Chapter II: Part 2

But, because that this Doctrine of Archimedes, perused, transcribed and examined by _Signor Francesco Buonamico_, in his _fifth Book of Motion, Chap. 29_, and afterwards by him confuted, might by the Authority of so renowned, and famous a Philosopher, be rendered dubious, and suspected of falsity; I have judged it necessary to defend it, if I am able so to do, and to clear _Archimedes_, from those censures, with which he appeareth to be charged. _Buonamico_ rejecteth the Doctrine of _Archimedes_, first[15], as not consentaneous with the Opinion of _Aristotle_, adding, that it was a strange thing to him, that the Water should exceed the Earth in Gravity[16], seeing on the contrary, that the Gravity of water, increaseth, by means of the participation of Earth. And he subjoyns presently after[17], that he was not satisfied with the Reasons of _Archimedes_, as not being able with that Doctrine, to assign the cause whence it comes, that a Boat and a Vessell, which otherwise, floats above the water, doth sink to the Bottom, if once it be filled with water; that by reason of the equality of Gravity, between the water within it, and the other water without, it should stay a top; but yet, nevertheless, we see it to go to the Bottom.

[15] His first Objection against the Doctrine of _Archimedes_.

[16] His Second Objection.

[17] His third Objection.

He farther addes[18], that _Aristotle_ had clearly confuted the Ancients, who said, that light Bodies moved upwards[19], driven by the impulse of the more grave Ambient: which if it were so, it should seem of necessity to follow, that all naturall Bodies are by nature heavy, and none light: For that the same would befall the Fire and Air, if put in the Bottom of the water. And, howbeit, _Aristotle_ grants a Pulsion in the Elements, by which the Earth is reduced into a Sphericall Figure, yet nevertheless, in his judgement; it is not such that it can remove grave Bodies from their naturall places, but rather, that it send them toward the Centre, to which (as he somewhat obscurely continues to say,) the water principally moves, if it in the interim meet not with something that resists it, and, by its Gravity, thrusts it out of its place: in which case, if it cannot directly, yet at least as well as it can, it tends to the Centre: but it happens, that light Bodies by such Impulsion, do all ascend upward: but this properly they have by nature, as also, that other of swimming. He concludes, lastly[20], that he concurs with _Archimedes_ in his Conclusions; but not in the Causes, which he would referre to the facile and difficult Separation of the _Medium_, and to the predominance of the Elements, so that when the Moveable superates the power of the _Medium_; as for example, Lead doth the Continuity of water, it shall move thorow it, else not.

[18] His fourth Objection.

[19] The _A_ncients denyed _A_bsolute Levity.

[20] The causes of Natation & Submersion, according to the
Peripateticks.

This is all that I have been able to collect, as produced against _Archimedes_ by _Signor Buonamico_: who hath not well observed the Principles and Suppositions of _Archimedes_; which yet must be false, if the Doctrine be false, which depends upon them; but is contented to alledge therein some Inconveniences, and some Repugnances to the Doctrine and Opinion of _Aristotle_. In answer to which Objections, I say, first[21], That the being of _Archimedes_ Doctrine, simply different from the Doctrine of _Aristotle_, ought not to move any to suspect it, there being no cause, why the Authority of this should be preferred to the Authority of the other: but, because, where the decrees of Nature are indifferently exposed to the intellectuall eyes of each, the Authority of the one and the other, loseth all a{u}thenticalness of Perswasion, the absolute power residing in Reason; therefore I pass to that which he alledgeth in the second place[22], as an absurd consequent of the Doctrine of _Archimedes_, namely, That water should be more grave than Earth. But I really find not, that ever _Archimedes_ said such a thing, or that it can be rationally deduced from his Conclusions: and if that were manifest unto me, I verily believe, I should renounce his Doctrine, as most erroneous. Perhaps this Deduction of _Buonamico_, is founded upon that which he citeth of the Vessel, which swims as long as its voyd of water, but once full it sinks to the Bottom, and understanding it of a Vessel of Earth, he infers against _Archimedes_ thus: Thou sayst that the Solids which swim, are less grave than water: this Vessell swimmeth: therefore, this Vessell is lesse grave than water. If this be the Illation. I easily answer, granting that this Vessell is lesse grave than water, and denying the other consequence, namely, that Earth is less Grave than Water. The Vessel that swims occupieth in the water, not only a place equall to the Mass of the Earth, of which it is formed; but equall to the Earth and to the Air together, contained in its concavity. And, if such a Mass compounded of Earth and Air, shall be less grave than such another quantity of water, it shall swim, and shall accord with the Doctrine of _Archimedes_; but if, again, removing the Air, the Vessell shall be filled with water, so that the Solid put in the water, be nothing but Earth, nor occupieth other place, than that which is only possest by Earth, it shall then go to the Bottom, by reason that the Earth is heavier than the water: and this corresponds well with the meaning of _Archimedes_. See the same effect illustrated, with such another Experiment, In pressing a Viall Glass to the Bottom of the water, when it is full of Air, it will meet with great resistance, because it is not the Glass alone, that is pressed under water, but together with the Glass a great Mass of Air, and such, that if you should take as much water, as the Mass of the Glass, and of the Air contained in it, you would have a weight much greater than that of the Viall, and of its Air: and, therefore, it will not submerge without great violence: but if we demit only the Glass into the water, which shall be when you shall fill the Glass with water, then shall the Glass descend to the Bottom; as superiour in Gravity to the water.

[21] The Authors answer to the first Objection.

[22] The Authors answer to the second Objection.

Returning, therefore, to our first purpose; I say, that Earth is more grave than water, and that therefore, a Solid of Earth goeth to the bottom of it; but one may possibly make a composition of Earth and Air, which shall be less grave than a like Mass of Water; and this shall swim: and yet both this and the other experiment shall very well accord with the Doctrine of _Archimedes_. But because that in my judgment it hath nothing of difficulty in it, I will not positively affirme that _Signor Buonamico_, would by such a discourse object unto _Archimedes_ the absurdity of inferring by his doctrine, that Earth was less grave than Water, though I know not how to conceive what other accident he could have induced thence.

Perhaps such a Probleme (in my judgement false) was read by _Signor Buonamico_ in some other Author, by whom peradventure it was attributed as a singular propertie, of some particular Water, and so comes now to be used with a double errour in confutation of _Archimedes_, since he saith no such thing, nor by him that did say it was it meant of the common Element of Water.

[Sidenote: The Authors answer to the third Objection.]

The third difficulty in the doctrine of _Archimedes_ was, that he could not render a reason whence it arose, that a piece of Wood, and a Vessell of Wood, which otherwise floats, goeth to the bottom, if filled with Water. _Signor Buonamico_ hath supposed that a Vessell of Wood, and of Wood that by nature swims, as before is said, goes to the bottom, if it be filled with water; of which he in the following Chapter, which is the 30 of the fifth Book copiously discourseth: but I (speaking alwayes without diminution of his singular Learning) dare in defence of _Archimedes_ deny this experiment, being certain that a piece of Wood which by its nature sinks not in Water, shall not sinke though it be turned and converted into the forme of any Vessell whatsoever, and then filled with Water: and he that would readily see the Experiment in some other tractable Matter, and that is easily reduced into several Figures, may take pure Wax, and making it first into a Ball or other solid Figure, let him adde to it so much Lead as shall just carry it to the bottome, so that being a graine less it could not be able to sinke it, and making it afterwards into the forme of a Dish, and filling it with Water, he shall finde that without the said Lead it shall not sinke, and that with the Lead it shall descend with much slowness: & in short he shall satisfie himself, that the Water included makes no alteration. I say not all this while, but that its possible of Wood to make Barkes, which being filled with water, sinke; but that proceeds not through its Gravity, encreased by the Water, but rather from the Nailes and other Iron Workes, so that it no longer hath a Body less grave than Water, but one mixt of Iron and Wood, more grave than a like Masse of Water. Therefore let _Signor Buonamico_ desist from desiring a reason of an effect, that is not in nature: yea if the sinking of the Woodden Vessell when its full of Water, may call in question the Doctrine of _Archimedes_, which he would not have you to follow, is on the contrary consonant and agreeable to the Doctrine of the Peripateticks, since it aptly assignes a reason why such a Vessell must, when its full of Water, descend to the bottom; converting the Argument the other way, we may with safety say that the Doctrine of _Archimedes_ is true, since it aptly agreeth with true experiments, and question the other, whose Deductions are fastened upon erroneouss Conclusions. As for the other point hinted in this same Instance, where it seemes that _Benonamico_ understands the same not only of a piece of wood, shaped in the forme of a Vessell, but also of massie Wood, which filled, _scilicet_, as I believe, he would say, soaked and steeped in Water, goes finally to the bottom that happens in some porose Woods, which, while their Porosity is replenished with Air, or other Matter less grave than Water, are Masses specificially less grave than the said Water, like as is that Viall of Glass whilest it is full of Air: but when, such light Matter departing, there succeedeth Water into the same Porosities and Cavities, there results a compound of Water and Glass more grave than a like Mass of Water: but the excess of its Gravity consists in the Matter of the Glass, and not in the Water, which cannot be graver than it self: so that which remaines of the Wood, the Air of its Cavities departing, if it shall be more grave _in specie_ than Water, fil but its Porosities with Water, and you shall have a Compost of Water and of Wood more grave than Water, but not by vertue of the Water received into and imbibed by the Porosities, but of that Matter of the Wood which remains when the Air is departed: and being such it shall, according to the Doctrine of _Archimedes_, goe to the bottom, like as before, according to the same Doctrine it did swim.

[Sidenote: The Authors answer to the fourth Objection.]

As to that finally which presents itself in the fourth place, namely, that the _Ancients_ have been heretofore confuted by _Aristotle_, who denying Positive and Absolute Levity, and truely esteeming all Bodies to be grave, said, that that which moved upward was driven by the circumambient Air, and therefore that also the Doctrine of _Archimedes_, as an adherent to such an Opinion was convicted and confuted: I answer first, that _Signor Buonamico_ in my judgement hath imposed upon _Archimedes_, and deduced from his words more than ever he intended by them, or may from his Propositions be collected, in regard that _Archimedes_ neither denies, nor admitteth Positive Levity, nor doth he so much as mention it: so that much less ought _Buonamico_ to inferre, that he hath denyed that it might be the Cause and Principle of the Ascension of Fire, and other Light Bodies[23]: having but only demonstrated, that Solid Bodies more grave than Water descend in it, according to the excess of their Gravity above the Gravity of that, he demonstrates likewise, how the less grave ascend in the same Water[24], accordng to its excess of Gravity, above the Gravity of them. So that the most that can be gathered from the Demonstration of _Archimedes_ is, that like as the excess of the Gravity of the Moveable above the Gravity of the Water, is the Cause that it descends therein, so the excess of the Gravity of the water above that of the Moveable, is a sufficient Cause why it descends not, but rather betakes it self to swim: not enquiring whether of moving upwards there is, or is not any other Cause contrary to Gravity: nor doth _Archimedes_ discourse less properly than if one should say: If the South Winde shall assault the Barke with greater _Impetus_ than is the violence with which the Streame of the River carries it towards the South, the motion of it shall be towards the North: but if the _Impetus_ of the Water shall overcome that of the Winde, its motion shall be towards the South. The discourse is excellent and would be unworthily contradicted by such as should oppose it, saying: Thou mis-alledgest as Cause of the motion of the Bark towards the South, the _Impetus_ of the Stream of the Water above that of the South Winde; mis-alledgest I say, for it is the Force of the North Winde opposite to the South, that is able to drive the Bark towards the South. Such an Objection would be superfluous, because he which alledgeth for Cause of the Motion the Stream of the Water, denies not but that the Winde opposite to the South may do the same, but only affirmeth that the force of the Water prevailing over the South Wind, the Bark shall move towards the South: and saith no more than is true. And just thus when _Archimedes_ saith, that the Gravity of the Water prevailing over that by which the moveable descends to the Bottom, such moveable shall be raised from the Bottom to the Surface alledgeth a very true Cause of such an Accident, nor doth he affirm or deny that there is, or is not, a vertue contrary to Gravity, called by some Levity, that hath also a power of moving some Matters upwards. Let therefore the Weapons of _Signor Buonamico_ be directed against _Plato_[25], and other _Ancients_, who totally denying _Levity_, and taking all Bodies to be grave, say that the Motion upwards is made, not from an intrinsecal Principle of the Moveable, but only by the Impulse of the _Medium_; and let _Archimedes_ and his Doctrine escape him, since he hath given him no Cause of quarelling with him. But if this Apologie, produced in defence of _Archimedes_, should seem to some insufficient to free him from the Objections and Arguments, produced by _Aristotle_ against _Plato_, and the other _Ancients_, as if they did also fight against _Archimedes_, alledging the Impulse of the Water as the Cause of the swimming of some Bodies less grave than it[26], I would not question, but that I should be able to maintaine the Doctrine of _Plato_ and those others to be most true, who absolutely deny Levity, and affirm no other Intrinsecal Principle of Motion to be in Elementary Bodies save only that towards the Centre of the Earth[27], nor no other Cause of moving upwards, speaking of that which hath the resemblance of natural Motion, but only the repulse of the _Medium_, fluid, and exceeding the Gravity of the Moveable[28]: and as to the Reasons of _Aristotle_ on the contrary, I believe that I could be able fully to answer them, and I would assay to do it, if it were absolutely necessary to the present Matter, or were it not too long a Digression for this short Treatise. I will only say, that if there were in some of our Ellementary Bodies an Intrinsecall Principle and Naturall Inclination to shun the Centre of the Earth, and to move towards the Concave of the Moon, such Bodies, without doubt, would more swiftly ascend through those _Mediums_ that least oppose the Velocity of the Moveable, and these are the more tenuous and subtle; as is, for example, the Air in comparison of the Water, we daily proving that we can with farre more expeditious Velocity move a Hand or a Board to and again in one than in the other[29]: nevertheless, we never could finde any Body, that did not ascend much more swiftly in the water than in the Air. Yea of Bodies which we see continually to ascend in the Water, there is none that having arrived to the confines of the Air, do not wholly lose their Motion[30]; even the Air it self, which rising with great Celerity through the Water, being once come to its Region it loseth all

[23] Of Natation, Lib. 1. Prop. 7.

[24] Of Natation, Lib. 1. Prop. 4.

[25] _Plato_ denyeth Positive Levity.

[26] The Authors defence of the doctrine of _Plato_ and the
_Ancients_, who absolutely deny Levity:

[27] According to _Plato_ there is no Principle of the Motion, of
descent in Naturall Bodies, save that to the Centre.

[28] No cause of the motion of Ascent, save the Impulse of the
_Medium_, exceeding the Moveable in Gravitie.

[29] Bodies ascend much swifter in the Water, than in the Air.

[30] All Bodies ascending through Water, lose their Motion,
comming to the confines of the Air.

[Sidenote: The lighter Bodies ascend more swiftly through Water.]

And, howbeit, Experience shewes, that the Bodies, successively less grave, do most expeditiously ascend in water, it cannot be doubted, but that the Ignean Exhalations do ascend more swiftly through the water, than doth the Air: which Air is seen by Experience to ascend more swiftly through the Water, than the Fiery Exhalations through the Air[31]: Therefore, we must of necessity conclude, that the said Exhalations do much more expeditiously ascend through the Water, than through the Air; and that, consequently, they are moved by the Impulse of the Ambient _Medium_, and not by an intrinsick Principle that is in them, of avoiding the Centre of the Earth; to which other grave Bodies tend.

[31] Fiery Exhalations ascend thorow the Water more swiftly than
doth the Air; & the Air ascends more swiftly thorow the Water,
than Fire thorow the Air.

[Sidenote: _T_he Authors confutation of the Peripateticks Causes
of Natation & Submersion.]

To that which for a finall conclusion, _Signor Buonamico_ produceth of going about to reduce the descending or not descending, to the easie and uneasie Division of the _Medium_, and to the predominancy of the Elements: I answer, as to the first part, that that cannot in any manner be admitted as a Cause, being that in none of the Fluid _Mediums_, as the Air, the Water, and other Liquids, there is any Resistance against Division[32], but all by every the least Force, are divided and penetrated, as I will anon demonstrate: so, that of such Resistance of Division there can be no Act, since it self is not in being. As to the other part, I say, that the predominancy of the Elements in Moveables[33], is to be considered, as far as to the excesse or defect of Gravity, in relation to the _Medium_: for in that Action, the Elements operate not, but only, so far as they are grave or light: therefore, to say that the Wood of the Firre sinks not, because Air predominateth in it, is no more than to say, because it is less grave than the Water. Yea, even the immediate Cause, is its being less grave than the Water[34]: and it being under the predominancy of the Air, is the Cause of its less Gravity: Therefore, he that alledgeth the predominancy of the Element for a Cause, brings the Cause of the Cause, and not the neerest and immediate Cause. Now, who knows not that the true Cause is the immediate, and not the mediate[35]? Moreover, he that alledgeth Gravity, brings a Cause most perspicuous to Sence[36]: The cause we may very easily assertain our selves; whether Ebony, for example, and Firre, be more or less grave than water: but whether Earth or Air predominates in them, who shall make that manifest? Certainly, no Experiment can better do it than to observe whether they swim or sink. So, that he who knows, not whether such a Solid swims, unless when he knows that Air predominates in it, knows not whether it swim, unless he sees it swim, for then he knows that it swims, when he knows that it is Air that predominates, but knows not that Air hath the predominance, unless he sees it swim: therefore, he knows not if it swims, till such time as he hath seen it swim.

[32] Water & other fluids void of Resistance against Division.

[33] _T_he predominancy of Elements in Moveables to be considered
only in relation to their excess or defect of Gravity in reference
to the _Medium_.

[34] _T_he immediate Cause of Natation is that the Moveable is
less grave than the Water.

[35] _T_he Peripateticks alledge for the reason of Natation the
Cause of the Cause.

[36] Gravity a Cause most perspicuous to sence.

Let us not then despise those Hints, though very dark, which Reason, after some contemplation, offereth to our Intelligence, and lets be content to be taught by _Archimedes_, that then any Body shall submerge in water[37], when it shall be specifically more grave than it, and that if it shall be less grave[38], it shall of necessity swim, and that it will rest indifferently in any place under water, if its Gravity be perfectly like to that of the water.

[37] Lib 1. of Natation Prop. 7

[38] Id. Lib. 1. Prop. 4.

These things explained and proved[39], I come to consider that which offers it self, touching what the Diversity of figure given unto the said Moveable hath to do with these Motions and Rests; and proceed to affirme, that,

[39] Id. Lib 1. Prop. 3.

THEOREME V.

[Sidenote: Diversity of Figure no Cause of its absolute Natation
or Submersion.]

_The diversity of Figures given to this or that Solid, cannot any
way be a Cause of its absolute Sinking or Swimming._

So that if a Solid being formed, for example, into a Sphericall Figure, doth sink or swim in the water, I say, that being formed into any other Figure, the same figure in the same water, shall sink or swim: nor can such its Motion by the Expansion or by other mutation of Figure, be impeded or taken away.

[Sidenote: The Expansion of Figure, retards the Velocity of the
ascent or descent of the Moveable in the water; but doth not
deprive it of all Motion.]

The Expansion of the Figure may indeed retard its Velocity, aswell of ascent as descent, and more and more according as the said Figure is reduced to a greater breadth and thinness: but that it may be reduced to such a form as that that same matter be wholly hindred from moving in the same water, that I hold to be impossible. In this I have met with great contradictors, who producing some Experiments, and in perticular a thin Board of Ebony, and a Ball of the same Wood, and shewing how the Ball in Water descended to the bottom, and the Board being put lightly upon the Water submerged not, but rested; have held, and with the Authority of _Aristotle_, confirmed themselves in their Opinions, that the Cause of that Rest was the breadth of the Figure, u{n}able by its small weight to pierce and penetrate the Resistance of the Waters Crassitude, which Resistance is readily overcome by the other Sphericall Figure.

This is the Principal point in the present Question, in which I perswade my self to be on the right side.

Therefore, beginning to investigate with the examination of exquisite Experiments that really the Figure doth not a jot alter the descent or Ascent of the same Solids, and having already demonstrated that the greater or less Gravity of the Solid in relation to the Gravity of the _Medium_ is the cause of Descent or Ascent: when ever we would make proof of that, which about this Effect the diversity of Figure worketh, its necessary to make the Experiment with Matter wherein variety of Gravities hath no place. For making use of Matters which may be different in their Specifical Gravities, and meeting with varieties of effects of Ascending and Descending, we shall alwayes be left unsatisfied whether that diversity derive it self really from the sole Figure, or else from the divers Gravity also. We may remedy this by takeing one only Matter, that is tractable and easily reduceable into every sort of Figure. Moreover, it will be an excellent expedient to take a kinde of Matter, exactly alike in Gravity unto the Water: for that Matter, as far as pertaines to the Gravity, is indifferent either to Ascend or Descend; so that we may presently observe any the least difference that derives it self from the diversity of Figure.

[Sidenote: An Experiment in Wax, that proveth Figure to have no
Operation in Natation & Submersion.]

Now to do this, Wax is most apt, which, besides its incapacity of receiveing any sensible alteration from its imbibing of Water, is ductile or pliant, and the same piece is easily reduceable into all Figures: and being _in Specie_ a very inconsiderable matter inferiour in Gravity to the Water, by mixing therewith a little of the fileings of Lead it is reduced to a Gravity exactly equall to that of the Water.

This Matter prepared, and, for example, a Ball being made thereof as bigge as an Orange or biger, and that made so grave as to sink to the bottom, but so lightly, that takeing thence one only Grain of Lead, it returns to the top, and being added, it submergeth to the bottom, let the same Wax afterwards be made into a very broad and thin Flake or Cake; and then, returning to make the same Experiment, you shall see that it being put to the bottom, it shall, with the Grain of Lead rest below, and that Grain deducted, it shall ascend to the very Surface, and added again it shall dive to the bottom. And this same effect shall happen alwaies in all sort of Figures, as wel regular as irregular: nor shall you ever finde any that will swim without the removall of the Grain of Lead, or sinke to the bottom unless it be added: and, in short, about the going or not going to the Bottom, you shall discover no diversity, although, indeed, you shall about the quick and slow descent: for the more expatiated and distended Figures move more slowly aswel in the diveing to the bottom as in the rising to the top; and the other more contracted and compact Figures, more speedily. Now I know not what may be expected from the diversity of Figures, if the most contrary to one another operate not so much as doth a very small Grain of Lead, added or removed.

Me thinkes I hear some of the Adversaries to raise a doubt upon my produced Experiment[40]. And first that they offer to my consideration, that the Figure, as a Figure simply, and disjunct from the Matter workes not any effect, but requires to be conjoyned with the Matter; and, furthermore, not with every Matter, but with those only, wherewith it may be able to execute the desired operation. Like as we see it verified by Experience, that the Acute and sharp Angle is more apt to cut, than the Obtuse; yet alwaies provided, that both the one and the other, be joyned with a Matter apt to cut, as for example, with Steel. Therefore, a Knife with a fine and sharp edge, cuts Bread or Wood with much ease, which it will not do, if the edge be blunt and thick: but he that will instead of Steel, take Wax, and mould it into a Knife, undoubtedly shall never know the effects of sharp and blunt edges: because neither of them will cut, the Wax being unable by reason of its flexibility, to overcome the hardness of the Wood and Bread. And, therefore, applying the like discourse to our purpose, they say, that the difference of Figure will shew different effects, touching Natation and Submersion, but not conjoyned with any kind of Matter, but only with those Matters which, by their Gravity, are apt to resist the Velocity of the water, whence he that would elect for the Matter, Cork or other light wood, unable, through its Levity, to superate the Crassitude of the water, and of that Matter should forme Solids of divers Figures, would in vain seek to find out what operation Figure hath in Natation or Submersion; because all would swim, and that not through any property of this or that Figure, but through the debility of the Matter, wanting so much Gravity, as is requisite to superate and overcome the Density and Crassitude of the water.

[40] An objection against the Experiment in Water.

Its needfull, therefore, if wee would see the effect wrought by the Diversity of Figure, first to make choice of a Matter of its nature apt to penetrate the Crassitude of the water. And, for this effect[41], they have made choice of such a Matter, as fit, that being readily reduced into Sphericall Figure, goes to the Bottom; and it is Ebony, of which they afterwards making a small Board or Splinter, as thin as a Lath, have illustrated how that this, put upon the Surface of the water, rests there without descending to the Bottom: and making, on the otherside, of the same wood a Ball, no less than a hazell Nut, they shew, that this swims not, but descendes. From which Experiment, they think they may frankly conclude, that the Breadth of the Figure in the flat Lath or Board, is the cause of its not descending to the Bottom, for as much as a Ball of the same Matter, not different from the Board in any thing but in Figure, submergeth in the same water to the Bottom. The discourse and the Experiment hath really so much of probability and likelyhood of truth in it, that it would be no wonder, if many perswaded by a certain cursory observation, should yield credit to it; nevertheless, I think I am able to discover, how that it is not free from falacy.

[41] An Experiment in Ebany, brought to disprove the Experiment
in Wax.

Beginning, therefore, to examine one by one, all the particulars that have been produced, I say, that Figures, as simple Figures, not only operate not in naturall things, but neither are they ever seperated from the Corporeall substance[42]: nor have I ever alledged them stript of sensible Matter, like as also I freely admit, that in our endeavouring to examine the Diversity of Accidents, dependant upon the variety of Figures, it is necessary to apply them to Matters, which obstruct not the various operations of those various Figures: and I admit and grant, that I should do very ill; if I would experiment the influence of Acutenesse of edge with a Knife of Wax, applying it to cut an Oak, because there is no Acuteness in Wax able to cut that very hard wood. But yet such an Experiment of this Knife, would not be besides the purpose, to cut curded Milk, or other very yielding Matter: yea, in such like Matters, the Wax is more commodious than Steel; for finding the diversity depending upon Angles, more or less Acute, for that Milk is indifferently cut with a Raisor, and with a Knife, that hath a blunt edge. It needs, therefore, that regard be had, not only to the hardness, solidity or Gravity of Bodies, which under divers figures, are to divide and penetrate some Matters, but it forceth also, that regard be had, on the other side, to the Resistance of the Matters, to be divided and penetrated. But since I have in making the Experiment concerning our Contest; chosen a Matter which penetrates the Resistance of the water; and in all figures descendes to the Bottome, the Adversaries can charge me with no defect; yea, I have propounded so much a more excellent Method than they, in as much as I have removed all other Causes, of descending or not descending to the Bottom, and retained the only sole and pure variety of Figures, demonstrating that the same Figures all descende with the only alteration of a Grain in weight: which Grain being removed, they return to float and swim; it is not true, therefore, (resuming the Example by them introduced) that I have gon{e} about to experiment the efficacy of Acuteness, in cutting with Matters unable to cut, but with Matters proportioned to our occasion, since they are subjected to no other variety, then that alone which depends on the Figure more or less acute.

[42] Figure is unseperable from Corporeall Substance.

[Sidenote: The answer to the Objection against the Experiment of
the Wax.]

But let us proceed a little farther, and observe, how that indeed the Consideration, which, they say, ought to be had about the Election of the Matter, to the end, that it may be proportionate for the making of our experiment, is needlessly introduced, declaring by the example of Cutting, that like as Acuteness is inefficient to cut, unless when it is in a Matter hard and apt to superate the Resistance of the wood or other Matter, which we intend to cut; so the aptitude of descending or not descending in water, ought and can only be known in those Matters, that are able to overcome the Renitence, and superate the Crassitude of the water. Unto which, I say, that to make distinction and election, more of this than of that Matter, on which to impress the Figures for cutting or penetrating this or that Body, as the solidity or obdurateness of the said Bodies shall be greater or less, is very necessary: but withall I subjoyn, that such distinction, election and caution would be superfluous and unprofitable, if the Body to be cut or penetrated, should have no Resistance, or should not at all withstand the Cutting or Penitration: and if the Knife were to be used in cutting a Mist or Smoak, one of Paper would be equally serviceable with one of _Damascus_ Steel: and so by reason the water hath not any Resistance against the Penitration of any Solid Body, all choice of Matter is superfluous and needless, and the Election which I said above to have been well made of a Matter reciprocall in Gravity to water, was not because it was necessary, for the overcoming of the crassitude of the water, but its Gravity, with which only it resists the sinking of Solid Bodies: and for what concerneth the Resistance of the crassitude, if we narrowly consider it, we shall find that all Solid Bodies, as well those that sink, as those that swim, are indifferently accomodated and apt to bring us to the knowledge of the truth in question. Nor will I be frighted out of the belief of these Conclusions, by the Experiments which may be produced against me, of many severall Woods, Corks, Galls, and, moreover, of subtle slates and plates of all sorts of Stone and Mettall, apt by means of their Naturall Gravity, to move towards the Centre of the Earth, the which, nevertheless, being impotent, either through the Figure (as the Adversaries thinke) or through Levity, to break and penetrate the Continuity of the parts of the water, and to distract its union, do continue to swimm without submerging in the least: nor on the other side, shall the Authority of _Aristotle_ move me, who in more than one place, affirmeth the contrary to this, which Experience shews me.

[Sidenote: No Solid of such Levity, nor of such Figure, but that
it doth penetrate the Crassitude of the Water.]

[Sidenote: Bodies of all Figures, laid upon the water, do
penetrate its Crassitude, and in what proportion.]

I return, therefore, to assert, that there is not any Solid of such Levity, nor of such Figure, that being put upon the water, doth not divide and penetrate its Crassitude: yea if any with a more perspicatious eye, shall return to observe more exactly the thin Boards of Wood, he shall see them to be with part of their thickness under water, and not only with their inferiour Superficies, to kisse the Superiour of the water, as they of necessity must have believed, who have said, that such Boards submerge not, as not being able to divide the Tenacity of the parts of the water: and, moreover, he shall see, that subtle shivers of Ebony, Stone or Metall, when they float, have not only broak the Continuity of the water, but are with all their thickness, under the Surface of it; and more and more, according as the Matters are more grave: so that a thin Plate of Lead, shall be lower than the Surface of the circumfused water, by at least twelve times the thickness of the Plate, and Gold shall dive below the Levell of the water, almost twenty times the thickness of the Plate, as I shall anon declare.

But let us proceed to evince, that the water yields and suffers it self to be penetrated by every the lightest Body; and therewithall demonstrate, how, even by Matters that submerge not, we may come to know that Figure operates nothing about the going or not going to the Bottom, seeing that the water suffers it self to be penetrated equally by every Figure.

[Sidenote: The Experiment of a Cone, demitted with its Base, and
after with its Point downwards.]

Make a Cone, or a Piramis of Cypress, of Firre, or of other Wood of like Gravity, or of pure Wax, and let its height be somewhat great, namely a handfull, or more, and put it into the water with the Base downwards: first, you shall see that it will penetrate the water, nor shall it be at all impeded by the largeness of the Base, nor yet shall it sink all under water, but the part towards the point shall lye above it: by which shall be manifest, first, that that Solid forbeares not to sink out of an inability to divide the Continuity of the water, having already divided it with its broad part, that in the opinion of the Adversaries is the less apt to make the division. The Piramid being thus fixed, note what part of it shall be submerged, and revert it afterwards with the point downwards, and you shall see that it shall not dive into the water more than before, but if you observe how far it shall sink, every person expert in Geometry, may measure, that those parts that remain out of the water, both in the one and in the other Experiment are equall to an hair: whence he may manifestly conclude, that the acute Figure which seemed most apt to part and penetrate the water, doth not part or penetrate it more than the large and spacious.

And he that would have a more easie Experiment, let him take two Cylinders of the same Matter, one long and small, and the other short, but very broad, and let him put them in the water, not distended, but erect and endways: he shall see, if he diligently measure the parts of the one and of the other, that in each of them the part submerged, retains exactly the same proportion to that out of the water, and that no greater part is submerged of that long and small one, than of the other more spacious and broad: howbeit, this rests upon a very large, and that upon a very little Superficies of water: therefore the diversity of Figure, occasioneth neither facility, nor difficulty, in parting and penetrating the Continuity of the water, and, consequently, cannot be the Cause of the Natation or Submersion. He may likewise discover the non operating of variety of Figures, in arising from the Bottom of the water, towards the Surface, by taking Wax, and tempering it with a competent quantity of the filings of Lead, so that it may become a considerable matter graver than the water: then let him make it into a Ball, and thrust it unto the Bottom of the water; and fasten to it as much Cork, or other light matter, as just serveth to raise it, and draw it towards the Surface: for afterwards changing the same Wax into a thin Cake, or into any other Figure, that same Cork shall raise it in the same manner to a hair.

This silenceth not my Antagonists, but they say, that all the discourse hitherto made by me little importeth to them, and that it serves their turn, that they have demonstrated in one only particular, and in what matter, and under what Figure pleaseth them, namely, in a Board and in a Ball of Ebony, that this put in the water, descends to the Bottom, and that stays atop to swim: and the Matter being the same, and the two Bodies differing in nothing but in Figure, they affirm, that they have with all perspicuity demonstrated and sensibly manifested what they undertook; and lastly, that they have obtained their intent. Nevertheless, I believe, and thinke, I can demonstrate, that that same Experiment proveth nothing against my Conclusion.

[Sidenote: In Experiments of Natation, the Solid is to be put
into, not upon the water.]

And first, it is false, that the Ball descends, and the Board not: for the Board shall also descend, if you do to both the Figures, as the words of our Question requireth; that is, if you put them both into the water.

[Sidenote: The Question of Natation stated.]

_The words were these. That the Antagonists having an opinion, that
the Figure would alter the Solid Bodies, in relation to the
descending or not descending, ascending or not ascending in the
same_ Medium, _as_ v. gr. _in the same water, in such sort, that, for
Example, a Solid that being of a Sphericall Figure, shall descend
to the Bottom, being reduced into some other Figure, shall not
descend: I holding the contrary, do affirm, that a Corporeall Solid
Body, which reduced into a Sphericall Figure, or any other, shall
go to the Bottom, shall do the like under whatsoever other Figure,
{&}c._

[Sidenote: Place defined according to Aristotle.]

But to be in the water, implies to be placed in the water, and by _Aristotles_ own Definition of place, to be placed, importeth to be invironed by the Superficies of the Ambient Body, therefore, then shall the two Figures be in the water, when the Superficies of the water, shall imbrace and inviron them: but when the Adversaries shew the Board of Ebony not descending to the Bottom, they put it not into the water, but upon the water, where being by a certain impediment (as by and by we will shew) retained, it is invironed, part by water, and part by air, which thing is contrary to our agreement, that was, that the Bodies should be in the water, and not part in water, and part in air.

_The which is again made manifest, by the questions being put as
well about the things which go to the Bottom, as those which arise
from the Bottom to swimme, and who sees not that things placed in
the Bottom, must have water about them._

[Sidenote: The confutation of the Experiment in the Ebany.]

It is now to be noted, that the Board of Ebany and the Ball, put into the water, both sink, but the Ball more swiftly, and the Board more slowly; and slower and slower, according as it shall be more broad and thin, and of this Tardity the breadth of the Figure is the true Cause: But these broad Boards that slowly descend, are the same, that being put lightly upon the water, do swimm: Therefore, if that were true which the Adversaries affirm, the same numerical Figure, would in the same numericall water, cause one while Rest, and another while Tardity of Motion, which is impossible: for every perticular Figure which descends to the Bottom[43], hath of necessity its own determinate Tardity and slowness, proper and naturall unto it, according to which it moveth, so that every other Tardity, greater or lesser is improper to its nature: if, therefore, a Board, as suppose of a foot square, descendeth naturally with six degrees of Tardity, it is impossible, that it should descend with ten or twenty, unless some new impediment do arrest it. Much less can it, by reason of the same Figure rest, and wholly cease to move; but it is necessary, that when ever it resteth, there do some greater impediment intervene than the breadth of the Figure. Therefore, it must be somewhat else, and not the Figure, that stayeth the Board of Ebany above water, of which Figure the only Effect is the retardment of the Motion, according to which it descendeth more slowly than the Ball. Let it be confessed, therefore, rationally discoursing, that the true and sole Cause of the Ebanys going to the Bottom, is the excess of its Gravity above the Gravity of the water: and the Cause of the greater or less Tardity, the breadth of this Figure, or the contractedness of that: but of its Rest, it can by no means be allowed, that the quallity of the Figure, is the Cause thereof: aswell, because, making the Tardity greater, according as the Figure more dilateth, there cannot be so immense a Dilatation, to which there may not be found a correspondent immence Tardity without redusing it to Nullity of Motion; as, because the Figures produced by the Antagonists for effecters of Rest, are the self same that do also go to the Bottom.

[43] Every perticular Figure hath its own peculiar Tardity.

I will not omit another reason, founded also upon Experience, and if I deceive not my self, manifestly concluding, how that the Introduction of the breadth or amplitude of Figure, and the Resistance of the water against penetration, have nothing to do in the Effect of descending, or ascending, or resting in the water. [D]Take a piece of wood or other Matter, of which a Ball ascends from the Bottom of the water to the Surface, more slowly than a Ball of Ebony of the same bignesse, so that it is manifest, that the Ball of Ebony more readily divideth the water in descending, than the other in ascending; as for Example, let the Wood be Walnut-tree. Then take a Board of Walnut-tree, like and equall to that of Ebony of the Antagonists, which swims; and if it be true, that this floats above water, by reason of the Figure, unable through its breadth, to pierce the Crassitude of the same, the other of Wallnut-tree, without all question, being thrust unto the Bottom, will stay there, as less apt, through the same impediment of Figure, to divide the said Resistance of the water. But if we shall find, and by experience see, that not only the thin Board, but every other Figure of the same Wallnut-tree will return to float, as undoubtedly we shall, then I must desier my opposers to forbear to attribute the floating of the Ebony, unto the Figure of the Board, in regard that the Resistance of the water is the same, as well to the ascent, as to the descent, and the force of the Wallnut-trees ascension, is lesse than the Ebonys force in going to the Bottom.

[D] The Figure & Resistance of the Medium against Division, have
nothing to do with the Effect of Natation or Submersion, by an
Experiment in Wallnut tree.

[Sidenote: An Experiment in Gold, to prove the non-operating of
Figure in Natation and Submersion.]

Nay, I will say more, that if we shall consider Gold in comparison of water, we shall find, that it exceeds it in Gravity almost twenty times, so that the Force and Impetus, wherewith a Ball of Gold goes to the Bottom, is very great. On the contrary, there want not matters, as Virgins Wax, and some Woods, which are not above a fiftieth part less grave than water, whereupon their Ascension therein is very slow, and a thousand times weaker than the _Impetus_ of the Golds descent: yet notwithstanding, a plate of Gold swims without descending to the Bottom, and, on the contrary, we cannot make a Cake of Wax, or thin Board of Wood, which put in the Bottom of the Water, shall rest there without ascending. Now if the Figure can obstruct the Penetration, and impede the descent of Gold, that hath so great an _Impetus_, how can it choose but suffice to resist the same Penetration of the other matter in ascending, when as it hath scarce a thousandth part of the _Impetus_ that the Gold hath in descending? Its therefore, necessary, that that which suspends the thin Plate of Gold, or Board of Ebony, upon the water, be some thing that is wanting to the other Cakes and Boards of Matters less grave than the water; since that being put to the Bottom, and left at liberty, they rise up to the Surface, without any obstruction: But they want not for flatness and breadth of Figure: Therefore, the spaciousnesse of the Figure, is not that which makes the Gold and Ebony to swim.

And, because, that the excess of their Gravity above the Gravity of the water, is questionless the Cause of the sinking of the flat piece of Ebony, and the thin Plate of Gold, when they go to the Bottom, therefore, of necessity, when they float, the Cause of their staying above water, proceeds from Levity, which in that case, by some Accident, peradventure not hitherto observed, cometh to meet with the said Board, rendering it no longer as it was before, whilst it did sink more ponderous than the water, but less.

Now, let us return to take the thin Plate of Gold, or of Silver, or the thin Board of Ebony, and let us lay it lightly upon the water, so that it stay there without sinking, and diligently observe its effect. And first, see how false the assertion of _Aristotle_, and our oponents is, to wit, that it stayeth above water, through its unability to pierce and penetrate the Resistance of the waters Crassitude: for it will manifestly appear, not only that the said Plates have penetrated the water, but also that they are a considerable matter lower than the Surface of the same, the which continueth eminent, and maketh as it were a Rampert on all sides, round about the said Plates, the profundity of which they stay swimming: and, according as the said Plates shall be more grave than the water, two, four, ten or twenty times, it is necessary, that their Superficies do stay below the universall Surface of the water, so much more, than the thickness of those Plates, as we shal more distinctly shew anon. In the mean space, for the more easie understanding of what I say, observe with me a little the present Scheme: in which let us suppose the Surface of the water to be distended, according to the Lines F L D B, upon which if one shall put a board of matter specifically more grave than water, but so lightly that it submerge not, it shall not rest any thing above, but shall enter with its whole thickness into the water: and, moreover, shall sink also, as we see by the Board A I, O I, whose breadth is wholly sunk into the water, the little Ramperts of water L A and D O incompassing it, whose Superficies is notably higher than the Superficies of the Board. See now whether it be true, that the said Board goes not to the Bottom, as being of Figure unapt to penetrate the Crassitude of the water.

[Sidenote: Why solids having penitrated the Water, do not proceed
to a totall Submersion.]