Archimedes
,
Natation of bodies
,
1662
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<
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>PROP. II. THEOR. II.</
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The Superficies of every Liquid that is conſiſtant and
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ſetled ſhall be of a Sphærical Figure, which Figure
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ſhall have the ſame Center with the Earth.
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>Let us ſuppoſe a Liquid that is of ſuch a conſiſtance as that it
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is not moved, and that its Superficies be cut by a Plane along
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by the Center of the Earth, and let the Center of the Earth
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be the Point K: and let the Section of the Superficies be the Line
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A B G D. </
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>I ſay that the Line A B G D is the Circumference of a
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Circle, and that the Center
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thereof is the Point K And
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if it be poſſible that it may
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not be the Circumference
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of a Circle, the Right
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Lines drawn ^{*} by the Point
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K to the ſaid Line A B G D
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ſhall not be equal. </
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<
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>There
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fore let a Right-Line be
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taken greater than ſome of thoſe produced from the Point K unto
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the ſaid Line A B G D, and leſſer than ſome other; and upon the
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Point K let a Circle be deſcribed at the length of that Line,
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Now the Circumference of this Circle ſhall fall part without the
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ſaid Line A B G D, and part within: it having been preſuppoſed
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that its Semidiameter is greater than ſome of thoſe Lines that may
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be drawn from the ſaid Point K unto the ſaid Line A B G D, and
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leſſer than ſome other. </
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>Let the Circumference of the deſcribed
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Circle be R B G H, and from B to K draw the Right-Line B K: and
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drawn alſo the two Lines K R, and K E L which make a Right
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Angle in the Point K: and upon the Center K deſcribe the Circum
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ference X O P in the Plane and in the Liquid. </
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<
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>The parts, there
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fore, of the Liquid that are ^{*} according to the Circumference
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X O P, for the reaſons alledged upon the firſt
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Suppoſition,
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are equi
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jacent, or equipoſited, and contiguous to each other; and both
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theſe parts are preſt or thruſt, according to the ſecond part of the
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Suppoſition,
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by the Liquor which is above them. </
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<
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>And becauſe the
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two Angles E K B and B K R are ſuppoſed equal [
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by the
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26.
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of
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3.
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<
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of Euclid,
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] the two Circumferences or Arches B E and B R ſhall
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be equal (foraſmuch as R B G H was a Circle deſcribed for ſatis
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faction of the Oponent, and K its Center:) And in like manner
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the whole Triangle B E K ſhall be equal to the whole Triangle
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B R K. </
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<
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>And becauſe alſo the Triangle O P K for the ſame reaſon </
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