Page:Discourse Concerning the Natation of Bodies.djvu/59

Rh the Gravity of the water, yet the case stands so, that the Rampart doth also contract it self, and the Cylinder contained in it doth deminish. Nevertheless it shall be demonstrated, how that the Cone A B D being of any supposed bignesse, and made at the first of a Matter exactly equall in Gravity to the Water, if there may be affixed to it some Weight, by means of which it may descend to the bottom, when submerged under water, it may also by vertue of the Rampart stay above without sinking.

Let, therefore, the Cone A B D be of any supposed greatnesse, and alike in specificall Gravity to the water. It is manifest, that being put lightly into the water, it shall rest without descending; and it shall advance above water, the Point AS T, tripple in height to the height of the Rampart E  S: Now, suppose the Cone A B D more depressed, so that it advance above water, only the Point A I R, higher by half than the Point A S T, with the Rampart about it C I R N. And, because, the Cone A B D is to the Cone A I R, as the cube of the Line S T is to the cube of the Line I R, but the Cylinder E S T O, is to the Cylinder C I R N, as the Square of S T to the Square of I R, the Cone A S T shall be Octuple to the Cone A I R, and the Cylinder E S T O, quadruple to the Cylinder C I R N: But the Cone A S T, is equall to the Cylinder E S T O: Therefore, the Cylinder C I R N, shall be double to the Cone A I R: and the water which might be contained in the Rampart C I R N, would be double in Mass and in Weight to the Cone A I R, and, therefore, would be able to sustain the double of the Weight of the Cone AIR: Therefore, if to the whole Cone A B D, there be added as much Weight as the Gravity of the Cone A I R, that is to say, the eighth part of the weight of the Cone A S T, it also shall be sustained by the Rampart C I R N, but without that it shall go to the bottome: the Cone A B D, being, by the addition of the eighth part of the weight of the Cone A S T, made specifically more grave than the water. But if the Altitude of the Cone A I R, were two thirds of the Altitude of the Cone A S T, the Cone A S T would be to the Cone A I R, as twenty seven to eight; and the Cylinder E S T O, to the Cylinder C I R N, as nine to four, that is, as twenty seven to twelve; and, therefore, the Cylinder C I R N, to the Cone A I R, as twelve to eight; and the excess of the Cylinder C I R N, above the Cone A I R, to the Cone A S T, as four to twenty seven: therefore if to the Cone A B D be added so much weight as is the four twenty sevenths of the weight of the Cone A S T, which is a little more then its seventh part, it also shall continue to swimme, and Rh