Page:Discourse Concerning the Natation of Bodies.djvu/56

 tend to the bottom: Therefore, the whole Cone F T O, as well in respect of the part submerged, as the part above water shall descend to the bottom. But if the Altitude of the Point F N S, shall be half the Altitude of the whole Cone F T O, the same Altitude of the said Cone F N S shall be Sesquialter to the Altitude E N: and, therefore, E N S C shall be double to the Cone F N S; and as much water in Mass as the Cylinder E N S C, would weigh as much as the part of the Cone F N S. But, because the other immerged part N T O S, is double in Gravity to the water, a Mass of water equall to that compounded of the Cylinder E N S C, and of the Solid N T O S, shall weigh less than the Cone F T O, by as much as the weight of a Mass of water equall to the Solid N T O S: Therefore, the Cone sha l also descend. Again, because the Solid N T O S, is septuple to the Cone F N S, to which the Cylinder E S is double, the proportion of the Solid N T O S, shall be to the Cylinder E N S C, as seaven to two: Therefore, the whole Solid compounded of the Cylinder E N S C, and of the Solid N T O S, is much less than double the Solid N T O S: Therefore, the single Solid N T O S, is much graver than a Mass of water equall to the Mass, compounded of the Cylinder E N S C, and of N T O S.

Hat Cone, therefore, that with its Base upwards, and its Cuspis downwards doth swimme, being dimitted with its Base downward must of necessity sinke. They have argued farre from the truth, therefore, who have ascribed the cause of Natation to waters resistance of Division, as to a passive principle, and to the breadth of the Figure, with which the division is to be made, as the Efficient.

I come in the fourth place, to collect and conclude the reason of that which I have proposed to the Adversaries, namely,