Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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ſhall be equal to the Triangle O X K; Therefore (by common
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Notion) ſubſtracting thoſe two ſmall Triangles O P K and O X K
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from the two others B E K and B R K, the two Remainders ſhall
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be equal: one of which Remainders ſhall be the Quadrangle
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B E O P, and the other B R X O. </
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>And becauſe the whole Quadran
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gle B E O P is full of Liquor, and of the Quadrangle B R X O,
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the part B A X O only is full, and the reſidue B R A is wholly void
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of Water: It followeth, therefore, that the Quadrangle B E O P
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is more ponderous than the Quadrangle B R X O. </
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>And if the ſaid
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Quadrangle B E O P be more Grave than the Quadrangle
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B R X O, much more ſhall the Quadrangle B L O P exceed in Gra
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vity the ſaid Quadrangle B R X O: whence it followeth, that the
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part O P is more preſſed than the part O X. But, by the firſt part
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of the Suppoſition, the part leſs preſſed ſhould be repulſed by the
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part more preſſed: Therefore the part O X muſt be repulſed by
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the part O P: But it was preſuppoſed that the Liquid did not
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move: Wherefore it would follow that the leſs preſſed would not
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be repulſed by the more preſſed: And therefore it followeth of
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neceſſity that the Line A
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B
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G D is the Circumference of a Circle,
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and that the Center of it is the point K. </
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>And in like manner ſhall
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it be demonſtrated, if the Surface of the Liquid be cut by a Plane
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thorow the Center of the Earth, that the Section ſhall be the Cir
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cumference of a Circle, and that the Center of the ſame ſhall be
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that very Point which is Center of the Earth. </
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>It is therefore mani
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feſt that the Superficies of a Liquid that is conſiſtant and ſetled
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ſhall have the Figure of a Sphære, the Center of which ſhall be
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the ſame with that of the Earth, by the firſt
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Propoſition
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; for it is
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ſuch that being ever cut thorow the ſame Point, the Section or Di
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viſion deſcribes the Circumference of a Circle which hath for Cen
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ter the ſelf-ſame Point that is Center of the Earth: Which was to
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be demonſtrated.</
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* O: through.</
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*
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i.e.
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Parallel.</
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>RIC. </
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>I do thorowly underſtand theſe your Reaſons, and ſince there is in them
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no umbrage of Doubting, let us proceed to his third
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Propoſition.
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>PROP. III. THEOR. III.</
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Solid Magnitudes that being of equal Maſs with the
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Liquid are alſo equal to it in Gravity, being demit-
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ted into the [^{*} ſetled] Liquid do ſo ſubmerge in the
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ſame as that they lie or appear not at all above the
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Surface of the Liquid, nor yet do they ſink to the
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Bottom.
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