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I Shal here at once discover the falsity and ridiculousness of a considerable part of our Authors Theorems, and reduce the rest to these following Propositions of Archi∣medes and Stevinus.
Archimedis Positio 1.
Ponatur humidi eam esse naturam, ut, parti∣bus ipsius aequaliter jacentibus & continuatis in∣ter sese, minus pressa à magis pressa expellatur. Ʋnaquae{que} autem pars ejus premitur humido supra ipsam existente ad perpendiculum, si hu∣midum sit descendens in aliquo aut ab alio aliquo pressum.
Prop. 2.
Omnis humidi consistentis atque manentis superficies Sphaerica est, cujus centrum est idem quod centrum terrae.
Prop. 5.
Solidarum magnitudinum quaecunque levior humido fuerit demissa in humidum manens, us{que} eò demergetur, ut tanta moles humidi, quanta est partis demersae, eandem quam tota magni∣tudo gravitatem habeat.
Prop. 6.
Solidae magnitudines humido leviores in hu∣midum impulsae, sursum feruntur tanta vi, quantò humidum molem habens magnitudini aequalem, gravius est ipsâ magnitudine.
Prop. 7.
Solidae magnitudines humido graviores de∣missae in humidum, ferentur deorsum, donec descendant: Et erunt in humido tantò leviores,
Stevini Postul. 3.
Pondus à quo vas minus altè deprimitur, le∣vius; quò altiùs, gravius; quò aeque altè, aequi∣pondium esse.
Prop. 5.
Corpus solidum materiae levioris quàm aqu•…•… cui innatat, pondere aequale est tantae aquae moli, quanta suae parti demergitur.
Prop. 8.
Corpus solidum in aqua levius est quàm in aëre, pondere aquae magnitudine sibi aequalis.
Prop. 10.
Aquae fundo horizonti parallelo tantum in∣sidet pondus, quantum est aquae columnae cujus basis fundo, altitudo perpendiculari ab aquae su∣perficie summa ad imam demissae aequalis sit.
Now, Reader, consider well these Pro∣positions: my Authors Theorems; and my Censure, which is this.
His first two are no Theorems; but only Suppositions. And the third, a sort of a definition, or rather, aliquid gratis dictum.
The fourth, as he wordeth it, is false: for a broad fluid counterpoyseth more then a narrower; seing a cylinder of Mercury
one inch thick and twenty-nine inches high, counterpoyseth a cylinder of Air of the same thickness, and of the altitude of the Atmosphere: and one two inches thick with the former height, counterpoyseth four times as much Air. As he explicateth it, it is true, and the same with Archimedes's second Proposition; for the Demonstra∣tion holds, suppose ye divide the fluid by several pipes, if they have entercourse.
Here he maketh a mystery of a very easie thing: for one pillar of water being ten times thicker then another of the same height, and consequently an hundred times heavier, hath no more effect then the other; for because of its base, it hath an hundred times as much resistance. And it is most clear, that if the resistance be pro∣portional to the pressure, the effect must constantly be the same.
His fift, is a part of Archimedes's first position.
His sixt also; for Archimedes's expulsion hindered with equal resistance on all sides, he calleth, Pressure on every side. I suppose he will hardly affirm, that this lateral pres∣sure was not known before him; seeing
Stevinus doth demonstrat, how much it is upon any plain howsoever inclining, in his Prop. 11. 12. 13. which our Author can∣not do yet; at least, there is nothing in his Book either so subtil or useful.
His seventh is the same with the last part of Stevinus's third Postulatum.
The eight is manifestly false, (if fluids have a Bensil, as he supposeth, Prop. 17. 19.) which I demonstrat from his own fi∣gure thus. The first foot E having one de∣gree of weight, and the second foot I ha∣ving equal quantity or dimension, and be∣ing lower then E, must have more weight; (according to his 17.) let it therefore have 1½ degrees of weight: then the weight of both these must be 2½. Now the third foot N, being of equal quantity with I, and lower, must (according to his 17.) have more gravity then it hath; (to wit, 1½) let it therefore have 2. degrees; and then the weight of all three is 4½ degrees: but 1. 2½, 4½, are not in Arithmetical progression; and therefore the Theorem is false.
I must take notice, that if our Author had understood so much as the terms of
Art; he would have said, The pressures of fluids are in direct proportion with their profun∣dities. His inference there concerning a Geometrical progression is false; for there are many Geometrical progressions more then 1, 2, 4, 8, &c. And it may be in many several progressions, albeit it nei∣ther be in Arithmetical nor Geometrical progression. And, suppose he had not con∣tradicted himself, his Theorem is evident from the 10. of Stevinus: For, according to it, the weights or pressures of fluids are equal to the weights of respective Cylin∣ders upon the same, or equal bases; but the weights of such Cylinders are in pro∣portion with their quantities, which is the same with the proportion of their alti∣tudes.
The ninth and tenth (as he explicateth himself) are only this, That fluids press up∣on bodies within themselves, and press up bodies lighter then themselves in specie; which is the same with his 6. and 13. The first of which we have examined already: and the o∣ther we leave to its own place. But what ground he hath for his sensible and insensible gravity, I shal discuss in the examination
of his Ars magna & nova, which is all built upon this wild notion.
His eleventh is manifestly false, as I shal afterward demonstrat from his own prin∣ciples: for the Cylinder acquireth only a greater base, (our Author must under∣stand that an Horizontal surface is the base, and sustains the pressure) and con∣sequently a greater resistance, which ma∣keth the same weight of less effect. It is e∣vident that a weight of lead cannot press two foot in square, so much as one: yea the pressures of the same weight are al∣wayes caeteris paribus in reciprocal propor∣tion with the surfaces they press; as it is known by all Mathematicians, except on∣ly such pitiful ones, as our Author.
The twelfth is evidently false; for, if ye take a bladder, or any tender vessel half full of water, and put the sides of it toge∣ther, the fluid shal be moved from the un∣equal pressure of the vertical surface.
The one half of the thirteenth is a part, but a very smal one, of Archimedes's se∣venth, and eigth: The other half is also a smal parcel of Archimedes's sixth.
His fourteenth is so much as he under∣stands
of Archimedes's fifth, and Stevinus's fifth.
The fifteenth, seventeenth and nine∣teenth are false; unless the fluid have a spring, or be heterogeneous; none of which he hath made out: but if it were made out, the thing is obious, and noticed by M. Boyl in the thirty-sixth Experiment; yet only in the Air, which is known to have a spring.
His sixteenth is ridiculous; seing we see daily fishes, little particles of earth, horse hairs, and many other such bodies betwixt the surface and bottom of the wa∣ter. Yea by adding a sufficient quantity of lead to a body lighter in specie then water, it may be made practicable: and is demon∣strat both by Archimedes and Stevinus, sup∣posing the water homogeneous; the con∣trair of which, our Author hath not yet made out. And more, even a bodie consi∣derably heavier in specie then water, beaten out thin and broad, especiallie if it be con∣cave below, may be suspended for a consi∣derable time betwixt the surface and bot∣tom of the water, providing it be laid pa∣rallel to the Horizon. But passing by all
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this, his method is unpracticable, and sup∣poseth, without proving any thing, that wa∣ter can suffer any degree of compression; and stones, lead, with other bodies, none at all.
His eighteenth is the same with Archi∣mede's seventh, and Stevinus's eighth.
His twentieth is the same with his se∣venth, otherwayes he grants it not exactly true.
His twentyone (as he wordeth it) is most manifest from that Statical demonstration I mentioned: For seing pressures of the same weight are in reciprocal proportion with their resistances, and the resistances or resisting surfaces can be diminished in infinitum; it is evident that the least weight can produce any pressure, whether the hea∣vy body be fluid or solid. But he explica∣teth himself otherwayes, relating to the spring of fluids, which is not yet proven in any fluid, save Air; and besides this, the Theorem is ridiculous, seing the spring of any part (where all are equally pressed) is equal to the spring of the whole: for one pound weight presseth one foot as much, as two pound presseth two; and even so in any spring.
His 22. and 23. are made manifest by Pecquet in his fourth Experiment, and M. Boyl in his 19. Physico-Mechanical Expe∣riment, yea throughout all that book and many others, constantly calling the weight and spring of the Air diverse, and yet brin∣ging them both in for that same effect.
The 24. is ridiculous; seing it is true and obvious in all things, if there be no pe∣netration of bodies.
The 25. is evidently false, seing wa∣ters upon the tops of hills support less, and in valleys more. Yea Doctor Wallace sho∣weth in his Mechanicks, pag. 728. that the Mercury both in M. Boyls Baroscop, and his, fell sometimes at Oxford below 28. inches, and other times above thirty, and in the page 740. he mentioneth unquestio∣nable experiments of 34. 52. and 55. in∣ches. The contrair of this Theorem is al∣so evident from many of our Authors own experiments, if any man think them wor∣thy the looking over. And suppose he had hit right, this is nothing but the old To∣ricellian Experiment.
His 26. is imperfect; first, seing he speaketh only of fluids to be pressed up, it
being also true in all other bodies. Se∣condly, he doth not determine how far the sphere of activity reaches; and yet all this is easily done and demonstrat from Stevinus his 10. For the body is pressed up, till it together with the fluid betwixt it and the bottom (not regarding what else inter∣veen, but reckoning all for fluid) be equal in weight with a column of fluid, whose height is the same with the height of the fluid, and its base the same with the base of the former fluids portion, or equal to it: and besides all these, this is not different from M. Boyls eleventh Paradox.
His 27. is to say, that a pound of wool weigheth as much, as a pound of lead.
His 28. is the same with that which he would say in the 4. and is true also in so∣lids; if ye speak only of columns: For two unequal columns of the same hight and matter press equally, seing their re∣sistances are proportional with their weights. In fluids (as I said alreadie) it is the same with Archimedes's Second.
His 29. might have been more general, to wit, That there can be no motion in fluids, without an unequal pressure: And then it
had been the same with Archimedes's first position.
His 30. is also a part of Archimedes's first position. For seing pressure is jud∣ged only by expulsion the effect of it; and the expulsion is always caused where the least resistance is, which may be in a croo∣ked line: wherefore then is not pressure also in crooked lines?
His 31. is the 10 of Stevinus. Here again he justleth with that great difficulty, which I discussed in the 4. and telleth there is no way to answer, but his.
In his 32. the Pondus & Potentia, are to say in plain Scots, a pressure and a resistance. He hath told in his 5. that in all fluids there was a pressure; but now it comes in his head, that a man may fancy a pressure with∣out a resistance; & therefore he must guard against that. I suppose here, that his defini∣tion of the Staticks is new; otherwise the Tron-lords are the greatest professors of it.
His 33. is to say, that there must be a motion, when the pressure is greater then the resistance; which is yet a part of Archi∣medes's first position, and never doubted of by the greatest ignorants.