Page:Discourse Concerning the Natation of Bodies.djvu/52

THEOREME. IX.

All Figures of all Matters, float by hep of the Rampart replenished with Air, and some but only touch the water.

All sorts of Figures of whatsoever Matter, albeit more grave than the Water, do by Benefit of the said Rampart, not only float, but some Figures, though of the gravest Matter, do stay wholly above Water, wetting only the inferiour Surface that toucheth the Water.

And these shall be all Figures, which from the inferiour Base upwards, grow lesser and lesser; the which we shall exemplifie for this time in Piramides or Cones, of which Figures the passions are common. We will demonstrate therefore, that,

It is possible to form a Piramide, of any whatsoever Matter preposed, which being put with its Base upon the Water, rests not only without submerging, but without wetting it more then its Base.

For the explication of which it is requisite, that we first demonstrate the subsequent Lemma, namely, that,

LEMMA II.

Solids whose Masses are in contrary proportion to their Specifick Gravities, ate equall in absolute Gravity.

Solids whose Masses answer in proportion contrarily to their Specificall Gravities, are equall in Absolute Gravities.

Let A C and B be two Solids, and let the Mass A C be to the Mass B, as the Specificall Gravity of the Solid B, is to the Specificall Gravity of the Solid A C: I say, the Solids A C and B are equall in absolute weight, that is, equally grave. For if the Mass A C be equall to the Mass B, then, by the Assumption, the Specificall Gravity of B, shall be equall to the Specificall Gravity of A C, and being equall in Mass, and of the same Specificall Gravity they shall absolutely weigh one as much as another. But if their Masses shall be unequall, let the Mass A C be greater, and in it take the part C, equall to the Mass B. And, because the Masses B and C are equall; the Absolute weight of B, shall have the same proportion to the Absolute weight of C, that the Specificall Gravity of B, hath to the Specificall Gravity of C; or of C A, which is the same in specie: But look what proportion the Specificall Gravity of B, hath to the Specificall Gravity of C A, the like proportion, by the Assumption, hath the Mass C A, to the Mass B; that is, to the Mass C: