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THEOREME. IX.

All Figures

of all Matters,

float by hep of

the Rampart re

pleniſhed with

Air, and ſome

but only touch

the water.

of all Matters,

float by hep of

the Rampart re

pleniſhed 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 Ram

part, 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.

grave than the Water, do by Benefit of the ſaid Ram

part, 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 up

wards, grow leſſer and leſſer; the which we ſhall exemplifie for

this time in Piramides or Cones, of which Figures the paſſions sre

common. We will demonſtrate therefore, that,

wards, grow leſſer and leſſer; the which we ſhall exemplifie for

this time in Piramides or Cones, of which Figures the paſſions sre

common. We will demonſtrate therefore, that,

It is poſſible to form a Piramide, of any whatſoever Matter propoſed,

which being put with its Baſe upon the Water, reſts not only without

ſubmerging, but without wetting it more then its Baſe.

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,

the ſubſequent Lemma, namely, that,

LEMMA II.

Solids whoſe

Maſſes are in

contrary pro

portion to their

Specifick Gra

vities, are equall

in abſolute Gra

vity.

Maſſes are in

contrary pro

portion to their

Specifick Gra

vities, are equall

in abſolute Gra

vity.

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 Speci

ficall Gravity of the Solid A C: I ſay, the Solids A C and B are

equall in abſolute weight, that is, equally grave. For

[Figure 12]

if the Maſs A C be equall to the Maſs B, then, by the

Aſſumption, the Specificall Gravity of B, ſhall be e

quall to the Specificall Gravity of A C, and being e

quall 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 pro

portion 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:

Maſs B, as the Specificall Gravity of the Solid B, is to the Speci

ficall Gravity of the Solid A C: I ſay, the Solids A C and B are

equall in abſolute weight, that is, equally grave. For

[Figure 12]

if the Maſs A C be equall to the Maſs B, then, by the

Aſſumption, the Specificall Gravity of B, ſhall be e

quall to the Specificall Gravity of A C, and being e

quall 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 pro

portion 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: