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. [Sidenote: Solids whose Masses are in contrary proportion to their Specifick Gravities are equall in absolute Gravity.] _Solids whose Masses answer in proportion contrarily to their Specificall Gravities, are equall in Absolute Gravities._ [Illustration] 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: Therefore, the absolute weight of B, to the absolute weight of C, is as the Mass A C to the Mass C: But as the Mass A C, is to the Mass C, so is the absolute weight of A C, to the absolute weight of C: Therefore the absolute weight of B, hath the same proportion to the absolute weight of C, that the absolute weight of A C, hath to the absolute weight of C: Therefore, the two Solids A C and B are equall in absolute Gravity: which was to be demonstrated. Having demonstrated this, I say, THEOREME X. [Sidenote: There may be Cones and Piramides of any Matter, which demitted into the water, rest only their Bases.] _That it is possible of any assigned Matter, to form a Piramide or Cone upon any Base, which being put upon the Water shall not submerge, nor wet any more than its Base._ [Illustration]