Part 4 (2/2)

+If any Solide Magnitude, Lighter then a Liquor, be let downe into the same Liquor, the waight of the same Magnitude, will be, to the Waight of the Liquor. (Which is aequall in quant.i.tie to the whole Magnitude,) in that proportion, that the parte, of the Magnitude settled downe, is to the whole Magnitude.+

By these verities, great Errors may be reformed, in Opinion of the Naturall Motion of thinges, Light and Heauy. Which errors, are in Naturall Philosophie (almost) of all m? allowed: to much trusting to Authority: and false Suppositions. As, +Of any two bodyes, the heauyer, to moue downward faster then the lighter.+

[A common error, noted.]

This error, is not first by me, Noted: but by one _Iohn Baptist de Benedictis_. The chief of his propositions, is this: which seemeth a Paradox.

+If there be two bodyes of one forme, and of one kynde, aequall in quant.i.tie or vnaequall,

[A paradox.]

they will moue by aequall s.p.a.ce, in aequall tyme: So that both theyr mouynges be in ayre, or both in water: or in any one Middle.+

Hereupon, in the feate of +Gunnyng+,

[N. T.]

certaine good discourses (otherwise) may receiue great amendement, and furderance.

[The wonderfull vse of these Propositions.]

In the entended purpose, also, allowing somwhat to the imperfection of Nature: not aunswerable to the precisenes of demonstration. Moreouer, by the foresaid propositions (wisely vsed.) The Ayre, the water, the Earth, the Fire, may be nerely, knowen, how light or heauy they are (Naturally) in their a.s.signed partes: or in the whole. And then, to thinges Elementall, turning your practise: you may deale for the proportion of the Elementes, in the thinges Compounded. Then, to the proportions of the Humours in Man: their waightes: and the waight of his bones, and flesh. &c. Than, by waight, to haue consideration of the Force of man, any maner of way: in whole or in part. Then, may you, of s.h.i.+ps water drawing, diuersly, in the Sea and in fresh water, haue pleasant consideration: and of waying vp of any thing, sonken in Sea or in fresh water &c. And (to lift vp your head a loft:) by waight, you may, as precisely, as by any instrument els, measure the Diameters of _Sonne_ and _Mone. &c._ Frende, I pray you, way these thinges, with the iust Balance of Reason. And you will finde Meruailes vpon Meruailes: And esteme one Drop of Truth (yea in Naturall Philosophie) more worth, then whole Libraries of Opinions, vndemonstrated: or not aunswering to Natures Law, and your experience. Leauing these thinges, thus: I will giue you two or three, light practises, to great purpose: and so finish my Annotation _Staticall_. In Mathematicall matters, by the Mechaniciens ayde, we will behold, here, the Commodity of waight.

[The practise Staticall, to know the proportion, betwene the Cube, and the Sphaere.]

Make a Cube, of any one Vniforme: and through like heauy stuffe: of the same Stuffe, make a Sphaere or Globe, precisely, of a Diameter aequall to the Radicall side of the Cube. Your stuffe, may be wood, Copper, Tinne, Lead, Siluer. &c. (being, as I sayd, of like nature, condition, and like waight throughout.) And you may, by Say Balance, haue prepared a great number of the smallest waightes: which, by those Balance can be discerned or tryed: and so, haue proceded to make you a perfect Pyle, company & Number of waightes: to the waight of six, eight, or twelue pound waight: most diligently tryed, all. And of euery one, the Content knowen, in your least waight, that is wayable. [They that can not haue these waightes of precisenes: may, by Sand, Vniforme, and well dusted, make them a number of waightes, somewhat nere precisenes: by halfing euer the Sand: they shall, at length, come to a least common waight.

Therein, I leaue the farder matter, to their discretion, whom nede shall pinche.] The _Venetians_ consideration of waight, may seme precise enough: by eight descentes progressionall, * halfing, from a grayne.

[I. D.

* For, so, haue you .256. partes of a Graine.]

Your Cube, Sphaere, apt Balance, and conuenient waightes, being ready: fall to worke.?. First, way your Cube. Note the Number of the waight.

Way, after that, your Sphaere. Note likewise, the Nuber of the waight. If you now find the waight of your Cube, to be to the waight of the Sphaere, as 21. is to 11: Then you see, how the Mechanicien and _Experimenter_, without Geometrie and Demonstration, are (as nerely in effect) tought the proportion of the Cube to the Sphere: as I haue demonstrated it, in the end of the twelfth boke of _Euclide_. Often, try with the same Cube and Sphaere. Then, chaunge, your Sphaere and Cube, to an other matter: or to an other bignes: till you haue made a perfect vniuersall Experience of it. Possible it is, that you shall wynne to nerer termes, in the proportion.

When you haue found this one certaine Drop of Naturall veritie, procede on, to Inferre, and duely to make a.s.say, of matter depending. As, bycause it is well demonstrated, that a Cylinder, whose heith, and Diameter of his base, is aequall to the Diameter of the Sphaere, is Sesquialter to the same Sphaere (that is, as 3. to 2:) To the number of the waight of the Sphaere, adde halfe so much, as it is: and so haue you the number of the waight of that Cylinder. Which is also Comprehended of our former Cube: So, that the base of that Cylinder, is a Circle described in the Square, which is the base of our Cube. But the Cube and the Cylinder, being both of one heith, haue their Bases in the same proportion, in the which, they are, one to an other, in their Ma.s.sines or Soliditie. But, before, we haue two numbers, expressing their Ma.s.sines, Solidities, and Quant.i.ties, by waight: wherfore,

[* =The proportion of the Square to the Circle inscribed.=]

we haue * the proportion of the Square, to the Circle, inscribed in the same Square. And so are we fallen into the knowledge sensible, and Experimentall of _Archimedes_ great Secret: of him, by great trauaile of minde, sought and found. Wherfore, to any Circle giuen, you can giue a Square aequall:

[* =The Squaring of the Circle, Mechanically.=]

* as I haue taught, in my Annotation, vpon the first proposition of the twelfth boke, And likewise, to any Square giuen, you may giue a Circle aequall:

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