SEVEN Philosophical Problems, AND TWO PROPOSITIONS OF GEOMETRY.

By Thomas Hobbes of Malmesbury.

With an Apology for Himself, and his WRITINGS.

Dedicated to the KING, in the year 1662.

LONDON: Printed for William Crook at the Green-Dragon without Temple-Bar, 1682.

TO THE KING.

THat which I do here most humbly present to Your Sacred Majesty, is the best Part of my Medi­tations upon the Natural Causes of Events, both of such as are commonly known, and of such as have been of late artificially exhi­bited by the Curious.

They are ranged under seven Heads. 1. Problems of Gravity. 2. Problems of Tides. 3. Problems of Vacuum. 4. Problems of Heat. 5. Problems of Hard and Soft. 6. Problems of Wind and Weather. 7. Problems of Motion Perpendicular, and Ob­lique, [Page] &c. To which I have added, Two Propositions of Geometry; One is, The Duplication of the Cube, hitherto sought in vain; The other, A Detection of the absurd Use of Arithmetick, as it is now applied to Geometry.

The Doctrine of Natural Causes hath not infallible and evident Principles. For there is no Effect which the Power of God cannot produce by many several ways.

But seeing all Effects are produced by Motion, he that supposing some one or more Motions can derive from them the necessity of that Effect whose Cause is re­quired, has done all that is to be expected from Natural Reason. And though he prove not that the thing was thus produ­ced, yet he proves that thus it may be pro­duced, when the Materials, and the power of Moving is in our hands; which is as useful as if the Causes themselves were known. And notwithstanding the absence [Page] of rigorous Demonstration, this Contem­plation of Nature (if not rendred obscure by empty terms) is the most Noble Im­ployment of the Mind that can be, to such as are at leisure from their necessary Bu­siness.

This that I have done I know is anun­worthy Present to be offered to a KING, though considered (as God considers Offe­rings) together with the Mind and For­tune of the Offerer, I hope will not be to Your Majesty unacceptable.

But that which I chiefly consider in it is, that my Writing should be tryed by Your Majesties Excellent Reason untain­ted with the Language that has been in­vented or made use of by Men when they were puzzled; and who is acquainted with all the Experiments of the time; and whose approbation (if I have the good Fortune to obtain it) will protect my reasoning from the Contempt of my Ad­versaries.

[Page] I will not break the custom of joyning to my Offering a Prayer; And it is, That Your Majesty will be pleased to pardon this following short Apo­logy for my Leviathan. Not that I rely upon Apologies, but upon Your Maje­sties most Gracious General Pardon.

That which is in it of Theology, con­trary to the general Current of Divines, is not put there as my Opinion, but pro­pounded with submission to those that have the Power Ecclesiastical.

I did never after, either in Writing or Discourse, maintain it.

There is nothing in it against Episco­pacy; I cannot therefore imagine what reason any Episcopal-man can have to speak of me (as I hear some of them do) as of an Atheist, or man of no Religion, unless it be for making the Authority of the Church wholly upon the Regal Power; which I hope Your Majesty will think is neither Atheism nor Heresie.

[Page] But what had I to do to meddle with matters of that nature, seeing Religion is not Philosophy, but Law?

It was written in a time when the pre­tence of Christ's Kingdom was made use of for the most horrid Actions that can be imagined; And it was in just Indignation of that, that I desired to see the bottom of that Doctrine of the Kingdom of Christ, which divers Ministers then Preached for a Pretence to their Rebellion; which may reasonably extenuate, though not ex­cuse the writing of it.

There is therefore no ground for so great a Calamny in my writing. There is no sign of it in my Life; and for my Re­ligion, when I was at the point of Death at St. Germains, the Bishop of Durham can bear witness of it, if he be asked. Therefore, I most humbly beseech Your Sacred Majesty not to believe so ill of me upon reports, that proceed often (and may do so now) from the displeasure which commonly ariseth from difference in Opi­nion; [Page] nor to think the worse of me, if snatching up all the Weapons to fight against Your Enemies, I lighted upon one that had a double edge.

Your Majesties Poor and most Loyal Subject, THOMAS▪ HOBBES.
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PHILOSOPHICAL PROBLEMS▪
CHAP. I. Problems of Gravity.

A.

WHat may be the cause, think you, that stones, and other bo­dies, thrown upward, or carried up and left to their liberty, fall down again (for ought a man can see) of their own accord? I do not think (with the old Philosophers) that they have any love to the Earth, or are sullen, that they will neither go nor stay. And yet I cannot imagine what body there is above that should drive them back.

B.

For my part, I believe the cause of their descending is not in any natural ap­petite of the bodies that descend, but rather that the Globe of the Earth hath some special motion, by the which it more easily casteth off the Air, than it doth other bo­dies. And then this descent of those we [Page 2] call heavy bodies, must of necessity follow; unless there be some empty spaces in the world to receive them. For when the Air is thrown off from the Earth, somewhat must come into the place of it, (in case the world be full) and it must be those things which are hardliest cast off, that is those things which we say are heavy.

A.

But suppose there be no place empty (for I will defer the Question till anon) how can the Earth cast off either the Air, or any thing else?

B.

I shall shew you how, and that by a familiar Example. If you lay both your hands upon a Basen with water in it, how little soever, and move it circularly, and continue that motion for a while, and you shall see the water rise upon the sides, and fly over; by which you may be assured that there is a kind of circulating motion, which would cast off such bodies as are contiguous to the body so moved.

A.

I know very well there is; and it is the same motion which Country people use to purge their Corn; For the Chaff and Straws, by casting the Grain to the side of the Seive, will come towards the middle. But I would see the Figure.

B.

Here it is. There is a Circle pricked out, whose Center is A, and three less Circles, whose Centers are B, C, D; let [Page 3] every one of them represent the Earth, as it goeth from B to C, and from C to D, always touching the uttermost Circle, and throwing off the Air, as is marked at E and F. And if the world were not full, there would follow by this scattering of the Air, a great deal of space left empty. But sup­posing the world full, there must be a per­petual shifting of the Air, one part into the place of another.

A.

But what makes a stone come down, suppose from G?

B.

If the Air be thrown up beyond G, it will follow, that at the last, if the moti­on be continued, all the Air will be above G, that is, above the stone; which cannot be, till the stone be at the Earth.

A.

But why comes it down still with en­creasing swiftness?

B.

Because as it descends, and is already in motion, it receiveth a new impression from the same cause, which is the Air, whereof as part mounteth, part also must descend, supposing as we have done the plenitude of the world. For, as you may observe by the Figure, the motion of the Earth, according to the Dia­meter of the uttermost Circle, is progres­sive; and so the whole motion is compoun­ded of two motions, one circular, and the other progressive; and consequently the [Page 4] Air ascends and circulates at once. And because the stone descending receiveth a new pressure in every point of its way, the motion thereof must needs be accelerated.

A.

'Tis true; For it will be accelerated equally in equal times; and the way it makes will encrease in a double proportion to the times, as hath heretofore been demonstra­ted by Galileo. I see the solution now of an Experiment, which before did not a little puzzle me. You know that if two plummets hang by two strings of equal length, and you remove them from the perpendicular equally, I mean in equal angles, and then let them go, they will make their turns and returns toge­ther, and in equal times; And though the arches they describe grow continually less and less, yet the times they spend in the greater arches, will still be equal to the time they spend in the lesser.

B.

'Tis true. Do you find any Experi­ment to the contrary?

A.

Yes; For if you remove one of the plum­mets from the perpendicular, so as (for ex­ample) to make an angle with the perpendi­cular of 80 degrees, and the other so as to make an angle of 60 degrees, they will not make their turns and returns in equal times.

B.

And what say you is the cause of this?

A.
[Page 5]

Because the arches are the spaces which these two motions describe, they must be in double proportion to their own times; which cannot be, unless they be let go from equal altitudes, that is, from equal angles.

B.

'Tis right; and the Experiment does not cross, but confirm the equality of the times in all the arches they describe, even from 90 degrees to the least part of one degree.

A.

But is it not too bold, if not extrava­gant, an assertion, to say the Earth is moved as a man shakes a Basen or a Seive? Does not the Earth move from West to East every day once, upon his own Center, and in the Ecliptick Circle once a year? And now you give it another odd motion; How can all these consist in one and the same body?

B.

Well enough. If you be a Shipboard under sail, do not you go with the Ship? Cannot you also walk upon the Deck? Cannot every drop of bloud move at the same time in your veins? How many mo­tions now do you assign to one and the same drop of bloud? Nor is it so extrava­gant a thing to attribute to the Earth this kind of motion; but that I believe if we certainly knew what motion it is that cau­seth the descent of bodies, we should find it either the same, or more extravagant. But seeing it can be nothing above that [Page 6] worketh this effect, it must be the Earth it self that does it; and if the Earth, then you can imagine no other motion to do it withal, but this; And you will wonder more, when by the same motion I shall give you a probable account of the causes of very many other works of Na­ture.

A.

But what part of the Heaven do you suppose the Poles of your pricked Circle point to?

B.

I suppose them to be the same with the Poles of the Ecliptick. For, seeing the Axis of the Earth in this Nation, and in the annual motion keeps parallel to it self, the Axis must in both motions be parallel as to sense. For, the Circle which the Earth describes, is not of visible magni­tude at the distance it is from the Sun.

A.

Though I understand well enough how the Earth may make a stone descend very swiftly under the Ecliptick, or not far from it, where it throws off the Air perpendicularly; yet about the Poles of the Circle methinks it should cast off the Air very weakly. I hope you will not say that bodies descend faster in places remote from the Poles, than nearer to them.

B.

No; but I ascribe it to the like mo­tion in the Sun and Moon. For such moti­ons meeting, must needs cast the stream [Page 7] of the Air towards the Poles; And then there will be the same necessity for the descent there, that there is in other places, though perhaps a little more slowly. For you may have observed that when it snows in the South Parts, the flakes of Snow are not so great as in the North; which is a probable sign they fall in the South from a greater height, and consequently disperse themselves more, as water does that falls down from a high and steep Rock.

A.

'Tis not improbable.

B.

In natural causes all you are to expect is but probability; which is better yet then making Gravity the cause, when the cause of Gravity is that you desire to know; and better then saying the Earth draws it, when the Question is, how it draws?

A.

Why does the Earth cast off Air more easily than it does Water, or any other heavy bodies?

B.

It is indeed the Earth that ca­steth off that Air which is next unto it. But it is that Air which casteth off the next Air; and so continually Air moveth Air; which it can more easily do then any other thing, because like bo­dies are more susceptible of one anothers motions; as you may see in two Lute­strings equally strained, what motion one [Page 8] string being stricken communicates to the Air, the same will the other receive from the Air; but strained to a differing note, will be less, or not at all moved. For there is no body but Air that hath not some in­ternal, though invisible motion of its parts. And it is that internal motion which di­stinguisheth all natural bodies one from another.

A.

What is the cause why certain Squibs, though their substance be either Wood or other heavy matter, made hollow and filled with Gunpowder, which is also heavy, do ne­vertheless when the Gunpowder is kindled, fly upwards?

B.

The same that keeps a man that swims from sinking, though he be heavier then so much water; He keeps himself up, and goes forward by beating back the water with his Feet; and so does a Squib, by beating down the Air with the stream of the fired Gunpowder, that proceeding from its Tail makes it recoil.

A.

Why does any Brass or Iron Vessel, if it be hollow, flote upon the water, being so very heavy?

B.

Because the Vessel and the Air in it, taken as one body, is more easily cast off than a body of water equal to it.

A.

How comes it to pass, that a Fish (especially such a broad Fish as a Turbut or [Page 9] a Plaice, which are broad and thin) in the bottom of the Sea, perhaps a mile deep, is not press'd to death with the weight of water that lies upon the back of it?

B.

Because all heavy bodies descend towards one point, which is the Center of the Earth, and consequently the whole Sea descending at once does arch it self so, as that the upper parts cannot press the parts next below them.

A.

It is evident; Nor can there be possi­bly any weight, as some suppose there is, of a Cylinder of Air, or Water, or of any other li­quid thing, while it remains in its own Ele­ment, or is sustained and inclosed in a Vessel, by which one part cannot press the other.

CHAP. II. Problems of Tides.

A.

WHat makes the Flux and Re­flux of the Sea twice in a natu­ral day?

B.

We must come again to our Basen of water; wherein you have seen, whilst it was moved, how the water mounteth up by the sides, and withal goes circling round about. Now if you should fasten to the inside of the Basen some bar from the bot­tom to the top, you would see the water, instead of going on, go back again from that bar, ebbing, and the water on the other side of the bar to do the same, but in counter-time; and consequently to be highest where the contrary streams meet together, and then return again, marking out four quarters of the Vessel, two by their meeting, which are the high waters, and two by their retiring, which are the low waters.

A.

What bar is that you find in the Ocean, that stops the current of the water, like that you make in the Basen?

B.

You know that the main Ocean lies East and West, between India and the [Page 11] Coast of America; and again, on the other side, between America and India. If there­fore the Earth have such a motion as I have supposed, it must needs carry the current of the Sea East and West; In which course, the bar that stoppeth it is the South part of America, which leaves no passage for the water, but the narrow Streight of Magellan. The Tide rises there­fore upon the Coast of America; And the rising of the same in this part of the world proceedeth from the swelling chiefly of the water there; and partly also from the North Sea, which lieth also East and West, and has a passage out of the South Sea by the Streight of Anian, between America and Asia.

A.

Does not the Mediterranean-Sea lie also East and West? why are there not the like Tides there?

B.

So there are, proportionable to their lengths, and quantity of water.

A.

At Genoa, at Ancona there are none at all, or not sensible.

B.

At Venice there are, and in the bot­tom of the Streights; and a current all along both the Mediterranean-Sea, and the Gulf of Venice; And it is the current that makes the Tides unsensible at the sides▪ but the check makes them visible at the bottom.

A.
[Page 12]

How comes it about that the Moon hath such a stroke in the business, as so sensibly to encrease the Tides at Full and Change?

B.

The motion I have hitherto supposed but in the Earth, I suppose also in the Moon, and in all those great Bodies that hang in the Air constantly, I mean the Stars, both fixed and errant. And for the Sun and Moon, I suppose the Poles of their motion to be the Poles of the Aequinoctial; which supposed, it will follow, (because the Sun, the Earth and the Moon at every Full and Change are almost in one streight line) that this motion of the Earth will be made swifter than in the Quarters. For this motion of the Sun and Moon being communicated to the Earth, that hath al­ready the like motion, maketh the same greater; and much greater when they are all three in one streight line, which is only at the Full and Change, whose Tides are therefore called Spring Tides.

A.

But what then is the cause that the Spring-Tides themselves are twice a year, namely when the Sun is in the Equinoctial, greater than at any other times?

B.

At other times of the year, the Earth being out of the Aequinoctial, the motion thereof, by which the Tides are made, will be less augmented, by so much as a motion in the obliquity of 23 degrees [Page 13] or thereabout (which is the distance be­tween the Aequinoctial and Ecliptick Cir­cles) is weaker then the motion which is without obliquity.

A.

All this is reasonable enough, if it be possible that such motions as you suppose in these bodies, be really there. But that is a thing I have some reason to doubt of; For, the throwing off of Air, consequent to these motions, is the cause, you say, that other things come to the Earth; And therefore the like motions in the Sun, and Moon, and Stars, casting off the Air, should also cause all other things to come to every one of them. From whence it will follow, that the Sun, Moon, and Earth, and all other bodies but Air, should presently come together into one heap.

B.

That does not follow: For if two bodies cast off the Air, the motion of that Air will be repress'd both ways, and diver­ted into a course towards the Poles on both sides; and then the two bodies can­not possibly come together.

A.

'Tis true. And besides, this driving off the Air on both sides, North and South, makes the like motion of Air there also. And this may answer to the Question, How a stone could fall to the Earth under the Poles of the Ecliptick, by the only casting off of Air?

B.
[Page 14]

It follows from hence, that there is a certain and determinate distance of one of these bodies (the Stars) from another, without any very sensible variation.

A.

All this is probable enough, if it be true that there is no Vacuum, no place empty in all the World. And supposing this motion of the Sun and Moon to be in the plain of the Aequinoctial, methinks that this should be the cause of the Diurnal motion of the Earth; And because this motion of the Earth is (you say) in the plain of the Aequinoctial, the same should cause also a motion in the Moon on her own Center, answerable to the Diurnal motion of the Earth.

B.

Why not? what else can you think makes the Diurnal motion of the Earth, but the Sun? And for the Moon, if it did not turn upon its own Center, we should see sometimes one, sometimes another face of the Moon, which we do not.

CHAP. III. Problems of Vacuum.

WHat convincing Argument is there to prove, that in all the world there is no empty place?

B.

Many; but I will name but one; and that is, the difficulty of separating two bodies hard and flat laid one upon another; I say, the difficulty, not the impossibility. It is possible, without introducing Vacu­um, to pull assunder any two bodies, how hard and flat soever they be, if the force used be greater than the resistance of the hardness. And in case there be any greater difficulty to part them, (besides what proceeds from their hardness) then there is to pull them further assunder when they are parted, that difficulty is Argument enough to prove there is no Vacuum.

A.

These Assertions need demonstration. And first, how does the difficulty of separa­tion argue the Plenitude of all the rest of the world?

B.

If two flat polish'd Marbles lie one upon another, you see they are hardly se­parated in all points at one and the same instant; and yet the weight of either of [Page 16] them it is enough to make them slide off one from the other. Is not the cause of this, that the Air succeeds the Marble that so slides, and fills up the place it leaves.

A.

Yes certainly. What then?

B.

But when you pull the whole Superficies assunder, not without great difficulty, what is the cause of that dif­ficulty?

A.

I think as most men do, that the Air cannot fill up the space between in an instant; For the parting is in an instant.

B.

Suppose there be Vacuum in that Air into which the Marble you pull off is to succeed, shall there be no Vacuum in the Air that was round about the two Marbles when they touched? Why cannot that Vacuum come into the place between? Air cannot succeed in an instant, because a body; and consequently cannot be mo­ved through the least space in an instant. But emptiness is not a body, nor is moved, but made by the act it self of separation. There is therefore (if you admit Vacuum) no necessity at all for the Air to fill the space left, in an instant. And therefore, with what ease the Marble coming off presseth out the Vacuum of the Air behind it, with the same ease will the Marbles be pulled assunder. Seeing then, if there were [Page 17] Vacuum, there would be no difficulty of Separation; it follows, because there is difficulty of separation, that there is no Vacuum.

A.

Well now, supposing the world full, how do you prove it possible to pull those Marbles assunder?

B.

Take a piece of soft wax; Do not you think the one half touches the other half as close as the smoothest Marbles? yet you can pull them assunder. But how? still as you pull, the wax grows continu­ally more and more slender; there being a perpetual parting or discession of the ou­termost part of the wax one from another; which the Air presently fills, and so there is a continual lessening of the wax, till it be no bigger than a hair, and at last sepa­ration. If you can do the same to a Pillar of Marble, till the outside give way, the effect will be the same, but much quicker, after it once begins to break in the Super­ficies; because the force that can master the first resistance of the hardness, will quickly dispatch the rest.

A.

It seems so by the brittleness of some hard bodies. But I shall afterward put some Questions to you, touching the nature of hard­ness. But now to return to our subject,

What reason can you render (without sup­posing Vacuum) of the effects produced in [Page 18] the Engine they use at Gresham Colledge?

B.

That Engine produceth the same effects, that a strong wind would pro­duce in a narrow room.

A.

How comes the wind in? You know the Engine is a hollow round pipe of brass; into which is thrust a Cylinder of wood co­vered with Leather, and fitted to the Cy­linder so exactly as no Air can possibly pass between the leather and the brass?

B.

I know it; and that they may thrust it up, there is a hole left in the Cylinder to let the Air out before it; which they can stop when they please. There is also in the bottom of the Cy­linder a passage into a hollow Globe of Glass; which passage they can also open and shut at pleasure. And at the top of that Globe there is a wide mouth to put in what they please to try conclusions on; and that also to be opened and shut as shall be needful. 'Tis of the nature of a Pop-gun which Children use, but great, costly, and more ingenious. They thrust forward, and pull back the wooden Cy­linder (because it requires much strength) with an Iron screw. What is there in all this to prove the possibility of Vacuum.

A.

Whan this wooden Cylinder covered with leather, fit and close is thrust home to the bottom, and the holes in the hollow Cy­linder [Page 19] of Brass close stopped, how can it be drawn back, as with the screw they draw it, but that the space it leaves must needs be empty. For it is impossible that any Air can pass into the place to fill it?

B.

Truly I think it close enough to keep out Straw and Feathers, but not to keep out Air, nor yet matter. For suppose they were not so exactly close but that there were round about a dis­tance for a small hair to lye between, Then will the pulling back of the Cylin­der of wood force so much Air in, as in retiring it forces back, and that without any sensible difficulty. And the Air will so much more swiftly enter as the passage is left more narrow. Or if they touch, and the contract be in some points, and not in all, the Air will enter as before in case the force be augmented accordingly. Lastly, though they touch exactly, if either the Leather yield, or the Brass (which it may do to the force of a strong screw) the Air will again enter. Do you think it possible to make two superficies so exquisitly touch in all points as you sup­pose, or Leather so hard as not to yield to the force of a screw? The Body of Leather will give passage both to Air and Water, as you will confess when you ride in Rainy and Windy weather. You [Page 20] may therefore be assured that in drawing out their wooden-leather Cylinder they force in as much Air as will fill the place it leaves, and that with as much swiftness as is answerable to the strength that drives it in. The effect therefore of their pump­ing is nothing else but a vehement Wind, a very vehement Wind coming in on all sides of the Cylinder at once into the hollow of the Brass Pipe, and into the hollow of the Glass Globe joyned to it.

A.

I see the reason already of one of their wonders, which is, that the Cylinder they pump with, if it be left to it self, af­ter it is pulled back will swiftly go up again. You will say the Air comes out again with the same violence by reflection; and I be­lieve it?

B.

This is argument enough that the place was not empty. For what can fetch or drive up the Sucker, as they call it, if the place within were empty; for that there is any weight in the Air to do it, I have already demonstrated to be im­possible.

Besides, you know, when they have sucked out (as they think) all the Air from the Glass Globe, they can neverthe­less both see through it what is done, and hear a sound from within when there is any made. Which (if there were no [Page 21] other, but there are many other,) is ar­gument enough that the place is still full of Air.

A.

What say you to the swelling of a Bladder even to bursting, if it be a little blown when it is put into the Receiver, (for so they call the Globe of Glass?)

B.

The stream of Air that from eve­ry side meeting together, and turning in an infinite number of small points, do pierce the Bladder in innumerable places with great violence at once, like so ma­ny invisible small wimbles; especially if the Bladder be a little blown before it be put in, that it may make a little resist­ance. And when the Air has once pierced it, it is easie to conceive, that it must af­terward by the same violent motion be extended till it break. If before it break you let in fresh Air upon it, the violence of the motion will thereby be tempered, and the Bladder be less extended. For that also they have observed. Can you imagine how a Bladder should be exten­ded, and broken, by being too full of Emptiness.

A.

How come living creatures to be killed in this Receiver, in so little a time as 3 or 4 minutes of an hour?

B.

If they suck into their lungs so vi­olent a wind thus made, you must needs [Page 22] think it will presently stop the passage of their bloud; and that is death; though they may recover if taken out before they be too cold. And so likewise will it put out fire; but the Coals taken out whilst they are hot, will revive again. 'Tis an ordinary thing in many Coal-pits, (whereof I have seen the experience,) that a wind proceeding from the sides of the Pit every way, will extinguish any fire let down into it, and kill the work­men, unless they be quickly taken out.

A.

If you put a vessel of water into the Receiver, and then suck out the Air, the water will boil. What say you to that?

B.

It is like enough it will dance in so great a bustling of the Air; but I never heard it would be hot. Nor can I imagine how Vacuum should make any thing dance. I hope you are by this time satis­fied, that no experiment made with the Engine at Gresham Colledge, is sufficient to prove that there is, or that there may be Vacuum.

A.

The World you know is finite, and consequently, all that infinite space with­out it, is empty. Why may not some of that Vacuum be brought in, and mingled with the Air here?

B.

I know nothing in matters without the World.

A.
[Page 23]

What say you to Torricellioes Ex­periment in Quick-silver, which is this. There is a Bason at A filled with Quick-sil­ver, suppose to B, And CD a hollow glass pipe filled with the same. Which if you stop with your finger at B, and so set it upright, and then if you take away your finger, the Quick-silver will fall from C downwards, but not to the bottom. For it will stop by the way, suppose at D. Is it not therefore ne­cessary that that space between C and D be left empty? Or will you say the Quick sil­ver does not exactly touch the sides of the glass pipe?

B.

I'le say neither. If a man thrust down into a vessel of Quick-silver a blown Bladder, will not that Bladder come up to the top?

A.

Yes certanly, or a Bladder of Iron, or of any thing else but Gold.

B.

You see then that Air can pierce Quick-silver.

A.

Yes, with so much force as the weight of Quick-silver comes to.

B.

When the Quick-silver is fallen to D, there is so much the more in the ba­son. And that takes up the place which so much Air took up before. Whither can this Air go if all the World without that glass pipe B C were full? There must needs be the same or as much Air come [Page 24] to that space (which only is empty) be­tween C and D. By what force? By the weight of the Quick-silver between D and B. Which Quick-silver weigheth now upward; or else it could never have raised that part higher, which was at first in the Bason. So you see the weight of Quick-silver can press the Air through Quick-silver up into the pipe, till it come to an equality of force as in D. Where the weight of the Quick-silver is equal to the force which is required in Air to go through it.

A.

If a man suck a Vial that has no­thing in it but Air, and presently dip the mouth of it into water, the water will as­cend into the Vial. Is not that an argument that part of the Air had been sucked out, and part of the room within the Vial left empty?

B.

No. If there were empty space in the World, why should not there be also some empty space in the Vial before it was sucked? And then why does not the water rise to fill that, when a man sucks the Vial he draws nothing out neither in­to his Belly not into his Lungs, nor into his Mouth; only he sets the Air within the glass into a circular motion, giving it at once an endeavour to go forth by the sucking, and an endeavour to go back [Page 25] by not receiving it into his mouth. And so with a great deal of labour glues his lips to the neck of the Vial. Then taking it off, and dipping the neck of the Vial into the water before the circulation cease, the Air with the endeavour it hath now gotten, pierces the water and goes out. And so much Air as goes out, so much matter comes up into the room of it.

CHAP. IIII. Problems of Heat and Light.

A.

WHat is the cause of Heat?

B.

How know you, that any thing is Hot but your self?

A.

Because I perceive by sense it Heats me.

B.

It is no good argument, The thing Heats me; therefore it is Hot. But what alteration do you find in your body at any time by being Hot?

A.

I find my skin more extended in Summer than in Winter; and am some­times fainter and weaker then ordinary, as if my Spirits were exhaled; and I sweat.

B.

Then that is it you would know the cause of. I have told you before that [Page 26] by the motion I suppose both in the Sun, and in the Earth, the Air is dissipated, and consequently that there would be an infinite number of small empty places but that the World being full, there comes from the next parts other Air into the spaces, they would else make empty. When therefore this motion of the Sun is excercised upon the Superficies of the Earth, if there do not come out of the Earth it self some corporal substance to supply that tearing of the Air, we must return again to the admission of Vacuum. If there do, then you see how by this motion fluid bodies are made to exhale out of the Earth. The like happens to a mans body or hand, which when he perceives, he says he is Hot. And so of the Earth when it sendeth forth Water and Earth together in Plants, we say it does it by Heat from the Sun.

A.

'Tis very probable, and no less pro­bable, that the same action of the Sun, is that which from the Sea and moist places of the Earth, but especially from the Sea fetcheth up the water into the Clouds. But there be many ways of Heating besides the action of the Sun or of Fire. Two pieces of Wood will take Fire if in Torning they be prest together.

B.

Here again you have a manifest la­ceration [Page 27] of the Air by the reciprocal and contrary motions of the two pieces of wood, which necessarily causeth a com­ing forth of whatsoever is Aereal or fluid within them, and (the motion pursued) a dissipation also of the other more solid parts into Ashes.

A.

How comes it to pass that a man is warmed even to sweating almost with every extraordinary labour of his body?

B.

It is easie to understand, how by that labour all that is liquid in his body is tossed up and down, and thereby part of it also cast forth.

A.

There be some things that make a man Hot without sweat or other evaporation, as Caustiques, Nettles and other things.

B.

No doubt. But they touch the part they so Heat, and cannot work that effect at any distance.

A.

How does Heat cause light, and that partially in some bodies more, in some less, though the Heat be equal?

B.

Heat does not cause Light at all. But in many Bodies, the same cause, that is to say, the same motion causeth both together; so that they are not to one a­nother as cause and effect, but are con­comitant Effects, sometimes of one and the same motion.

A.

How?

B.
[Page 28]

You know the rubbing or heard pressing of the Eye, or a stroke upon it makes an apparition of Light without and before it, which way soever you look. This can proceed from nothing else but from the restitution of the Organ pressed or stricken, unto its former ordi­nary situation of parts. Does not the Sun by his thrusting back the Air upon you eyes press them? Or does not those bo­dies whereon the Sun shines (though by reflection) do the same, though not so strongly? And do not the Organs of Sight, the Eye, the Heart, and Brains resist that pressure by an endeavour of restitution outwards? Why then should there not be without and before the Eye, an apparition of Light in this case as well as in the other?

A.

I grant there must. But what is that which appears after the pressing of the eye? For there is nothing without, that was not there before; or if there were, methinks another should see it better, or as well as he; or if in the dark, methinks it should en­lighten the place.

B.

It is a fancy, such as is the appear­ance of your face in a Looking-glass; such as is a Dream; such as is a Ghost; such as is a spot before the Eye that hath stared upon the Son or Fire. For all these [Page 29] are of the Regiment of Fancy, without any body concealed under them, or be­hind them, by which they are pro­duced.

A.

And when you look towards the Sun or Moon, why is not that also which ap­pears before your Eyes at that time a fancy?

B.

So it is. Though the Sun it self be a real Body, yet that bright Circle of a­bout a foot Diameter cannot be the Sun, unless there be two Suns, a greater and a lesser. And because you may see that which you call the Sun, both above you in the Skie, and before you in the Water, and two Suns (by distorting your Eye) in two places of the Skie, one of them must needs be Fancy. And if one, both. All sense is Fancy though the cause be al­ways in a real Body.

A.

I see by this that those things which the Learned call the Accidents of Bodies, are indeed nothing else but diversity of Fancy; and are inherent in the Sentient, and not in the Objects, except Motion and Quan­tity. And I perceive by your Doctrine you have been tampering with Leviathan. But how comes Wood with a certain degree of Heat to shine, and Iron also with a greater degree; but no Heat at all to be able to make water shine?

B.

That which shineth hath the same [Page 30] Motion in its parts that I have all this while supposed in the Sun and Earth. In which Motion there must needs be a competent degree of swiftness, to move the sense, that is, to make it visible. All Bodies that are not fluid will shine with Heat, if the Heat be very great. Iron will shine and Gold will shine; but wa­ter will not, because the parts are carried away before they attain to that degree of swiftness; which is requisite.

A.

There are many fluid Bodies, whose parts evaporate, and yet they make a flame, as Oyl, and Wine, and other strong drinks:

B.

As for Oyl I never saw any infla­med by it self; how much soever Heated, therefore I do not think they are the parts of the Oyl, but of the combustible bo­dy oyled that shine, but the parts of Wine and strong Drinks have partly a strong Motion of themselves, and may be made to shine, but not with boiling, but by adding to them as they rise the flame of some other body.

A.

How can it be known that the par­ticles of Wine have such a Motion as you suppose?

B.

Have you ever been so much dis­tempered with drinking Wine, as to think the Windows and Table move?

A.

I confess (though you be not my Con­fessor,) [Page 31] I have, but very seldom, and I remember the window seemed to go and come in a kind of circling Motion, such as you have described. But what of that?

B.

Nothing, but that it was the Wine that caused it; which having a good de­gree of that Motion before, did when it was Heated in the Veins, give that con­cussion (which you thought was in the window,) to the Veins themselves, and (by the continuation of the parts of mans Body) to the Brain; and that was it which made the window seem to move.

A.

What is Flame? For I have often thought the Flame that comes out of a small heap of Straw, to be more (before it hath done Flaming,) then a hundred times the Straw it self.

B.

It was but your Fancy. If you take a stick in your hand by one end, the other end burning, and move it swiftly, the burning end, if the Motion be circu­lar, shall seem a circle; if streight, a streight line of Fire, longer or shorter, according to the swiftness of the Motion, or to the space it moves in. You know the cause of that.

A.

I think it is, because the impression of that visible Object, which was made at the first instant of the Motion did last till it was ended. For then it will follow that it [Page 32] must be visible all the way, the impressions in all points of the time being equal.

B.

The cause can be no other. The smallest spark of Fire flying up seems a line drawn upward; and again by that swift circular Motion which we have supposed for the cause of Light, seems also broader then it is. And consequently the Flame of every thing must needs seem much greater then it is.

A.

What are those sparks that flie out of the Fire?

B.

They are small pieces of the wood or Coals, or other Fuel loosened and car­ried away with the Air that cometh up with them. And being extiguished be­fore their parts be quite dissipated into others, are so much Soot, and black, and may be fired again.

A.

A Spark of Fire may be stricken out of a cold stone. It is not therefore Heat that makes this shining.

B.

No 'Tis the Motion that makes both the Heat and shining; and the stroke makes the Motion. For every of those Sparks, is a little parcel of the stone, which swiftly moved, imprinteth the same Motion into the matter prepared, or [...] receive it.

A.

How comes the Light of the Sun to burn almost any combustible matter by re­refraction [Page 33] through a convex glass, and by re­flection from a concave?

B.

The Air moved by the Sun presseth the convex glass in such manner as the action continued through it, proceedeth not in the same streight line by which it proceeded from the Sun, but tendeth more toward the center of the body it enters. Also when the action is con­tinued through the convex body it bend­eth again the same way. By which means the whole action of the Sun-beams are enclosed within a very small compass; in which place therefore there must be a very vehement Motion; and conse­quently if there be in that place com­bustible matter, such as is not very hard kindle, the parts of it will be dissipated, and receive that Motion which worketh on the Eye as other Fire does.

The same reason is to be given for burning by Reflection. For there also the Beams are collected into almost a point.

A.

Why may not the Sun-beams be such a Body as we call Fire, and pass through the pores of the glass so disposed as to ca­ry them to a point, or very near?

B.

Can there be a glass that is all pores; If there cannot, then cannot this effect be produced by the passing of Fire through the pores. You have seen men [Page 34] llght their Tobacco at the Sun with a burning glass, or with a ball of Cristal, held which way they will indifferently. Which must be impossible, unless the ball were all pores. Again, neither you nor I can conceive any other Fire then we have seen, nor then such as water will put out. But not only a solid Globe of Glass or Cristal will serve for a burning Glass, but also a hollow one filled with water. How then does the Fire from the Sun pass through the glass of water with­out being put out before it come to the matter they would have it burn?

A.

I know not. There comes nothing from the Sun. If there did, there is come so much from it already, that at this day we had had no Sun,

CHAP. V. Problems of Hard and Soft.

A.

WHat call you Hard, and what Soft.

B.

That body whereof no one part is easily put out of its place, without removing the whole, is that which I and all men call Hard; and the contrary Soft. So that they, are but degrees one of another.

A.

What is the cause that makes one bo­dy Harder then another, or (seeing you say they are but degrees of one another) what makes one body Softer then another, and the same body sometimes Harder, sometimes Softer?

B.

The same Motion which we have supposed from the beginning for the cause of so many other effects. Which Motion not being upon the center of the part moved, but the part it self going in a­nother circle to and again, it is not neces­sary that the Motion be perfectly circular. For it is not circulation, but the recipro­cation, I mean the to and again that does cast off, and lacerrate the Air, and con­sequently produce the fore-mentioned effects.

[Page 93] For the cause therefore of Hardness, I suppose the reciprocation of Motion in those things which are Hard, to be very swift, and in very small circles.

A.

This is somewhat hard to believe. I would you could supply it with some visible experience.

B.

When you see (for example) a Cross-bow bent, do you think the parts of it stir?

A.

No. I am sure they do not.

B.

How are you sure? You have no argument for it, but that you do not see the Motion. When I see you sitting still, must I believe there is no Motion in your parts within, when there are so many ar­guments to convince me there is.

A.

What argument have you to convince me that there is Motion in a Cross-bow when it stands bent?

B.

If you cut the string, or any way set the Bow at liberty it will have then a very visible Motion. What can be the cause of that?

A.

Why the setting of the Bow at liberty.

B.

If the Bow had been crooked be­fore it was bent, and a string tied to both ends, and then cut asunder, the Bow would not have stir'd. Where lies the difference?

A.

The Bow bent has a Spring; unbent it has none, how crooked soever.

B.
[Page 37]

What mean you by Spring?

A.

An endeavour of restitution to it's former posture.

B.

I understand Spring as well as I do endeavour.

A.

I mean a Prnciple or beginning of Motion in a contrary way to that of the force which bent it.

B.

But the beginning of Motion is al­so Motion, how insensible soever it be. And you know that nothing can give a beginning of Motion to it self. What is it therefore that gives the Bow (which you say you are sure was at rest when it stood bent) its first endeavour to return to its former posture?

A.

It was he that bent it.

B.

That cannot be. For he gave it an endeavour to come forward, and the Bow endeavours to go backward.

A.

Well, grant that endeavour be Mo­tiou, and Motion in the Bow unbent, how do you derive from thence, that being set at liberty it must return to its former posture?

B.

Thus There being within the Bow a swift (though invisible) Motion of all the parts, and consequently of the whole; the bending causeth that Motion, which was along the Bow (that was beaten out when it was hot into that length) to o­perate [Page 38] a cross the length in every part of it, and the more by how much it is more bent; and consequently endeavours to unbend it all the while it stands bent. And therefore when the force which kept it bent is removed, it must of necessity re­turn to the posture it had before.

A.

But has that endeavour no effect at all before the impediment be removed? For if endeavour be Motion, and every Motion have some effect more or less, methinks this endavour should in time produce some­thing.

B.

So it does. For in time (in a long time) the course of this internal Motion will lie along the Bow, not according to the former, but to the new acquired posture. And then it will be as uneasie to return it to its former posture, as it was before to bend it.

A.

That's true. For Bows long bent lose their appetite to restitution, long custom be­coming nature. But from this internal re­ciprocation of the parts, how do you infer the Hardness of the whole Body.

B.

If you apply force to any single part of such a body, you must needs disorder the Motion of the next parts to it before it yield, and there disordered, the Motion of the next again must also be disordered; and consequently no one part can yield [Page 39] without force sufficient to disorder all. But then the whole body must also yield. Now when a body is of such a nature as no single part can be removed without removing the whole, men say that body is Hard.

A.

Why does the Fire melt divers Hard bodies, and yet not all?

B.

The hardest bodies are those wherein the Motion of the parts are the most swift, and yet in the least circles.

Wherefore if the Fire, the Motion of whose parts are swift, and in greater cir­ciles, he made so swit, as to be strong enough to master the Motion of the parts of the Hard body, it will make those parts to move in a greater compass, and there­by weaken their resistance, that is to say, Soften them, which is a degree of liquefaction. And when the Moton is so weakened, as that the parts lose their co­herence by the force of their own weight, then we count the body melted.

A.

Why are the Hardest things the most brittle, insomuch that what force soever is enough to bend them, is enough also to break them?

B.

In bending a Hard body, as (for example) a Rod of Iron, you do not inlarge the space of the internal Motion of the parts of Iron, as the Fire does; [Page 40] but you master and interrupt the Motion, and that chiefly in one place. In which place the Motion that makes the Iron Hard being once overcome, the prosecu­tion of that bending must needs suddenly master the Motions of the parts next unto it, being almost mastered before.

A.

I have seen a small piece of glass, the figure whereof is this A A B C. Which piece of glass if you bend toward to top, as in C, the whole body will shatter asunder into a Million of pieces, and be like to so much dust. I would fain see you give a pro­bable reason of that.

B.

I have seen the Experiment. The making of the glass, is thus, They dip an Iron Rod into the molten glass that stands in a Vessel within the Furnace. Upon which Iron Rod taken out, there will hang a drop of molten but tough Mettal of the figure you have described, which they let fall into the water. So that the main drop comes first to the water, and after it the tail, which though streight whilst it hung on the end of the Rod, yet by falling into the water becomes croo­ked. Now you know the making of it, you may consider what must be the conse­quence of it. Because the main drop A comes first to the water, it is therefore first quenched, and consequently that the Mo­tion [Page 41] of the parts of that drop, which by the Fire were made to be moved in a lar­ger compass, is by the water made to shrink into lesser circles towards the o­ther end B, but with the same or not much less swiftness.

A.

Why so?

B.

If you take any long piece of Iron, Glass, or other uniform and continued body; and having Heated one end there­of, you hold the other end in your hand, and so quench it suddenly, though be­fore, you held it easily enough, yet now it will burn your fingers.

A.

It will so.

B.

You see then how the Motion of the parts from A toward C is made more violent and in less compass by quenching the other parts first. Besides, the whole Motion that was in all the parts of the main drop A, is now united in the small end B C. And this I take to be the cause why that small part B C is so exceeding stiff. Seeing also this Motion in every small part of the glass, is not only circular, but proceeds also all along the glass from A to B, the whole Motion compounded will be such as the Motion of Spinning any Soft matter unto Thread, and will dispose the whole body of the glass in Threads, which in other Hard bodies are called the grain.

[Page 42] Therefore if you bend this body (for example) in C (which to do will require more force then a man would think that has not tryed) those threads of Glass must needs be all bent at the same time, and stand so, till by the breaking of the Glass at C, they be all at once set at li­berty. And then all at once being sud­denly unbent, like so many brittle, and over-bent Bows, their Strings breaking, be shivered in pieces.

A.

'Tis like enough to be so. And if nature have betrayed her self in any thing, I think it is in this, and in that other ex­perience of the Cross-bow; which strongly and evidently demonstrates the internal reciprocation of the Motion, which you sup­pose to be in the internal parts of every Hard body. And I have observed somewhat in Looking-glasses which much confirms that there is some such Motion in the internal parts of Glass, as you have supposed for the cause of Hardness. For let the Glass be A B, and let the Object at C be a Candle, and the Eye at D. Now by divers Refle­ctions and Refractions in the two superficies of the Glass, if the Lines of Vision be ve­ry oblique, you shall see many images of the Candle, as E, F, G, in such order and position as is here described. But if you re­move your Eye to C, and the Candle to D, [Page 43] they will appear in a situation manifestly different from this. Which you will yet more plainly perceive if the Looking-Glass be coloured, as I have obseved in Red and Blew Glasses; and could never conceive any probable cause of it, till now you tell me of this secret Motion of the parts a­cross the grain of the Glass, acquired by cooling it this or that way.

B.

There be very many kinds of Hard bodies, Metals, Stones, and other kinds in the bowels of the Earth, that have been there ever sence the beginning of the World; and I believe also many dif­ferent sorts of Juices that may be made Hard. But for one general cause of Hard­ness it can be no other then such an in­ternal Motion of parts as I have already described, whatsoever may be the cause of the several concomitant qualities of their Hardness in particular.

A.

We see water Hardened every Frosty day. It's likely therefore you may give a pribable cause of Ice. What is the cause of Freezing of the Ocean towards the Poles of the Earth?

B.

You know the Sun being always between the Tropicks, and (as we have supposed) always casting off the Air; and the Earth likewise casting it off from it's self, there must needs on both [Page 44] sides be a great Stream of Air towards the Poles, shaving the superficies of the Earth and Sea, in the Northern and Sou­thern Climates. This shaving of the Earth and Sea by the Stream of Air must needs contract and make to shrink those little Circles of the internal parts of Earth and Water, and consequently Harden them, first at the superficies, into a thin skin, which is the first Ice; and after­wards the same Motion continuing, and the first Ice co-operating, the Ice be­comes thicker. And this I conceive to be the cause of the Freezing of the Ocean.

A.

If that be the cause, I need not ask how a Bottle of water is made to Freeze in warm weather with Snow, or Ice mingled with Salt. For when the Bottle is in the midst of it, the Wind that goeth out both of the Salt and of the Ice as they dissolve, must needs shave the superficies of the Bottle, and the Bottle work accordingly on the water without it, and so give it first a thin skin, and at last thicken it into a so­lid piece of Ice. But how comes it to pass that water does not use to Freeze in a deep Pit?

B.

A deep Pit is a very thick Bottle, and such as the Air cannot come at but only at the top, or where the Earth is very loose and spungy.

A.
[Page 45]

Why will not Wine Freeze as well as Water?

B.

So it will when the Frost is great enough. But the internal Motion of the parts of Wine and other Heating Li­quors is in greater Circles and stronger then the Motion of the parts of water; and therefore less easily to be Frozen, e­specally quite through, because those parts that have the strongest Motion retire to the center of the Vessel.

CHAP. VI. Problems of Rain, Wind, and other WEATHER.

A.

WHat is the original cause of Rain? and how is it gene­rated?

B.

The motion of the Air (such as I have described to you already) tending to the dis-union of the parts of the Air, must needs cause a continual endeavour (there being no possibility of Vacuum) of whatsoever fluid parts there are upon the face of the Earth and Sea, to supply the place which would else be empty.

This makes the water, and also very small and loose parts of the Earth and Sea [Page 46] to rise, and mingle themselves with the Air, and to become mist and Clouds. Of which the greatest quantity arise there, where there is most water, namely, from the large parts of the Ocean; which are the South Sea, the Indian Sea, and the Sea that divideth Europe and Africa from America; over which the Sun, for the greatest part of the year is perpendicular, and consequently raiseth a greater quan­tity of water. Which afterwards gathe­red into Clouds, falls down in Rain.

A.

If the Sun can thus draw up the wa­ter; though but in small drops, why can it not as easily hold it up?

B.

It is likely it would also hold them up, if they did not grow greater by meeting together, nor were carried away by the Air towards the Poles.

A.

What makes them gather together?

B.

It is not improbable that they are carried against Hills, and there stopt till more overtake them. And when they are carried towards the North or South where the force of the Sun is more obli­que and thereby weaker, they descend gently by their own weight. And be­cause they tend all to the center of the Earth, they must needs be united in their way for want of room, and so grow big­ger. And then it Rains.

A.
[Page 47]

What is the reason it Rains so seldom, but Snows so often upon very high Moun­tains?

B.

Because perhaps when the water is drawn up higher then the highest Mountains, where the course of the Air between the Aequator and the Poles is free from stopping, the Stream of the Air Freezeth it into Snow. And 'tis in those places only where the Hills shelter it from that Stream, that it falls in Rain.

A.

Why is there so little Rain in Egypt, and yet so much in other parts nearer the Aequinoctial, as to make the Nile over­flow the Countrey?

B.

The cause of the falling of Rain, I told you was the the stopping, and con­sequently the collection of Clouds about great Mountains, especially when the Sun is near the Aequinoctial, and there­by draws up the water more potently, and from greater Seas. If you consider therefore that the Mountains in which are the springs of Nile, lye near the Aequinoctial and are exceeding great, and near the Indian Sea, you will not think it strange there should be great store of Snow. This as it melts makes the Rain of Nile to rise, which in April and May going on toward Egypt arri­ved there about the time of the Solstice, and overflow the Countrey.

A.
[Page 48]

Why should not the Nile then over­flow that Countrey twice a year? For it comes twice a year to the Aequinoctial.

B.

From the Autumnal Aequinox, the Sun goeth on toward the Southern Tro­pique. And therefore cannot dissolve, the Snow on that side of the Hills that look towards Egypt.

A.

But then there ought to be such ano­ther Innundation Southward.

B.

No doubt but there is a greater descent of water there in their Summer then at other times; as there must be wheresoever there is much Snow melted. But what should that innundate, unless it should overflow the Sea that comes close to the foot of those Mountains? And for the cause why it seldom Rains in Egypt, it may be this, That there are no very high Hills near it to collect the Clouds. The Mountains whence Nile riseth being near 2000 Miles off. The nearest on one side are the Mountains of Nubia, and on the other side Sina, and the Mountains of Arrabia.

A.

Whence think you proceed the Winds?

B.

From the Motion (I think) espe­cially of the Clouds, partly also from whatsoever is moved in the Air.

A.

It is manifest, that the Clouds are [Page 49] moved by the Winds; so that there were Winds before any clouds could be moved. Therefore I think you make the Effect before the Cause.

B.

If nothing could move a Cloud but Wind, your objection were good. But you allow a Cloud to descend by it's own weight. But when it so descends, it must needs move the Air before it, even to the Earth, and the Earth again repel it, and so make lateral Winds every way. Which will carry forwards other Clouds if there be any in their way, but not the Cloud that made them The Vapour of the water rising into Clouds, must needs also as they rise, raise a Wind?

A.

I grant it. But how can the slow motion of a Cloud make so swift a Wind as it does?

B.

It is not one or two little Clouds, but many and great ones that do it. Be­sides, when the Air is driven into places already covered; it cannot but be much the swifter for the narrowness of the passage

A.

Why does the South Wind more often then any other bring Rain with it?

B.

Where the Sun hath most power, and where the Seas are greatest, that is in the South, there is most water in the Air; which a South wind can only bring [Page 50] to us. But I have seen great showers of Rain sometimes also when the wind hath been North, but it was in Summer, and came first, I think, from the South or West, and was but brought back from the North.

A.

I have seen at Sea very great Waves when there was no Wind at all. What was it then that troubled the Water?

B.

But had you not Wind enough pre­sently after?

A.

We had a Storm within a little more then a quarter of an hour after.

B.

That Storm was then coming and had moved the Water before it. But the Wind you could not perceive, for it came downwards with the descending of the Clouds, and pressing the Water bounded above your Sail till it came very near. And that was it that made you think there was no Wind at all.

A.

How comes it to pass that a Ship should go against the Wind which moves it, even almost point blank, as if it were not driven but drawn?

B.

You are to know first, that what Body soever is carryed against another Body, whether perpendicularly, or ob­liquely, it drives it in a perpendicular to the superficies it lighteth on. As for Ex­ample, a Bullet shot against a flat wall, [Page 51] maketh the Stone (or other matter it hits) to retire in a perpendicular to that flat; or, if the Wall be round, towards the center, that is to say, per­pendicularly. For if the way of the motion be oblique to the Wall, the mo­tion is compounded of two motions, one parrallel to the Wall, and the other perpendicular. By the former whereof the Bullet is carried along the Wall side, by the other it approacheth to it. Now the former of these motions can have no effect upon it; all the battery is from the motion perpendicular, in which it approacheth. And therefore the part it hits must also retire perpendicularly. If it were not so, a Bullet with the same swiftness would execute as much oblique­ly shot, as perpendicularly; which you know it does not.

A.

How do you apply this to a Ship?

B.

Let A. B. be the Ship, the head of it A. If the Wind blow just from A. to­wards B. 'tis true, the Ship cannot go forward howsoever the sail be set. Let C. D. be perpendicular to the Ship, and let the Sail E. C. be never so little oblique to it, and F. C. perpendicular to E. C. and then you see the Ship will gain the space D. F. to the headward.

A.

It will so, but when it is very near [Page 52] to the Wind it will go forward very slowly, and make more way with her side to the Lee­ward.

A.

It will indeed go slower in the pro­portion of the Line A. E. to the Line C. E. But the Ship will not go so fast as you think sideward: One is the force of that Wind which lights on the side of the Ship it self; the other is, the bellying of the Sail; for the former, it is not much because the Ship does not easily put from her the Water with her side; and belly­ing of the Sail, gives some little hold for the Wind to drive the Ship a stern.

A.

For the motion sideward I agree with you; but I had thought the bellying of the Sail, had made the Ship go faster.

B.

But it does not; only in a fore-wind it hinders least.

A.

By this reason a broad thin Board should make the best Sail.

B.

You may easily foresee the great in­commodities of such a Sail. But I have seen tryed in little what such a Wind can do in such a case. For I have seen a Board set upon four truckles, with a staff set up in the midst of it for a Mast, and another very thin and broad Board fastned to that staff in the stead of a Sail; and so set as to receive the Wind very obliquely, I mean so as to be within a point of the [Page 53] Compass directly opposite to it; and so placed upon a reasonable smooth pave­ment where the Wind blew somewhat strongly. The event was first, that it stood doubting whether it should stir at all or no, but that was not long; and then it ran a head extream swiftly, till it was overthrown by a Rub.

A.

Before you leave the Ship tell me how it comes about that so small a thing as a Rudder, can so easily turn the greatest Ship?

B.

'Tis not the Rudder only, there must also be a stream to do it; you shall never turn a Ship with a Rudder in a standing pooll, nor in a natural current.

You must make a stream from head to stern, either with Oares or with Sails: when you have made such a stream, the turning of the Rudder obliquely holds the Water from passing freely; and the Ship or Boat cannot go on directly, but as the Rudder inclines to the stern, so will the Ship turn. But this is too well known to insist upon: you have observed, that the Rudders of the greatest Ships are not very broad, but go deep into the Water, whereas Western Barges, though but small Vessels, have their Rudders much broader, which argues that the holding of Water from passing is the [Page 54] office of a Rudder: and therefore to a Ship that draws much Water the Rud­der is made deep accordingly, and in Barges that draw little Water, the Rud­ders as less deep, must so much the more be extended in breadth.

A.

What makes Snow?

B.

The same cause which (speaking of Hardness) I supposed for the cause of Ice. For the Stream of Air proceeding from. That both the Earth and the Sun cast off the Air, and consequently maketh a stream of Air from the Aequinoctial to­wards the Poles, passing amongst the Clouds, shaving those small drops of Water whereof the Clouds consist, and congeals them as they do the Water of the Sea, or of a River. And these small frozen drops are that which we call Snow.

A.

But then how are great drops frozen in­to Hailstones, and that especially (as we see they are) in Summer?

B.

It is especially in Summer; and hot weather, that the drops of Water which make the Clouds, are great enough; but it is then also that Clouds are sooner and more plentifully carryed up. And there­fore the current of the Air strengthned between the Earth and the Clouds, be­comes more swift; and thereby freezeth [Page 55] the drops of Water, not in the Cloud it self, but as they are falling. Nor does it freeze them throughly, the time of their falling not permitting it, but gives them only a thin coat of Ice; as is mani­fest by their suddain dissolving.

A.

Why are not somteimes also whole Clouds when pregnant and ready to drop, frozen into one piece of Ice?

B.

I belive they are so whensoever it Thunders.

A.

But upon what ground do you believe it?

B.

From the manner or kind of noise they make, namely a crack; which I see not how it can possibly be made by Wa­ter or any other soft Bodies whatsoever.

A.

Yes, the Powder they call Aurum Fulminans, when throughly warm, gives just such another crack as Thunder.

B.

But why may not every small grain of that Aurum Fulminans by it self be heard, though a heap of them together be soft, as is any heap of Sand. Salts of all sorts are of the nature of Ice. But Gold is dissolved into Aurum Fulminans by Nitre and other Salts. And the least grain of it gives a little crack in the fire by it self. And therefore when they are so warmed by degrees, the crack can­not chuse but be very great.

A.
[Page 56]

But before it be Aurum Fulminans they use to wash away the Salt (which they call dulcifying it,) and then they dry it gently by degrees.

B.

That is, they exhale the pure Wa­ter that is left in the Powder, and leave the Salt behind to Harden with drying. Other Powder made of Salts without a­ny Gold in them will give a crack as great as Aurum Fulminans. A very great Chymist of our times hath written, that Salt of Tarter, Salt-peter, and a little Brimstone ground together into a Pow­der, and dryed, a few grains of that Powder will be made by the fire to give as great a Clap as a Musquet.

A.

Me thinks it were worth your tryal to see what effect a Quart or a Pint of Au­rum Fulminans would produce, being put into a great Gun made strong enough on purpose, and the Breech of the Gun set in hot Cinders, so as to heat by degrees, till the Powder fly.

B.

I pray you try it your self; I can­not spare so much Money.

A.

What is it that breaketh the Clouds when they are frozen?

B.

In very hot weather the Sun raiseth from the Sea and all moist places abun­dance of Water, and to a great height. And whilst this Water hangs over us in [Page 57] Clouds, or is again descending, it raiseth other Clouds, and it hapens very often that they press the Air between them, and squeeze it through the Clouds themselves very violently; which as it passes shaves and hardens them in the manner decla­red.

A.

That has already been granted, my question is what breaks them?

B.

I must here take in one supposition more.

A.

Then your Basen (it seems) holds not all you have need of.

B.

It may for all this, for the suppositi­on I add is no more but this; that what internal motion I ascribe to the Earth, and other the Concrete parts of the World, is to be supposed also in every of their parts how small soever; for what reason is there to think, in case the whole Earth have in truth the motion I have ascribed to it, that one part of it taken away, the remaining part should love that moti­on. If you break a Load-stone both parts will retain their vertue, though weakened according to the diminution of their quantity; I suppose therefore in every small part of the Earth, the same kind of motion, which I have supposed in the whole: and so I recede not yet from my Basen.

A.
[Page 58]

Let it be supposed, and withall, that abundance of Earth (which I see you aim at,) be drawn up together with the Water. What then?

B.

Then if many pregnant Clouds, some ascending and some descending meet together, and make concavities between, and by the pressing out of the Air, as I have said before, become Ice; those Atomes (as I may call them) of Earth will be by the straining of the Air through the water of the Clouds, be left behind, and remain in the Cavities of the Clouds, and be more in number then for the proportion of the Air therein. There­fore for want of liberty they must needs justle one another, and become (as they are more and more streightened of room) more and more swift, and consequently at last break the Ice suddenly and violent­ly, now in one place, and by and by in another; and make thereby so many claps of Thunder, and so many Flashes of Lightning. For the Air Recoiling up­on our Eyes, is that which maketh those Flashes to our Fancy.

A.

But I have seen Lightning in a very clear Evening, when there has been neither Thunder nor Clouds.

B.

Yes in a clear evening; because the Clouds and the Rain were below the [Page 59] Horison, perhaps 40 or 50 Miles off; so that you could not see the Clouds nor hear the Thunder.

A.

If the Clouds be indeed Frozen into Ice, I shall not wonder if they be sometimes also so scituated, as (like Looking-Glasses) to make us see sometimes three or more Suns by Refraction and Reflection.

CHAP. VII. Problems of Motion Perpendicular, Ob­lique; of Pression and Percussion; Re­flection and Refraction; Attraction and Repulsion.

IF a Bullet from a certain point given, be shot against a wall Perpendicularly and again from the same Point Oblique, What will be the proportion of the Forces wherewith they urge the wall?

For Example, let the wall be A B, a point given E, a Gun C E that carries the Bullet Perpendicularly to F, and another Gun D E that carries the like Bullet with the same swiftness Oblique to G; In what proportion will their Forces be upon the Wall?

B.

The force of the stroke Perpendi­cular from E to F will be greater then [Page 60] the Oblique force from E to G, in the proportion of the line E G to the line E F.

A.

How can the difference be so much? Can the Bullet lose so much of its force in the way from E to G?

B.

No we will suppose it loseth no­thing of its swiftness. But the cause is, That their swiftness being equal, the one is longer in coming to the wall then the other, in Proportion of Time, as E G to E F. For though their swiftness be the same▪ considered in themselves, yet the swiftness of their approach to the wall is greater in E F then in E G, in proportion of the lines themselves.

A.

When a Bullet enters not, but re­bounds from the wall, does it make the same Angle going off, which it did falling on, as the Sun-beams do?

B.

If you measure the Angles close by the wall there difference will not be ensible; otherwise it will be great e­nough, For the Motion of the Bullet grows continually weaker. But it is not so with the Sun-beams which press con­tinually and equally.

A.

What is the cause of Reflection? When a body can go no further on, it has lost its Motion. Whence then comes the Motion by which it reboundeth?

B.
[Page 91]

This Motion of rebounding or re­flecting proceedeth from the resistance. There is a difference to be considered between the Reflection of Light, and of a Bullet, answerable to their different Motions, pressing and striking. For the action which makes Reflection of Light, is the Pressure of the Air upon the Re­flecting Body, caused by the Sun, or o­ther shining body, and is but a contra­ry endeavour; as if two men should press with their breasts upon the two ends of a Staff, though they did not remove one another, yet they would find in themselves a great disposition to press backward upon whatsoever is behind them, though not a total going out of their places. Such is the way of Reflect­ing Light. Now, when the falling on of the Sun-beams is Oblique, the action of them is nevertheless Perpendicular to the Superficies it falls on. And therefore the Reflecting Body, by resisting, turneth back that Motion Perpendicularly, as from F to E, but taketh nothing from the force that goes on parallel in the line of E H; because the Motion never presses. And thus of the two Motions from F to E, and from E to H is a com­pounded Motion in the line F H, which maketh an Angle in B G, equal to the Angle F G E.

[Page 42] But in Percussion (which is the Mo­tion of the Bullet against a wall,) the Bullet no sooner goeth off then it loseth of its swiftness, and inclineth to the Earth by its weight. So that the Angles made in falling on and going off, cannot be equal, unless they be measured close to the point where the stroke is made.

A.

If a man set a Board upright upon its edge, though it may very easily be cast down with a little Pressure of ones finger, yet a Bullet from a Musquet shall not throw it down but go through it. What is the cause of that?

B.

In pressing with your finger you spend time to throw it down. For the Motion you give to the part you touch is communicated to every other part before it fall. For the whole cannot fall till every part be moved. But the stroke of a Bullet is so swift, as it breaks through before the Motion of the part it hits can be communicated to all the other parts that must fall with it.

A.

The stroke of a Hammer will drive a Nail a great way into a piece of Wood on a sudden. What weight laid upon the head of a Nail, and in how much time will do the same? It is a question I have heard propounded amonst Naturalists,

B.

The different manner of the ope­ration [Page 43] of weight from the operation of a stroke, makes it uncalculable. The suddenness of the stroke upon one point of the wood takes away the time of re­sistance from the rest. Therefore the Nail enters so far as it does. But the weight not only gives them time, but also aug­ments the resistance; but how much, and in how much time, is (I think) im­possible to determine.

A.

What is tbe difference between Re­flection and Recoiling?

B.

Any Reflection may (and not un­properly) be called recoiling; but not contrariwise every Recoiling Reflection. Reflection is always made by the Re-acti­on of a Body prest or stricken; but Re­coiling not always. The Recoiling of a Gun is not caused by its own pressing up­on the Gun-powder, but by the force of the Powder it self, inflamed and moved every way alike:

A.

I had thought it had been by the sudden re-entring of the Air after the flame and Bullet were gone out. For it is impossible that so much room as is left empty by the discharging of the Gun, should be so sud­denly filled with the Air that entereth at the Touch-hole.

B.

The flame is nothing but the Pow­der it self, which scattered into its smal­lest [Page 64] parts seems, of greater bulk by much, then in truth it is, because they shine. And as the parts scatter more and more, so still more Air gets between them, en­tring not only at the Touch-hole, but al­so at the mouh of the Gun. which two ways being opposite, it will be much too weak to make the Gun Recoil.

A.

I have heard that a great Gun char­ged too much or too little, will Shoot (not above, nor below but) besides the mark; and charged with one certain charge be­tween both will hit it.

B.

How that should be I cannot ima­gine. For when all things in the cause are equal, the effects cannot be unnequal. As soon as Fire is given, and before the Bul­let be out, the Gun begins to Recoil. If then there be any unevenness or rub in the ground more on one side then on the other, it shall shoot besides the mark, whether too much, or too little, or justly charged; because if the line wherein the Gun Recoileth decline, the way of the Bullet will also decline to the contrary side of the mark. Therefore I can ima­gine no cause of this event, but either in the ground it Recoils on, or in the une­qual weight of the parts of the Breech.

A.

How comes Refractin?

B.

When the action is in a line Per­pendicular [Page 65] to the superficies of the Body wrought upon, there will be no Refracti­on at all. The action will proceed still in the same straight Line, whether it be Pres­sion as in Light, or in Percussion as in the shooting of a Bullet. But when the Pression is Oblique, then will the Refraction be that way which the Na­ture of the Bodies through which the Action proceeds shall determin.

H.

How is light Refracted?

B.

If is pass through a Body of less, into a Body of greater resistance, and to the Point of the Superficies it falleth on, you draw a Line Perpen­dicular to the same superficies, the Action will proceed not in the same Line by which it fell on, but in another Line bending toward that Perpen­diculare.

A.

What is the reason of that?

B.

I told you before, that the falling on worketh only in the Perpendicular; But as soon as the Action proceedeth fur­ther inward then a meer touch, it worketh partly in the Perpendicular, and partly forward, and would proceed in the same line in which it fell on, but for for the greater resistance which now weakneth the Motion forward, and makes it to incline towards the Perpen­dicular.

A.
[Page 66]

In transparent Bodies it may be so; but there be Bodies through which the Light cannot pass at all.

B.

But the Action by which Light is made, passeth through all Bodies. For this Action is Pression; and whatsoever is prest, presseth that which is next be­hind, and so continually. But the cause why there is no Light seen through it, is the uneveness of the parts within, whereby the Action is by an infinite number of Reflections so diverted and weakned, that before it hath proceeded through, it hath not strength left towork upon the Eye strongly enough to produce sight.

A.

If the Body being transparent the Acti­on proceed quite through, into a Body again of less resistance, as out of Glass into the Air, which way shall it then proceed in the Air?

B.

From the Point where it goeth forth, draw a Perpendicular to the su­perficies of the Glass, the Action now freed from the resistance it suffered, will go from that Perpendicular, as much as it did before come towards it.

A.

When a Bullet from out of the Air entreth into a Wall of Earth, will that al­so be Refracted towards the Perpendicu­lar?

B.
[Page 67]

If the Earth be all of one kind, it will. For the parallel Motion, will there also at the first entrance be resisted, which it was not before it entred.

A.

How then comes a Bullet, when shot very Obliquely into any broad Water, and having entred, yet to rise, again into the Air?

B.

When a Bullet is shot very Ob­liquely, though the Motion be never so swift, yet approach downwards to the Water is very slow, and when it cometh to it, it casteth up much Wa­ter before it, which with its weight presseth downwards again, and maketh the Water to rise under the Bullet with force enough to master the weak Moti­on of the Bullet downwards, and to make it rise in such manner as Bodies use to rise by Reflection.

A.

By what Motion (seeing you ascribe all Effects to Motion) can a Load-stone draw Iron to it?

B.

By the same Motion hitherto sup­posed. But though all the smallest parts of the Earth have this Motion, yet it is not supposed that their Motions are in equal Circles; nor that they keep just time with one another; nor that they have all the same Poles. If they had, all Bodies would draw one another [Page 68] alike. For such an agreement of Moti­on, of Way, of Swiftness, of Poles, cannot be maintained without the con­junction of the Bodies themselves in the Center of their common Motion, but by violence.

If therefore the Iron have but so much of the Nature of the Load-stone as re­dily to receive from it the like Motion, as one String of a Lute doth from another String strained to the same Note (as it is like enough it hath, the Load-stone being but one kind of Iron Ore) it must needs after that Motion received from it, (unless the greatness of the weight hinder) come nearer to it, be­cause at distance their Motions will differ in time, and oppose each other where­by they will be forced to a common Cen­ter. If the Iron be lifted up from the Earth, the Motion of the Load-stone must be stronger, or the Body of it near­er, to overcome the Weight; and then the Iron will leap up to the Load-stone as as Swiftly as from the same distance, it would fall down to the Earth; but if both the Stone and the Iron be set float­ing upon the Water, the attraction will begin to be manifest at a greater distance, because the hindrance of the weight is in part removed.

A.
[Page 69]

But why does the Load-stone if it float on a Calm Water, never fail to place it self at last in the Meridian just North and South.

B.

Not so, just in the Meridian, but almost in all places with some variations. But the cause I think is, that the Axis of this Magnetical Motion is parallel to the Axis of the Ecliptique, which is the Ax­is of the like Motion in the Earth, and consequently that it cannot freely exercise its Natural Motion in any other Scituation.

A.

Whence may this consent of Motion in the Load-stone and the Earth proceed? Do you think (as some have written) that the Earth is a great Load-stone?

B.

Dr. Gilbert that was the first that wrote any thing of this Subject ration­ally, inclines to that opinion. Decartes thought the Earth (excepting this upper crust of a few Miles depth) to be of the same Nature with all other Stars, and bright. For my part I am content to be ignorant; but I believe the Load stone hath given its virtue by a long habitude in the Mine, the Vein of it lying in the plain of some of the Meridians, or ra­ther of some of the great Circles that pass through the Poles of the Ecliptique, which are the same with the Poles of [Page 70] the like Motion supposed in the Earth.

A.

If that be true▪ I need not ask why the filings of Iron laid on a Load-stone equally distant from its Poles will lie paral­lel to the Axis, but one each side incline to the Pole that is next it. Nor why by drawing a Load-ston all a long a Needle of Iron, the Needle will receive the same Poles Nor why when the Load-stone and Iron (or two Load-stones) are put together floating upon Water, will fall one of them a Stern of the other, that their like parts may look the same way, and their unlike touch, in which Action they are commonly said to Repel one another. For all this may be deriv'd from the union of their Motions. One thing more I desire to know, and that is; What are those things they call Spirits? I mean Ghosts, Fairies, Hobgoblins, and the like Apparitions.

B.

They are no part of the Subject of Natural Philosophy.

A.

That which in all Ages, and all places is commonly seen (as those have been, un­less a great part of Mankind by Lyers) cannot, I think, be supernatural.

B.

All this that I have hitherto said, though upon better ground than can be had for a discourse of Ghosts, you ought to take but for a Dream.

A.
[Page 71]

I do so. But there be some Dreams more like sense then others. And that which is like sense pleases me as well (in natural Philosophy) as if it were the very truth.

B.

I was Dreaming also once of these things; but was weakened by their noise. And they never came into any Dream of mine since, unless Apparitionrs in Dreams and Ghoasts be all one.

CHAP. VIII. The Delphique Problem or Duplica­tion of the Cube.

A.

HAve you seen a Printed Paper sent from Paris, containing the Duplication of the Cube, written in French?

B.

Yes. It was I that Writ it, and sent it thither to be Printed, on purpose to see what objections would be made to it by our Professors of Algebra here.

A.

Then you have also seen the confuta­tions of it by Algebra.

B.

I have seen some of them; and have one by me. For there was but one that was rightly Calculated, and that is it which I have kept.

A.
[Page 72]

Your Demonstration then is confuted though but by one.

B.

That does not follow. For though an Arithmetical Calculation be true in Numbers, yet the same may be, or rather must be false, if the Units be not con­stantly the same.

A.

Is their Calculation so inconstant, or rather so foolish as you make it?

B.

Yes. For the same number is some­times so many Lines, sometimes so many Plains, and sometimes so many Solids; as you shall plainly see, if you will take the pains to examine first a Demonstra­tion I have to prove the said Duplication, and after that, the Algebrique Calculation which is pretended to confute it. And not only that this one is false, but also any other Arithmetical account used in Geometry, unless the numbers be always so many Lines, or always so many super­ficies, or always many solids.

A.

Let me see the Geometrical Demon­stration.

B.

There it is: Read it.

To find a Cube double to a Cube given.

LEt the side of the Cube given be V D. Produce V D to A, till A D be double to D V. Then make [Page 73] the square of A D, namely A B C D. Divide A B and C D in the middle at E and F. Draw E F. Draw also A C cutting E F in I. Then in the sides B C and A D take B R and A S each of them equal to A I or I C.

Lastly, divide S D in the middle at T, and upon the Center T, with the distance T V, describe a semi-circle cutting A D in Y, and D C in X.

I say the Cube of D X is double to the Cube of D V. For the three lines D Y, D X, D V are in continual pro­portion. And Cntinuing the semi-cir­cle V X Y till it cut the line R S drawn and produced in Z, the line S Z, will be equal to D X. And drawing X Z it will pass through T. And the four lines T V, T X, T Y and T Z will be equal. And therefore joyning Y X and Y Z, the Figure V X Y Z will be a Rectan­gle.

Produce C D to P so as D P be equal to A D. Now if Y Z produced fall on P, there will be three Rectangle equi­angled Triangles, D P Y, D Y X, and D X V; and consequently four con­tinual proportionals, D P, D Y, D X▪ and D V, whereof D X is the least of the means. And therefore the Cube of D X will be double to the Cube of D V.

A.
[Page 74]

That's true; and the Cube of D Y will be double to the Cube of D X; and the Cube of D P double to the Cube of D Y. But that Y Z produced, falls upon P, is the thing they deny, and which you ought to demonstrate.

B.

If Y Z produced fall not on P, then draw P Y, and from V let fall a perpendicular upon P Y, suppose at u. Divide P V in the midst at a, and joyn a u; which done a u will be equal to a V or a P. For because V u P is a right Angle, the point u will be in the semi-circle whereof P V is the Dia­meter.

Therefore drawing V R, the Angle u V R will be a right Angle.

A.

Why so?

B.

Because T V and T Y are equal; and T D, T Sequal; S V will also be equal to D V. And because D P and R S are equal and parallel, R Y will be equal and parallel to P V. And there­fore V R and P Y that joyn them will be equal and parallel. And the Angles P u V, R V u will be alternate, and consequently equal. But P u V is a right Angle; therefore also R V u will be a right Angle.

A.

Hitherto all is evident. Proceed.

B.

From the point Y raise a perpen­dicular [Page 75] cutting V R wheresoever in t, and then (because P Y and V R are parallel) the Angle Y t V will be a right Angle. And the figure u Y t V a Rectangle, and u t equal to Y V. But Y V is equal to Z X; and therefore Z X is equal to u t. And u t must pass through the point T (For the Diame­ters of any Rectangle, divide each o­ther in the middle) therefore Z and u are the same point, and X and t the same point. Therefore Y Z produced falls upon P. and D X is the lesser of the two means between A D and D V. And the Cube of D X double to the Cube of D V which was to be de­mostraten.

A

I cannot imagine what fault there can be in this Demonstration, and yet there is one thing which seems a little strange to me. And 'tis this. You take B R, which is half the Diagonal, and which is the sine of 45 degrees, and which is also the mean proportional between the two Extreams. And yet you bring none of these proprieties into your Demonstration. So that though you argue from the Construction, yet you do not argue from the Cause. And this per­haps your adversaries will object (at least) against the Art of you Demonstratieon, or [Page 76] enqure by what luck you pitched upon half the Diagonal for your Foundation.

B.

I see you let nothing pass. But for answer you must know, That if a man argue from the negative of the truth, though he know not that it is the truth which is denyed, yet he will fall at last, after many consequences, into one absur­dity or another. For though false do of­ten produce Truth, yet it produces also absurdity, as it hath done here. But Truth produceth nothing but Truth. Therefore in Demonstrations that tend to absurdity, it is no good Logick to require all along the operation of the cause.

A.

Have you drawn from hence no Corollaries?

B.

No. I leave that for others that will; unless you take this for a Corollary, That, what Arithmetical Calculation so­ever contradicts it, is false.

A.

Let me see now the Algebrical De­monstration against it.

B.

Here it is.

Let A B or A D be equal to 2

Then D F or D V is equal to 1

And B R or A S is equal to the square root of 2

And A V equal to 3 want the square root of 2.

The Cube of A B is equal to 8

[Page 77] The Cube of D Y is equal to 45 want the Square Root of 1682 that is almost equal to 4

For 45 want the Square Root of 6681 is equal to 4

Therefore D Y is a little less then the greater of the two Means between AD and DV.

A.

There is I see some little difference between this Arithmetical aud your Geo­metrical Demonstration. And though it be insensible, yet if his Calculation be true, yours must needs be false, which I am sure cannot be.

B.

His Calculation is so true, that there is never a Proposition in it false, till he come to the conclusion, that the Cube of D Y. is equal to 45, want the square Root of 1682. But that, and the rest, is false.

A.

I shall easily see that A D. is certain­ly 2, whereof D V. is 1, and A V. is cer­tainly 3, whereof D V. is 1.

B.

Right.

A.

And B R. is without doubt the square Root of 2.

B.

Why, what is 2?

A.

2, is the Line A D. as being dou­ble to D V. which is 1.

B.

And so, the Line B R. is the square Root of the Line A D.

A.
[Page 78]

Out upon it it, it's absurd. Why do you grant it to be true in Arithme­tick?

B.

In Arithmetick the numbers consist of so many Units; and are never consi­dered there as nothings. And therefore every one Line has some Latitude, and if you allow to BI. the Semi-diagonal the same Latitude you do to AB. or to BR. you will quickly see the Square of half the Diagonal to be equal to twice the Square of half AB.

A.

Well, but then your Demonstration is not confuted; for the Point Y, will have Latitude enough to take in that little dif­ference which is between the Root of 1681 and the Root of 1682. This putting off an Vuit sometimes for one Line, sometimes for one Square, must needs marr the reckon­ing. Again he says the Cube of AB. is e­qual to 8. but seeing AB. is 2, the Cube of AB. must be just equal to four of its own sides; so that the Vnit which was be­fore sometimes a Line, sometimes a Square, is now a Cube.

B.

It can be no otherwise when you so apply Arithmetick to Geometry, as to mumber the Lines of a Plain, or the Plains of a Cube.

A.

In the next place, I find that the Cube of DY. is equal to 45, want the [Page 79] Square Root of 1622. What is that 45? Lines, or Squares, or Cubes?

B.

Cubes, Cubes of DV.

A.

Then if you add to 45 Cubes of DV. the Square Root of 1682, the sum will be 45 Cubes of DV. And if you add to the Cube of DY. the same Root of 1682, the sum will be the Cube of DY. plus the Square Root of 1682. And these two sums must be equal.

B.

They must so.

A.

But the Square Root of 1682, being a Line, adds nothing to a Cube; therefore the Cube alone of DY. which he says is e­qual almost to 4. Cubes of DV. is equal to 45 Cubes of the same DV.

B.

All these impossibilities do neces­sarily follow the confounding of Arith­metick and Geometry.

A.

I pray you let me see the Operation by which the Cube of DY. (that is the Cube of 3, want the Root of 2,) is found equal to 45, want the Square Root of 1682.

[Page 80] A detection of the absurd use of Arith­metick as it is now applyed to Geo­metry.

B.

Here it is.

3—r. 2.

3—r. 2.

—r. 18 ✚2:

9—r. 18

9—r. 72 ✚2.

3—r. 2.

—r. 162✚12—r. 8.

27—r. 648✚6

27—r. 658—r. 162✚18—r. 8.

A.

Why for two Roots of 18 do you put the Root of 72.

B.

Because 2 Roots of 18 is equal to one Root of 4 times 18, which is 72.

A.

Next we have, That the Root of 2 Multiplyed into 2, makes the Root of 8. How is that true?

B.

Does it not make 2 Roots of 2? And is not BR. the Root of 2, and 2 BR equal to the Diagonal? And is not [Page 81] the diagonal the root of a square equal to 8 squares of DV?

A.

'Tis true. But here the root of 8 is put for the Cube of the root of 2. Can a line be equal to a Cube?

B.

No. But here we are in Arith­metick again, and 8 is a Cubique num­ber.

A.

How does the root of 2 multiplyed into the root of 72 make 12?

B.

Because it makes the root of 2 times 72, that is to say the root of 144 which is 12.

A.

How does 9 roots of 2 make the root of 162?

B.

Because it makes the root of 2 squares of 9, that is the root of 162.

A.

How does 3 roots of 72 make the root of 648?

B.

Because it makes the root of 9 times 72, that is of 648.

A.

For the total Sum I see 27 and 18 which make 45. Therefore the root of 648 together with the root of 162 [...] and of 8, which are to be deducted from 45, ought to be equal to the root of 1682.

B.

So they are. For 648 multiplyed by 162 makes 104976 of which the dou­ble root is—648 and 648 and 162 added together make —810.

[Page 82]Therefore the root of 948, added to the root of 162 makes the root of—1459

Again 1458 into 8 is 11664. The dou­ble root whereof is—216.

The Sum of 1458 and 8 added toge­ther is—1466.

The Sum of 1466 and 216 is 1682, and the root, the root of—1682.

A.

I see the Calculation in numbers is right, though false in lines. The reason whereof can be no other then some difference between multiplying numbers into lines or plains, and multiplying lines into the same lines or plains.

B.

The difference is manifest. For when you multiply a number into lines, the product is lines; as the number 2 mul­tiplyed into 3 lines is no more then 3 lines 2 times told. But if you multiply lines in­to lines you make plains, and if you multi­ply lines into plains you make solid bo­dies. In Geometry there are but three dimensions, Length, Superficies, and Body. In Arithmetick there is but one, and that is Number or Length which you will. And though there be some Numbers cal­led Plain, others Solid, others Plano-solid, others Square, others Cubique, others Square-square, others Quadrato-cubique, others Cubi-cubique &c. yet are all these but one dimension, namely Num­ber, [Page 83] or a file of things Numbered.

A.

But seeing this way of Calculation by Numbers is so apparently false, what is the reason this Calculation came so near the truth.

B.

It is because in Arithmetick Units are not Nothings, and therefore have breadth. And therefore many Lines set together make a superficies though their breadth be insensible. And the greater the number is into which you divide your Line, the less sensible will be your errour.

A.

Archimedes, to find a streight Line equal to the circumferrence of a Circle, used this may of extracting Roots. And 'tis the way also by which the Table of Sines, Se­cants aud Tangents have been calculated, Are they all Cut?

B.

As for Archimedes, there is no man that does more admire him then I do. But there is no man that cannot Err. His reasoning is good. But he ads all other Geometricans before and after him, have had two Principles that cross one another when they are applyed to one and the same Science. One is, that a Point is no part of a Line which is true in Geometry, where a part of a Line when it is called a Point, is not reckon­ed; another is, that a Unit is part of a [Page 84] Number which is also true; but when they reckon by Arethmetick in Geome­try, there a Unit is somtimes part of a Line, sometimes a part of a Square, and sometimes part of a Cube.

As for the Table of Sines, Secants and Tangents, I am not the first that find fault with them. Yet I deny not but they are true enough for the reckoning of Acres in a Map of Land.

A.

What a deal of Labour has been lost by them that being Professors of Geometry have read nothing else to their Auditors but such stuff as this you have here seen. And some of them have written great Books of it in strange characters, such as in troublesome times, a man would suspect to be a Cypher.

B.

I think you have seen enough to satisfie you, that what I have written heretofore concerning the Quadrature of the Circle, and of other Figures made in imitation of the Parabola, has not been yet confuted.

A.

I see you have wrested out of the hands of our Antagonists this weapon of Algebra, so as they can never make use of it again. Which I consider as a thing of much more consequence to the science of Geometry, then either of the Duplication of the Cube, or the finding of two mean Proportionals, or the Quadrature of a Circle, or all these Problems put together.

FINIS.

Books Written by this Author, and Printed for William Crooke.

  • 1 DE Mirabilibus Pecci, in Quarto Latin, in Octavo in English and Lantin.
  • 2 Three Papers to the Royal Society a­gainst Dr. Wallis.
  • 3 Lumathematica.
  • 4 Prima partis Doctrinae Wallisianae de Motu Censura Brevis.
  • 5 Resetum Geometricum, sive propositio­nes aliquot frustra antehac tentatae.
  • 6 Principia & Poblemata aliquot Geo­metrica, ante desperata, nunc brevi­ter explicata & demonstrata.
  • 7 Quadratura Circuli Cubatio Sphaere du­plicatio Cubi Breviter demonstrata.
  • 8 Consideration on his Loyalty, Reputati­on, Religion and Manners; by himself.
  • 9 De Principio & Ratione Geometri.
  • 20 The Travels of Vlises Translated from Homer.
  • 11 Epistol. ad Dr. Wood.
  • 12 The Translation of all Homers Works into English.
  • 13 The Epitome of the Civil Wars of En­land from 1640 to 1660.
  • 14 Aristotles Rhetorick Translated into English by him, with his own Rhetorick to it.
  • [Page] 15 A Dialogue betwixt a Student in the Common-Laws of England, and a Phi­losopher in which is set forth the Er­rors in some Practise.
  • 16 A Narration of Heresie and the Pun­nishment thereof.
  • 17 Ten Dialogues of Natural Philosophy.
  • 18 A Poem in Latin of his Life.
  • 19—idem the same in English.
  • 20 His Life written in Latin, part by himself and the rest by Dr. R. B. wherein is contained the most mate­rial parts of his Life.
  • 21 Seven Philosophical Problems, and two Propositions of Geometry. With an Apology for Himself, and his Writings. Dedicated to the King, in the year 1662.

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