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. [Illustration] COROLARY I. [Sidenote: Much less shall the said Cone swim, if one immerge a part thereof.] _I say farther; that much lesse shall the said Cone stay afloat, if one immerge a part thereof._ Which you may see, comparing with the water as well the part that shall immerge as the other above water. Let us therefore of the Cone A B D, submergeth part N T O S, and advance the Point N S F above water. The Altitude of the Cone F N S, shall either be more than half the whole Altitude of the Cone F T O, or it shall not be more: if it shall be more than half, the Cone F N S shall be more than half of the Cylinder E N S C: for the Altitude of the Cone F N S, shall be more than Sesquialter of the Altitude of the Cylinder E N S C: And, because the Matter of the Cone is supposed to be double in Specificall Gravity to the water, the water which would be contained within the Rampart E N S C, would be less grave absolutely than the Cone F N S; so that the whole Cone F N S cannot be sustained by the Rampart: But the part immerged N T O S, by being double in Specificall Gravity to the water, shall tend to the bottom: Therefore, the whole _C_one 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 _C_ylinder E N S C, would weigh as much as the part of the _C_one 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 _C_ylinder E N S C, and of the Solid N T O S, shall weigh less than the _C_one F T O, by as much as the weight of a Mass of water equall to the Solid N T O S: Therefore, the _C_one sha{l}l also descend. Again, because the Solid N T O S, is septuple to the Cone F N S, to which the _C_ylinder E S is double, the proportion of the Solid N T O S, shall be to the _C_ylinder E N S C, as seaven to two: Therefore, the whole Solid compounded of the _C_ylinder 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 _C_ylinder E N S C, and of N T O S.