Page:Discourse Concerning the Natation of Bodies.djvu/54

COROLARY I.

Amongst Cones of the same Base, those of least Altitude shall sink the least.

That making upon the same Basis, a Cone of a less Altitude, it shall be also less grave, and shall so much the more rest without Submersion.

COROLARY II.

There may be Cones and Piramides of any Matter, which demitted with the Point downwards do float atop.

It is manifest, also, that one may make Cones and Piramids of any Matter whatsoever, more grave than the water, which being put into the water, with the Apix or Point downwards, rest without Submersion.

Because if we reassume what hath been above demonstrated, of Prisms and Cylinders, and that on Bases equall to those of the said Cylinders, we make Cones of the same Matter, and three times as high as the Cylinders, they shall rest afloat, for that in Mass and Gravity they shall be equall to those Cylinders, and by having their Bases equall to those of the Cylinders, they shall leave equall Masses of Air included within the Ramparts. This, which for Example sake hath been demonstrated, in Prisms, Cylinders, Cones and Piramids, might be proved in all other Solid Figures, but it would require a whole Volume (such is the multitude and variety of their Symptoms and Accidents) to comprehend the particuler demonstration of them all, and of their severall Segments: but I will to avoid prolixity in the present Discourse, content my self, that by what I have declared every one of ordinary Capacity may comprehend, that there is not any Matter so grave, no not Gold it self, of which one may not form all sorts of Figures, which by vertue of the superiour Air adherent to them, and not by the Waters Resistance of Penetration, do remain afloat, so that they sink not. Nay, farther, I will shew, for removing that Error, that,

THEOREME XI.

A Piramide or Cone, demitted with the Point downwards shal swim, with its Base downward shall sink.

A Piramide or Cone put into the Water, with the Point downward shall swimme, and the same put with the Base downwards shall sinke, and it shall be impossible to make it float.

Now the quite contrary would happen, if the difficulty of Penetrating the water, were that which had hindred the descent, for that the said Cone is far apter to pierce and penetrate with its sharp Point, than with its broad and spacious Base.

And, to demonstrate this, let the Cone be A B C, twice as grave as the water, and let its height be tripple to the height of the Rampart D A E C: I say, first, that being put lightly into the water with the

Point