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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 AC, is to the Maſs C,

ſo is the abſolute weight of A C, to the abſolute weight of C: There

fore the abſolute weight of B, hath the ſame proportion to the abſo

lute weight of C, that the abſolute weight of A C, hath to the ab

ſolute weight of C: Therefore, the two Solids A C and B are equall

in abſolute Gravity: which was to be demonſtrated. Having de

monſtrated this, I ſay,

as the Maſs A C to the Maſs C: But as the Maſs AC, is to the Maſs C,

ſo is the abſolute weight of A C, to the abſolute weight of C: There

fore the abſolute weight of B, hath the ſame proportion to the abſo

lute weight of C, that the abſolute weight of A C, hath to the ab

ſolute weight of C: Therefore, the two Solids A C and B are equall

in abſolute Gravity: which was to be demonſtrated. Having de

monſtrated this, I ſay,

THEOREME X.

That it is poſſible of any aſſigned Matter, to form a Pi-

ramide or Cone upon any Baſe, which being put upon

the Water ſhall not ſubmerge, nor wet any more than

its Baſe.

ramide or Cone upon any Baſe, which being put upon

the Water ſhall not ſubmerge, nor wet any more than

its Baſe.

There may be

Cones and Pira

mides of any

Matter, which

demittedinto the

water, reſt only

their Baſes.

Cones and Pira

mides of any

Matter, which

demittedinto the

water, reſt only

their Baſes.

Let the greateſt poſſible Altitude of the Rampart be the Line D B,

and the Diameter of the Baſe of the Cone to be made of any Mat

ter aſſigned B C, at right angles to D B: And as the Specificall Gravity

of the Matter of the Piramide or Cone to be made, is to the Specificall

Gravity of the water, ſo let the Altitude of the

[Figure 13]

Rampart D B, be to the third part of the Piramide

or Cone A B C, deſcribed upon the Baſe, whoſe

Diameter is B C: I ſay, that the ſaid Cone A B C,

and any other Cone, lower then the ſame, ſhall reſt

upon the Surface of the water B C without ſinking.

Draw D F parallel to B C, and ſuppoſe the Priſme

or Cylinder E C, which ſhall be tripple to the Cone

A B C. And, becauſe the Cylinder D C hath the ſame proportion

to the Cylinder C E, that the Altitude D B, hath to the Altitude B E:

But the Cylinder C E, is to the Cone A B C, as the Altitude E B is to

the third part of the Altitude of the Cone: Therefore, by Equality of

proportion, the Cylinder D C is to the Cone A B C, as D B is to the

third part of the Altitude B E: But as D B is to the third part of B E,

ſo is the Specificall Gravity of the Cone A B C, to the Specificall Gra

vity of the water: Therefore, as the Maſs of the Solid D C, is to the

Maſs of the Cone A B C, ſo is the Specificall Gravity of the ſaid Cone,

to the Specificall Gravity of the water: Therefore, by the precedent

Lemma, the Cone A B C weighs in abſolute Gravity as much as a

Maſs of Water equall to the Maſs D C: But the water which by the

impoſition of the Cone A B C, is driven out of its place, is as much

as would preciſely lie in the place D C, and is equall in weight to the

Cone that diſplaceth it: Therefore, there ſhall be an Equilibrium,

and the Cone ſhall reſt without farther ſubmerging. And its ma

nifeſt,

and the Diameter of the Baſe of the Cone to be made of any Mat

ter aſſigned B C, at right angles to D B: And as the Specificall Gravity

of the Matter of the Piramide or Cone to be made, is to the Specificall

Gravity of the water, ſo let the Altitude of the

[Figure 13]

Rampart D B, be to the third part of the Piramide

or Cone A B C, deſcribed upon the Baſe, whoſe

Diameter is B C: I ſay, that the ſaid Cone A B C,

and any other Cone, lower then the ſame, ſhall reſt

upon the Surface of the water B C without ſinking.

Draw D F parallel to B C, and ſuppoſe the Priſme

or Cylinder E C, which ſhall be tripple to the Cone

A B C. And, becauſe the Cylinder D C hath the ſame proportion

to the Cylinder C E, that the Altitude D B, hath to the Altitude B E:

But the Cylinder C E, is to the Cone A B C, as the Altitude E B is to

the third part of the Altitude of the Cone: Therefore, by Equality of

proportion, the Cylinder D C is to the Cone A B C, as D B is to the

third part of the Altitude B E: But as D B is to the third part of B E,

ſo is the Specificall Gravity of the Cone A B C, to the Specificall Gra

vity of the water: Therefore, as the Maſs of the Solid D C, is to the

Maſs of the Cone A B C, ſo is the Specificall Gravity of the ſaid Cone,

to the Specificall Gravity of the water: Therefore, by the precedent

Lemma, the Cone A B C weighs in abſolute Gravity as much as a

Maſs of Water equall to the Maſs D C: But the water which by the

impoſition of the Cone A B C, is driven out of its place, is as much

as would preciſely lie in the place D C, and is equall in weight to the

Cone that diſplaceth it: Therefore, there ſhall be an Equilibrium,

and the Cone ſhall reſt without farther ſubmerging. And its ma

nifeſt,