Archimedes
,
Natation of bodies
,
1662
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wards according to that ſame Perpendicular
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which paſſeth thorow B; and the Portion
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which is within the Liquid ſhall move up
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wards acording to that paſſing thorow G:
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From whence it is manifeſt that the Solid
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ſhall turn about in ſuch manner, as that
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its Baſe ſhall in no wiſe touch the Surface
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of the Liquid; for that now when it touch
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eth but in one Point only, it moveth down
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wards on the part towards L. </
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>And though
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N O ſhould not cut
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K, yet ſhall the ſame hold true.</
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(a)
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By 10 of the
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fifth.
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<
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>PROP. VIII. THE OR. VIII.</
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The Right Portion of a Rightangled Conoid, when it
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ſhall have its Axis greater than ſeſquialter of the Se
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mi-parameter, but leſſe than to be unto the ſaid Semi
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parameter, in proportion as fifteen to fower, if it
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have a leſſer proportion in Gravity to the Liquid, than
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the Square made of the Exceſſe by which the Axis is
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greater than Seſquialter of the Semi-parameter hath
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to the Square made of the Axis, being demitted into
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the Liquid, ſo as that its Baſe touch not the Liquid,
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it ſhall neither return to Perpendicularity, nor conti
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nue inclined, ſave only when the Axis makes an
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Angle with the Surface of the Liquid, equall to that
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which we ſhall preſently ſpeak of.
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>Let there be a Portion as hath been ſaid; and let B D be equall
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to the Axis: and let B K be double to K D; and R K equall
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to the Semi-parameter: and let C B be Seſquialter of B R:
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C D ſhall be alſo Sefquialter of K R. </
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>And as the Portion is to the
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Liquid in Gravity, ſo let the Square F Q be to the Square D B;
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and let F be double to Q: It is manifeſt, therefore, that F Q hath
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to D B, leſs proportion than C B hath to B D; For C B is the
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Exceſs by which the Axis is greater than Seſquialter of the Semi
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parameter: And, therefore, F Q is leſs than B C; and, for the
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ſame reaſon, F is leſs than B R. </
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<
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>Let R
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be equall to F; and draw
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E perpendicular to B D; which let be in power or contence the
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half of that which the Lines K R and
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B containeth; and
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draw a Line from B to E: It is to be demonſtrated, that the </
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