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 downwards, it shall not descend to the bottom: for the Aeriall Cylinder contained betwixt the Ramparts D A C E, is equall in Mass to the Cone A B C; so that the whole Mass of the Solid compounded of the Air D A C E, and of the Cone A B C, shall be double to the Cone A C B: And, because the Cone A B C is supposed to be of Matter double in Gravity to the water, therefore as much water as the whole Masse D A B C E, placed beneath the Levell of the water, weighs as much as the Cone A B C: and, therefore, there shall be an Equilibrium, and the Cone A B C shall descend no lower. Now, I say farther, that the same Cone placed with the Base downwards, shall sink to the bottom, without any possibility of returning again, by any means to swimme.
Let, therefore, the Cone be A B D, double in Gravity to the water,
and let its height be tripple the height of the Rampart of water L B: It is already manifest, that it shall not stay wholly out of the water, because the Cylinder being comprehended betwixt the Ramparts L B D P, equall to the Cone A B D, and the Matter of the Cone, [beig double in Gravity] to the water, it is evident that the weight of the said Cone shall be double to the weight of the Mass of water equall to the Cylinder L B D P: Therefore it shall not rest in this state, but shall descend.