Page:Discourse Concerning the Natation of Bodies.djvu/58

56 Cone weighing equally with the water, the part submerged S B D T, becomes indifferent to move downwards or upwards; and the Cone A S T, being equall in Mass to the water that would be contained in the concave of the Rampart E S T O, shall be also equall unto it in Gravity: and, therefore, there shall be a perfect Equilibrium, and, consequently, a Rest. Now here ariseth a doubt, whether the Cone A B D may be made heavier, in such sort, that when it is put wholly under water, it goes to the bottom, but yet not in such sort, as to take from the Rampart the vertue of sustaining it that it sink not, and, the reason of the doubt is this: that although at such time as the Cone A B D is specifically as grave as the water, the Rampart E S T O sustaines it, not only when the point A S T is tripple in height to the Altitude of the Rampart E S, but also when a lesser part is above water; [for although in the Descent of the Cone the Point A S T by little and little diminisheth, and so likewise the Rampart E S T O, yet the Point diminisheth in greater proportion than the Rampart, in that it diminisheth according to all the three Dimensions, but the Rampart according to two only, the Altitude still remaining the same; or, if you will, because the Cone S T goes diminishing, according to the proportion of the cubes of the Lines that do successively become the Diameters of the Bases of emergent Cones, and the Ramparts diminish according to the proportion of the Squares of the same Lines; whereupon the proportions of the Points are alwayes Sesquialter of the proportions of the Cylinders, contained within the Rampart; so that if, for Example, the height of the emergent Point were double, or equall to the height of the Rampart, in these cases, the Cylinder contained within the Rampart, would be much greater than the said Point, because it would be either sesquialter or tripple, by reason of which it would perhaps serve over and above to sustain the whole Cone, since the part submerged would no longer weigh any thing;] yet, nevertheless, when any Gravity is added to the whole Mass of the Cone, so that also the part submerged is not without some excesse of Gravity above the Gravity of the water, it is not manifest, whether the Cylinder contained within the Rampart, in the descent that the Cone shall make, can be reduced to such a proportion unto the emergent Point, and to such an excesse of Mass above the Mass of it, as to compensate the excesse of the Cones Specificall Gravity above the Gravity of the water: and the Scruple ariseth, because that howbeit in the descent made by the Cone, the emergent Point A S T diminisheth, whereby there is also a diminution of the excess of the Cones Gravity above Rh