- None
- Concordance
- Figures
- Thumbnails

the Gravity of the water, yet the caſe ſtands ſo, that the Rampart

doth alſo contract it ſelf, and the Cylinder contained in it doth de

miniſh. Nevertheleſs it ſhall be demonſtrated, how that the Cone

A B D being of any ſuppoſed bigneſſe, and made at the firſt of a

Matter exactly equall in Gravity to the Water, if there may

be affixed to it ſome Weight, by means of which it may deſcend to

the bottom, when ſubmerged under water, it may alſo by vertue of

the Rampart ſtay above without ſinking.

doth alſo contract it ſelf, and the Cylinder contained in it doth de

miniſh. Nevertheleſs it ſhall be demonſtrated, how that the Cone

A B D being of any ſuppoſed bigneſſe, and made at the firſt of a

Matter exactly equall in Gravity to the Water, if there may

be affixed to it ſome Weight, by means of which it may deſcend to

the bottom, when ſubmerged under water, it may alſo by vertue of

the Rampart ſtay above without ſinking.

Let, therefore, the Cone A B D be of any ſuppoſed greatneſſe,

and alike in ſpecificall Gravity to the water. It is manifeſt, that

being put lightly into the water, it ſhall reſt without deſcending;

and it ſhall advance above water, the Point

[Figure 18]

AS T, tripple in height to the height of the

Rampart E S: Now, ſuppoſe the Cone A B D

more depreſſed, ſo that it advance above wa

ter, only the Point A I R, higher by half than

the Point A S T, with the Rampart about it

C I R N. And, becauſe, the Cone A B D is

to the Cone A I R, as the cube of the Line S T

is to the cube of the Line I R, but the Cylin

der E S T O, is to the Cylinder C I R N, as the Square of S T to

the Square of I R, the Cone A S T ſhall be Octuple to the Cone

A I R, and the Cylinder E S T O, quadruple to the Cylinder C I R N:

But the Cone A S T, is equall to the Cylinder E S T O: Therefore,

the Cylinder C I R N, ſhall be double to the Cone A I R: and the

water which might be contained in the Rampart C I R N, would be

double in Maſs and in Weight to the Cone A I R, and, therefore,

would be able to ſuſtain the double of the Weight of the Cone AIR:

Therefore, if to the whole Cone A B D, there be added as much

Weight as the Gravity of the Cone A I R, that is to ſay, the eighth

part of the weight of the Cone A S T, it alſo ſhall be ſuſtained by

the Rampart C I R N, but without that it ſhall go to the bottome:

the Cone A B D, being, by the addition of the eighth part of the

weight of the Cone A S T, made ſpecifically more grave than the

water. But if the Altitude of the Cone A I R, were two thirds

of the Altitude of the Cone A S T, the Cone A S T would be to the

Cone A I R, as twenty ſeven to eight; and the Cylinder E S T O, to

the Cylinder C I R N, as nine to four, that is, as twenty ſeven to

twelve; and, therefore, the Cylinder C I R N, to the Cone A I R,

as twelve to eight; and the exceſs of the Cylinder C I R N, above

the Cone A I R, to the Cone A S T, as four to twenty ſeven: there

fore if to the Cone A B D be added ſo much weight as is the four

twenty ſevenths of the weight of the Cone A S T, which is a little

more then its ſeventh part, it alſo ſhall continue to ſwimme, and

and alike in ſpecificall Gravity to the water. It is manifeſt, that

being put lightly into the water, it ſhall reſt without deſcending;

and it ſhall advance above water, the Point

[Figure 18]

AS T, tripple in height to the height of the

Rampart E S: Now, ſuppoſe the Cone A B D

more depreſſed, ſo that it advance above wa

ter, only the Point A I R, higher by half than

the Point A S T, with the Rampart about it

C I R N. And, becauſe, the Cone A B D is

to the Cone A I R, as the cube of the Line S T

is to the cube of the Line I R, but the Cylin

der E S T O, is to the Cylinder C I R N, as the Square of S T to

the Square of I R, the Cone A S T ſhall be Octuple to the Cone

A I R, and the Cylinder E S T O, quadruple to the Cylinder C I R N:

But the Cone A S T, is equall to the Cylinder E S T O: Therefore,

the Cylinder C I R N, ſhall be double to the Cone A I R: and the

water which might be contained in the Rampart C I R N, would be

double in Maſs and in Weight to the Cone A I R, and, therefore,

would be able to ſuſtain the double of the Weight of the Cone AIR:

Therefore, if to the whole Cone A B D, there be added as much

Weight as the Gravity of the Cone A I R, that is to ſay, the eighth

part of the weight of the Cone A S T, it alſo ſhall be ſuſtained by

the Rampart C I R N, but without that it ſhall go to the bottome:

the Cone A B D, being, by the addition of the eighth part of the

weight of the Cone A S T, made ſpecifically more grave than the

water. But if the Altitude of the Cone A I R, were two thirds

of the Altitude of the Cone A S T, the Cone A S T would be to the

Cone A I R, as twenty ſeven to eight; and the Cylinder E S T O, to

the Cylinder C I R N, as nine to four, that is, as twenty ſeven to

twelve; and, therefore, the Cylinder C I R N, to the Cone A I R,

as twelve to eight; and the exceſs of the Cylinder C I R N, above

the Cone A I R, to the Cone A S T, as four to twenty ſeven: there

fore if to the Cone A B D be added ſo much weight as is the four

twenty ſevenths of the weight of the Cone A S T, which is a little

more then its ſeventh part, it alſo ſhall continue to ſwimme, and