Page:Discourse Concerning the Natation of Bodies.djvu/57

 THEOREME XII.

He truth of this Proposition is sufficiently manifest in all those Solid Figures, that determine in their uppermost part in a plane Superficies: for making such Figures of some Matter specifically as grave as the water, putting them into the water, so that the whole Mass be covered, it is manifest, that they shall rest in all places, provided, that such a Matter equall in weight to the water, may be exactly adjusted: and they shall by consequence, rest or lie even with the Levell of the water, without making any Rampart. If, therefore, in respect of the Matter, such Figures are apt to rest without submerging, though deprived of the help of the Rampart, it is manifest, that they may admit so much encrease of Gravity, (without encreasing their Masses) as is the weight of as much water as would be contained within the Rampart, that is made about their upper plane Surface: by the help of which being sustained, they shall rest afloat, but being bathed, they shall descend, having been made graver than the water. In Figures, therefore, that determine above in a plane, we may cleerly comprehend, that the Rampart added or removed, may prohibit or permit the descent: but in those Figures that go lessening upwards towards the top, some Persons may, and that not without much seeming Reason, doubt whether the same may be done, and especially by those which terminate in a very acute Point, such as are your Cones and small Piramids. Touching these, therefore, as more dubious than the rest, I will endeavour to demonstrate, that they also lie under the same Accident of going, or not going to the Bottom, be they of any whatever bigness. Let therefore the Cone be A B D, made of a matter specifically as grave as the water; it is manifest that being put all under water, it shall rest in all places (alwayes provided, that it shall weigh exactly as much as the water, which is almost impossible to effect) and that any small weight being added to it, it shall sink to the bottom: but if it shall descend downwards gently, I say, that it shall make the Rampart E S T O, and that there shall stay out of the water the point A S T, tripple in height to the Rampart E S: which is manifest, for the Matter of Rh