from Counselling the Com­mon-Wealth.

26. An Argument from Conjugates, is as oft as in a probable syllogism; the one the Conjugates in the major proposition, is the subject of the major Term; as, He that doth Justly is Just.

27. The first General Topick for the In­venting of Arguments, is from the whole and its parts. And an Argument from the thing divided to the divided members, is as oft as the thing divided is the middle Term, and the dividing Members the Major Ex­tream, in a Probable Syllogism. And an Argument from the dividing Members, to the thing divided, is as oft as the di­viding Members are the middle Term, and the thing divided the Major Extream.

28. The sixth General Topick, is from Genus and Species; And an Argument from Genus and Species, is when we prove that a thing doth not agree with the Genus, be­cause it doth not agree with the species; o [...] that it doth not agree with the species, be­cause it doth not agree with the genus.

29. The seventh General Topick for the Inventing of Arguments, is from Definition, and Division. We raise an Argument from the Topick or Definition, when we seek for [Page 203] the Definition of either Extream, that is, of the Subject or the Predicate in the question, which being found, is put into the place of the Mean, that it may be known whether the Extreams should be conjoyned or sepa­rated; thus we prove that Peter is a man, because he is a Rational living Creature. We argue from the Topick of Division, when we shew something to agree with the dividing Members, because it agrees with the thing divided, or not to agree with the thing di­vided, because it doth not agree with any of the Dividing Members.

30. Inartificial Arguments, are only such as are raised from Divine or Humane Te­stimony. And an Argument is raised from Testimony, as oft as the Authority of him that beareth witness, is the middle Term, a­greeing or not agreeing with the Major Ex­tream.

CHAP. VII. Of a Sophistical Syllogism.

A Sophistical Syllogysm, is a Captious Ar­gumentation, which is seemingly, or apparently true, but is indeed deceitful.

2. Sophistical, or Fallacious Arguing, is either in respect of the Words or of the Things.

3. Fallacies in Words, are five; Ambigui­tie, Amphibolie, Composition, Division, and Figure of a Word.

4. Fallacies in things are seven, Accident, Of a thing spoken after a sort, to a thing spoken Simply; Ignorance of the Argu­ment; a false or wrong Cause, Consequent, Beginning of the Question, and an asking of many Questions.

CHAP. VIII. Of Method.

MEthod is the disposing of things belong­ing to the same Matter or Subject, so, as that they may be best understood, and ea­siest remembred.

2. Method is two-fold, Natural or Arbitrary.

3. A Natural Method is that, in which the order of Nature and our distinct Know­ledge is observed.

4. In a Natural Method, we must speak first of Generals, and then of Particulars, and as we proceed from one thing to ano­ther, every part must have a dependence on that, which was last spoken of by some apt transition.

5. A Natural Method is either Total, or Partial.

6. A Total Method is that, in which a whole Science is Methodically ordered or dispersed. And this is either, Synthetical, or Analytical.

7. A Synthetical or Compositive Method is that, which begins with the first and most simple Principles, and so proceeds to those which do arise from, or are Composed of the first Principles.

8. An Analytical or Resolutive Method, is [Page 206] that, which begins with the end, and so pro­ceeds still lower and lower, till we come to the first and most Simple beginnings.

9. A Partial Method is that, by which a­ny part of any Art or Science is Methodi­cally ordered or disposed: or by which any particular Theme or Subject is handled by it self.

10. An Arbitrary Method is that, which not regarding the Natural order, is fitted for such a confused Knowledge, as may be most taking with the People, or sure best with their Capacities.

And thus much concerning Method, which is the fourth and last-Logical Instrument; and with this I shall conclude these my Lo­gical Precepts, and last Part of my English A­cademy: He that desires to be more fully ac­quainted with these Arts and Sciences, may for all, but Musick, Read my other particu­lar Tracts of these Subjects, till some body that hath more knowledge in them, shall fur­nish us with more ample and perfect Instru­ctions; and as for Musick, I am much of Opinion, that Mr. Playford's Introduction may very well serve, to Instruct our Youth in the first Principles of that excellent Science; For which, and all other helps of Learning, To the only Wise God, be all Honour and Glory, now and for ever. Amen.