Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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1 - 30
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121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
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421 - 450
451 - 480
481 - 510
511 - 540
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is D A to C G, or B E. </
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<
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>The proportion therefore of the Elevations
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of the Planes equal to C D and C E, is the ſame with the proportion
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of the Longitudes D C and C E: Therefore, by the firſt Corollary of
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the precedent Sixth Propoſition, the Times of the Dcſcent along the
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ſame ſhall be equal: Which mas to be proved.
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Take the ſame another way: Draw F S perpendicular to the
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Horizontal Parallel A S. </
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>Becauſe the Triangle C S F is like to
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the Triangle D G C, it ſhall be, that as S F is to F C, ſo is G C
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to C D. </
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>And becauſe the Triangle C F G is like to the Triangle
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D C A, it ſhall be, that as F C is to C G, ſo is C D to D A:
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Therefore,
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ex æquali,
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as
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S F is to C G, ſo is C G to
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D A: Thorefore C G is a
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Mean-proportional between
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S F and D A: And as DA
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is to S F, ſo is the Square
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D A unto the Square C G
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Again, the Triangle A C D
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being like to the Triangle
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C G F, it ſhall be, that as
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D A is to D C, ſo is G C
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to C F: and, Alternately,
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as D A is to G C, ſo is D C to C F; and as the Square of D A
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is to the Square of C G, ſo is the Square of D C to the Square of
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C F. </
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>But it hath been proved that the Square D A is to the
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Square C G as the Line D A is to the Line F S: Therefore, as the
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Square D C is to the Square C F, ſo is the Line D E to F S: There
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fore, by the ſeventh fore-going, in regard that the Elevations D A
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and F S, of the Planes C D, and C F are in double proportion to
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their Planes; the Times of the Motions along the ſame ſhall be
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equal.
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>THEOR. X. PROP. X.</
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<
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>The Times of the Motions along ſeveral Inclina
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tions of Planes whoſe Elevations are equal,
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are unto one another as the Lengths of thoſe
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Planes, whether the Motions be made from
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Reſt, or there hath proceeded a Motion from
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the ſame height.</
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Let the Motions be made along A B C, and along A B D, until
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they come to the Horizon D C, in ſuch ſort as that the Motion
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along A B precedeth the Motions along B D and B C. </
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<
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>I ſay,
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that the Time of the Motion along B D, is to the Time along B C, as
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