Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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the
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Impetus,
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which it obtaineth in C, whoſe Meaſure is ſuppoſed to be
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A C, Let A S be a Mean-proportional betwixt B A and A C. </
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<
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>We will
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demonſtrate that the
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Impetus
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in B is to the
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Impetus
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in C, as S A is to
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A C. </
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<
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>Let the Horizontal Line C D be double to the ſaid A C; and B E
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double to B A. </
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<
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>It appeareth by what hath been demonſtrated, That the
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Cadent along A C being turned along the Horizon C D, and according
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to the
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Impetus
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acquired in C, with an Equable Motion, ſhall paſs the
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Space C D in a Time equal to that
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in which the ſaid A C is paſſed
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with an Accelerate Motion; and
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likewiſe that B E is paſſed in the
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ſame time as A B: But the Time of
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the Deſcent along A B is A S: There
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fore the Horizontal Line B E is
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paſſed in A S. </
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<
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>As the Time S A is
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to the Time A C, ſo let E B be to
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B L. </
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>And becauſe the Motion by
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B E is Equable, the Space B L ſhall be paſſed in the Time A C ac
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cording to the Moment of Celerity in B: But in the ſame Time A C
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the Space C D is paſſed, according to the Moment of Velocity in C:
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the Moments of Velocity therefore are to one another as the Spaces
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which according to the ſame Moments are paſſed in the ſame Time:
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Therefore the Moment of Velocity in C is to the Moment of Celerity in
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B, as D C is to B L. </
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<
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>And becauſe as D C is to B E, ſo are their halfs,
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to wit, C A to A B: but as E B is to B L, ſo is B A to A S: Therefore,
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exæquali,
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as D C is to B L, ſo is C A to A S: that is, as the Moment
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of Velocity in C is to the Moment of Velocity in B, ſo is C A to A S; that
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is, the Time along C A to the Time along A B. </
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<
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>I he manner of Meaſu
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ring the
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Impetus,
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or the Moment of Velocity upon a Line along which it
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makes a Motion of Deſcent is therefore manifeſt; which
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Impetus
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is indeed ſuppoſed to encreaſe according to the Proportion of the
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Time.
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But this, before we proceed any farther, is to be premoniſhed, that in
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regard we are to ſpeak for the future of the Motion compounded of the
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Equable Horizontal, and of the Naturally Accelerate downwards, (for
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from this Mixtion reſults, and by it is deſigned the Line of the Project,
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that is a Parabola;) it is neceſſary that we define ſome common meaſure
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according to which we may meaſure the Velocity,
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Impetus,
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or Moment
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of both the Motions. </
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>And ſeeing that of the Equable Motion the de
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grees of Velocity are innumerable, of which you may not take any
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promiſcuouſly, but one certain one which may be be compared and con
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joyned with the Degree of Velocity naturally Accelerate. </
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<
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>I can think of
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no more eaſie way for the electing and determining of that, than by aſ
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ſuming another of the ſame kind. </
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<
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>And that I may the better expreſs
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my meaning; Let A C be Perpendicular to the Horizon C B; and A C
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