Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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C O to the Square O F; foraſmuch as C D, D O, and O F are Propor
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tionals: And as C A is to A B, ſo is the Square C V to the Square
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V B: Therefore C O hath greater proportion to O F, than C V to V B:
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Therefore, by the foregoing Lemma, C O is greater than C V. </
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<
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>It is
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manifeſt moreover, that the Time along D C is to the Time along
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D B C, as D O C is to D O together with C V.
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>SCHOLIUM.</
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>From theſe things that have been demonſtrated may evidently
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be gathered, that the ſwifteſt of all Motions betwixt Term
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and Term is not made along the ſhorteſt Line, that is by the
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Right, but along a portion of a Circle.</
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For in the Quadrat B A E C, whoſe Side B C is erect to the Hori
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zon, let the Arch A C be divided into any number of equal parts,
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A D, D E, E F, F G, G C; and let Right-lines be drawn from C to
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the Points A, D, E, F, G, H; and alſo by Lines joyn A D, D E, E F,
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F G. and G C. </
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>It is manifest, that the Motion along the two Lines
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A D C is ſooner performed than along the
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ſole Line A C, or D C out of Reſt in D:
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But out of Reſt in A, D C is ſooner paſt
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than the two A D C: But along the two
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D E C out of Reſt in A the Deſcent is
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likewiſe ſooner made than along the ſole
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C D: Therefore the Deſcent along the
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three Lines A D E C ſhall be performed
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ſooner than along the two A D C. </
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<
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>And
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in like manner the Deſcent along A D E
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preceding, the Motion is more ſpeedily con
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ſummated along the two EFC than along the ſole FC: Therfore along the
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four A D E F C the Motion is quicklier accompliſhed than along the
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three A D E C: And ſo, in the laſt place, along the two F G C after the
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precedent Deſcent along A D E F the Motion will be ſooner conſumma
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ted than along the ſole F C: Therefore along the five A D E F G C
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the Deſcent ſhall be effected in a yet ſhorter Time than along the four
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A D E F C: Whereupon the nearer by inſcribed Poligons we approach
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the Circumference, the ſooner will the Motion be performed between the
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two aſſigned points A C.
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And that which is explained in a Quadrant, holdeth true likewiſe
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in a Circumference leſſe than the Quadrant: and the Ratiocination is
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the ſame.
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