Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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Table of figures
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241 - 270
271 - 300
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331 - 331
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but one Point only. </
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>For let it be de
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mitted into the Liquid, as hath been
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ſaid; and let it firſt be ſo inclined, as
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that its Baſe do not in the leaſt
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touch the Surface of the Liquid. </
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<
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>And
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then it being cut thorow the Axis,
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by a Plane erect unto the Surface of
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the Liquid, let the Section of the
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Portion be A N Z G; that of the
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Liquids Surface E Z; the Axis of
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the Portion and Diameter of the
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Section B D; and let B D be cut in
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the Points K and R, as before; and
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draw N L parallel to E Z, and touching the Section A N Z G
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in N, and N S perpendicular to
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B D. Now, ſeeing that the Por
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tion is in Gravity unto the Liquid,
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as the Square made of the Line
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is to the Square B D;
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ſhall
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be equall to N T: Which is to
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be demonſtrated as above: And,
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therefore, N T is alſo equall to
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V I: The Portions, therefore,
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A V Q and E N Z are equall to
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one another. </
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the Equall and like Portions A V
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Q L and A N Z G, there are drawn A Q and E Z, cutting off
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equall Portions, that from the
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Extremity of the Baſe, this not
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from the Extreme, that which is
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drawn from the Extremity of the
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Baſe, ſhall make the Acute Angle
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with the Diameter of the Portion
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leſſer: and in the Triangles N L S
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and V
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C, the Angle at L is
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greater than the Angle at
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:
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Therefore, B S ſhall be leſſer
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than B C; and S R leſſer than
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C R: and, conſequently, N X
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greater than V H; and X T leſſer than H I. Seeing, therefore,
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that V Y is double to Y I; It is manifeſt, that N X is greater than
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double to X T. </
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<
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>Let N M be double to M T: It is manifeſt, from what
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hath been ſaid, that the Portion ſhall not reſt, but will incline, untill
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that its Bafe do touch the Surface of the Liquid: and it toucheth it in
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one Point only, as appeareth in the Figure: And other things </
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