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Cone weighing equally with the water, the part ſubmerged S B D T,

becomes indifferent to move downwards or upwards; and the Cone

A S T, being equall in Maſs to the water that would be contained in

the concave of the Rampart E S T O, ſhall be alſo equall unto it in

Gravity: and, therefore, there ſhall be a perfect Equilibrium, and,

conſequently, a Reſt. Now here ariſeth a doubt, whether the

Cone A B D may be made heavier, in ſuch ſort, that when it is put

wholly under water, it goes to the bottom, but yet not in ſuch ſort,

as to take from the Rampart the vertue of ſuſtaining it that it ſink not,

and, the reaſon of the doubt is this: that although at ſuch time as

the Cone A B D is ſpecifically as grave as the water, the Rampart

E S T O ſuſtaines it, not only when the point A S T is tripple in

height to the Altitude of the Rampart E S, but alſo when a leſſer

part is above water; [for although in the Deſcent of the Cone the

Point A S T by little and little diminiſheth, and ſo likewiſe the

Rampart E S T O, yet the Point diminiſheth in

[Figure 17]

greater proportion than the Rampart, in that

it diminiſheth according to all the three Di

menſions, but the Rampart according to two

only, the Altitude ſtill remaining the ſame;

or, if you will, becauſe the Cone S T goes di

miniſhing, according to the proportion of the

cubes of the Lines that do ſucceſſively become

the Diameters of the Baſes of emergent Cones,

and the Ramparts diminiſh according to the proportion of the

Squares of the ſame Lines; whereupon the proportions of the Points

are alwayes Seſquialter of the proportions of the Cylinders, con

tained within the Rampart; ſo that if, for Example, the height of

the emergent Point were double, or equall to the height of the

Rampart, in theſe caſes, the Cylinder contained within the Ram

part, would be much greater than the ſaid Point, becauſe it would be

either ſeſquialter or tripple, by reaſon of which it would perhaps

ſerve over and above to fuſtain the whole Cone, ſince the part ſub

merged would no longer weigh any thing;] yet, nevertheleſs, when

any Gravity is added to the whole Maſs of the Cone, ſo that alſo the

part ſubmerged is not without ſome exceſſe of Gravity above the

Gravity of the water, it is not manifeſt, whether the Cylinder con

tained within the Rampart, in the deſcent that the Cone ſhall make,

can be reduced to ſuch a proportion unto the emergent Point, and to

ſuch an exceſſe of Maſs above the Maſs of it, as to compenſate the

exceſſe of the Cones Specificall Gravity above the Gravity of the wa

ter: and the Scruple ariſeth, becauſe that howbeit in the deſcent

made by the Cone, the emergent Point A S T diminiſheth, whereby

there is alſo a diminution of the exceſs of the Cones Gravity above

becomes indifferent to move downwards or upwards; and the Cone

A S T, being equall in Maſs to the water that would be contained in

the concave of the Rampart E S T O, ſhall be alſo equall unto it in

Gravity: and, therefore, there ſhall be a perfect Equilibrium, and,

conſequently, a Reſt. Now here ariſeth a doubt, whether the

Cone A B D may be made heavier, in ſuch ſort, that when it is put

wholly under water, it goes to the bottom, but yet not in ſuch ſort,

as to take from the Rampart the vertue of ſuſtaining it that it ſink not,

and, the reaſon of the doubt is this: that although at ſuch time as

the Cone A B D is ſpecifically as grave as the water, the Rampart

E S T O ſuſtaines it, not only when the point A S T is tripple in

height to the Altitude of the Rampart E S, but alſo when a leſſer

part is above water; [for although in the Deſcent of the Cone the

Point A S T by little and little diminiſheth, and ſo likewiſe the

Rampart E S T O, yet the Point diminiſheth in

[Figure 17]

greater proportion than the Rampart, in that

it diminiſheth according to all the three Di

menſions, but the Rampart according to two

only, the Altitude ſtill remaining the ſame;

or, if you will, becauſe the Cone S T goes di

miniſhing, according to the proportion of the

cubes of the Lines that do ſucceſſively become

the Diameters of the Baſes of emergent Cones,

and the Ramparts diminiſh according to the proportion of the

Squares of the ſame Lines; whereupon the proportions of the Points

are alwayes Seſquialter of the proportions of the Cylinders, con

tained within the Rampart; ſo that if, for Example, the height of

the emergent Point were double, or equall to the height of the

Rampart, in theſe caſes, the Cylinder contained within the Ram

part, would be much greater than the ſaid Point, becauſe it would be

either ſeſquialter or tripple, by reaſon of which it would perhaps

ſerve over and above to fuſtain the whole Cone, ſince the part ſub

merged would no longer weigh any thing;] yet, nevertheleſs, when

any Gravity is added to the whole Maſs of the Cone, ſo that alſo the

part ſubmerged is not without ſome exceſſe of Gravity above the

Gravity of the water, it is not manifeſt, whether the Cylinder con

tained within the Rampart, in the deſcent that the Cone ſhall make,

can be reduced to ſuch a proportion unto the emergent Point, and to

ſuch an exceſſe of Maſs above the Maſs of it, as to compenſate the

exceſſe of the Cones Specificall Gravity above the Gravity of the wa

ter: and the Scruple ariſeth, becauſe that howbeit in the deſcent

made by the Cone, the emergent Point A S T diminiſheth, whereby

there is alſo a diminution of the exceſs of the Cones Gravity above