A Discourse Presented to the Most Serene Don Cosimo II., Great Duke of Tuscany, Concerning the Natation of Bodies Vpon, and Submersion In, t · Galileo Galilei
COROLARY I.
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. [Sidenote: Part of the Cones towards the Cuspis removed, it shall still sink.] _From whence it followeth, that though one should remove and take away the part of the Cone F N S, the sole remainder N T O S would go to the bottom._
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