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A44011 Seven philosophical problems and two propositions of geometry by Thomas Hobbes of Malmesbury ; with an apology for himself and his writings. Hobbes, Thomas, 1588-1679. 1682 (1682) Wing H2259; ESTC R28663 37,975 99

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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 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 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. 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 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. 'T is 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. 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
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. 'T is 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 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. 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 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 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 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 must be visible all the way the impressions in all points of the time being
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 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. 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 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. 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. 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 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
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 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 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 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 'T is 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 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 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 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 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 'T is 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. 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 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 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 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