Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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<
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>THEOR. III. PROP. III.</
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>The Times in which the ſame Space is paſt tho
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row by unequal Velocities, have the ſame pro
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portion to each other as their Velocities contra
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rily taken.</
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Let the two unequal Velocities be A the greater, and B the leſſe:
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and according to both theſe let a Motion be made thorow the ſame
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Space C D. </
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>I ſay the Time in which the Velocity A paſſeth the
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Space C D, ſhall be to the Time in which the Velocity B paſſeth the
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ſaid Space, as the Velocity B to the Velocity A. </
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>As A is to B, ſo let
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C D be to C E: Then, by the
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former Propoſition, the Time in
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which the Velocity A paſſeth
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C D, ſhall be the ſame with
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the Time in which B paſſeth
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C E. </
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>But the Time in which
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the Velocity B paſſeth C E, is
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to the Time in which it paſſeth C D, as C E is to C D: Therefore
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the Time in which the Velocity A paſſeth C D, is to the Time in which
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the Velocity B paſſeth the ſame C D, as C E is to C D; that is, the Ve
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locity B is to the Velocity A: Which was to be proved.
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>THEOR. IV. PROP. IV.</
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>If two Moveables move with an Equable Mo
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tion, but with unequal Velocities, the Spaces
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which they paſſe in unequal Times, are to each
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other in a proportion compounded of the pro
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portion of the Velocities, and of the propor
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tion of the Times.</
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Let the two Moveables moving with an Equable Motion, be E and
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F: And let the proportion of the Velocity of the Moveable E be
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to the Velocity of the Moveable F, as A is to B: And let the Time
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in which E is moved, be unto the Time in which F is moved, as C is
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to D. </
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<
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>I ſay the Space paſſed by E, with the Velocity A in the Time C, is to
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the Space paſſed by F, with the Velocity B in the Time D, in a proportion
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compounded of the proportion of the Velocity A to the Velocity B, and of
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