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COROLLARY II.

It followes, moreover, that a Solid leſs grave than the water, being put

into a Veſſell of any imaginable greatneſs, and water being circumfuſed

about it to ſuch a height, that as much water in Maſs, as is the part of

the Solid ſubmerged, doth/> weigh abſolutely as much as the whole Solid;

it ſhall by that water be juſtly ſuſtained, be the circumfuſed Water in

quantity greater or leſſer.

into a Veſſell of any imaginable greatneſs, and water being circumfuſed

about it to ſuch a height, that as much water in Maſs, as is the part of

the Solid ſubmerged, doth/> weigh abſolutely as much as the whole Solid;

it ſhall by that water be juſtly ſuſtained, be the circumfuſed Water in

quantity greater or leſſer.

For, if the Cylinder or Priſme M, leſs grave than the water, v.

gra. in Subſequiteriall proportion, ſhall be put into the capaci

ous Veſſell A B C D, and the water raiſed about it, to three

quarters of its height, namely, to its Levell A D: it ſhall be ſuſtained

and exactly poyſed in Equi

librium. The ſame will hap

pen, if the Veſſell E N S F

[Figure 6]

were very ſmall, ſo, that be

tween the Veſſell and the So

lid M, there were but a very

narrow ſpace, and only capable of ſo much water, as the hundredth

part of the Maſs M, by which it ſhould be likewiſe raiſed and erected,

as before it had been elevated to three fourths of the height of the

Solid: which to many at the firſt ſight, may ſeem a notable Paradox,

and beget a conceit, that the Demonſtration of theſe effects, were

ſophiſticall and fallacious: but, for thoſe who ſo repute it, the Ex

periment is a means that may fully ſatisfie them. But he that ſhall

but comprehend of what Importance Velocity of Motion is, and how

it exactly compenſates the defect and want of Gravity, will ceaſe to

wonder, in conſidering that at the elevation of the Solid M, the great

Maſs of water A B C D abateth very little, but the little Maſs of

water E N S F decreaſeth very much, and in an inſtant, as the Solid

M before did liſe, howbeit for a very ſhort ſpace: Whereupon the

Moment, compounded of the ſmall Abſolute Gravity of the water

E N S F, and of its great Velocity in ebbing, equalizeth the Force and

and Moment, that reſults from the compoſicion of the immenſe Gra

vity of the water A B C D, with its great ſlowneſſe of ebbing;

ſince that in the Elevation of the Sollid M, the abaſement of the leſ

gra. in Subſequiteriall proportion, ſhall be put into the capaci

ous Veſſell A B C D, and the water raiſed about it, to three

quarters of its height, namely, to its Levell A D: it ſhall be ſuſtained

and exactly poyſed in Equi

librium. The ſame will hap

pen, if the Veſſell E N S F

[Figure 6]

were very ſmall, ſo, that be

tween the Veſſell and the So

lid M, there were but a very

narrow ſpace, and only capable of ſo much water, as the hundredth

part of the Maſs M, by which it ſhould be likewiſe raiſed and erected,

as before it had been elevated to three fourths of the height of the

Solid: which to many at the firſt ſight, may ſeem a notable Paradox,

and beget a conceit, that the Demonſtration of theſe effects, were

ſophiſticall and fallacious: but, for thoſe who ſo repute it, the Ex

periment is a means that may fully ſatisfie them. But he that ſhall

but comprehend of what Importance Velocity of Motion is, and how

it exactly compenſates the defect and want of Gravity, will ceaſe to

wonder, in conſidering that at the elevation of the Solid M, the great

Maſs of water A B C D abateth very little, but the little Maſs of

water E N S F decreaſeth very much, and in an inſtant, as the Solid

M before did liſe, howbeit for a very ſhort ſpace: Whereupon the

Moment, compounded of the ſmall Abſolute Gravity of the water

E N S F, and of its great Velocity in ebbing, equalizeth the Force and

and Moment, that reſults from the compoſicion of the immenſe Gra

vity of the water A B C D, with its great ſlowneſſe of ebbing;

ſince that in the Elevation of the Sollid M, the abaſement of the leſ

ſer water E S, is performed juſt ſo much more ſwiftly than the great

Maſs of water A C, as this is more in Maſs than that which we thus

demonſtrate.