Scan | Original |
---|---|

11 | |

12 | |

13 | |

14 | |

15 | |

16 | |

17 | |

18 | |

19 | |

20 | |

21 | |

22 | |

23 | |

24 | |

25 | |

26 | |

27 | |

28 | |

29 | |

30 | |

31 | |

32 | |

33 | |

34 | |

35 | |

36 | |

37 | |

38 | |

39 | |

40 |

water is to the elevation of the Priſme, as the abſolute Gravity of

the Priſme, is to the abſolute Gravity of the water: Therefore, the

Moment reſulting from the abſolute Gravity of the water A F, and

the Velocity of the Motion of declination, with which Moment it

forceth the Priſme D G, to riſe and aſcend, is equall to the Moment

that reſults from the abſolute Gravity of the Priſme D G, and from

the Velocity of the Motion, wherewith being raiſed, it would aſcend:

with which Moment it reſiſts its being raiſed: becauſe, therefore,

ſuch Moments are equall, there ſhall be an Equilibrium between the

water and the Solid. And, it is manifeſt, that putting a little more

water unto the other A F, it will increaſe the Gravity and Moment,

whereupon the Priſme D G, ſhall be overcome, and elevated till that

the only part B F remaines ſubmerged. Which is that that was to

be demonſtrated.

the Priſme, is to the abſolute Gravity of the water: Therefore, the

Moment reſulting from the abſolute Gravity of the water A F, and

the Velocity of the Motion of declination, with which Moment it

forceth the Priſme D G, to riſe and aſcend, is equall to the Moment

that reſults from the abſolute Gravity of the Priſme D G, and from

the Velocity of the Motion, wherewith being raiſed, it would aſcend:

with which Moment it reſiſts its being raiſed: becauſe, therefore,

ſuch Moments are equall, there ſhall be an Equilibrium between the

water and the Solid. And, it is manifeſt, that putting a little more

water unto the other A F, it will increaſe the Gravity and Moment,

whereupon the Priſme D G, ſhall be overcome, and elevated till that

the only part B F remaines ſubmerged. Which is that that was to

be demonſtrated.

in ſpecie than the water, ſubmerge only ſo far, that as much water in

Maſs, as is the part of the Solid ſubmerged, doth weigh abſolutely as

much as the whole Solid.

For, it being ſuppoſed, that the Specificall Gravity of the water,

is to the Specificall Gravity of the Priſme D G, as the Altitude

D F, is to the Altitude F B; that is, as the Solid D G is to the

Solid B G; we might eaſily demonſtrate, that as much water in Maſs

as is equall to the Solid B G, doth weigh abſolutely as much as the

whole Solid D G; For, by the Lemma foregoing, the Abſolute

Gravity of a Maſs of water, equall to the Maſs B G, hath to the Ab

ſolute Gravity of the Priſme D G, a proportion compounded of the

proportions, of the Maſs B G to the Maſs G D, and of the Specifick

Gravit 7 of the water, to the Specifick Gravity of the Priſme: But

the Gravity in ſpecie of the water, to the Gravity in ſpecie of the

Priſme, is ſuppoſed to be as the Maſs G D to the Maſs G B. There

fore, the Abſolute Gravity of a Maſs of water, equall to the Maſs

B G, is to the Abſolute Gravity of the Solid D G, in a proportion

compounded of the proportions, of the Maſs B G to the Maſs G D,

and of the Maſs D G to the Maſs G B; which is a proportion of

equalitie. The Abſolute Gravity, therefore, of a Maſs of Water

equall to the part of the Maſs of the Priſme B G, is equall to the Ab

ſolute Gravity of the whole Solid D G.

is to the Specificall Gravity of the Priſme D G, as the Altitude

D F, is to the Altitude F B; that is, as the Solid D G is to the

Solid B G; we might eaſily demonſtrate, that as much water in Maſs

as is equall to the Solid B G, doth weigh abſolutely as much as the

whole Solid D G; For, by the Lemma foregoing, the Abſolute

Gravity of a Maſs of water, equall to the Maſs B G, hath to the Ab

ſolute Gravity of the Priſme D G, a proportion compounded of the

proportions, of the Maſs B G to the Maſs G D, and of the Specifick

Gravit 7 of the water, to the Specifick Gravity of the Priſme: But

the Gravity in ſpecie of the water, to the Gravity in ſpecie of the

Priſme, is ſuppoſed to be as the Maſs G D to the Maſs G B. There

fore, the Abſolute Gravity of a Maſs of water, equall to the Maſs

B G, is to the Abſolute Gravity of the Solid D G, in a proportion

compounded of the proportions, of the Maſs B G to the Maſs G D,

and of the Maſs D G to the Maſs G B; which is a proportion of

equalitie. The Abſolute Gravity, therefore, of a Maſs of Water

equall to the part of the Maſs of the Priſme B G, is equall to the Ab

ſolute Gravity of the whole Solid D G.