Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667
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ſide A C, as many equal parts as we pleaſe, A D, D E, E F, F G,
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and drawing by the points D, E, F, G, right lines parallel to the baſe
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B C. </s>
<s>Now let us imagine the parts marked in the line A C, to be
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equal times, and let the parallels drawn by the points D, E, F, G,
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repreſent unto us the degrees of velocity accelerated, and
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ing equally in equal times; and let the point A be the ſtate of reſt,
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from which the moveable departing, hath
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v. </s>
<s>g.
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in the time A D,
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acquired the degree of velocity D H, in the ſecond time we will
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ſuppoſe, that it hath increaſed the velocity from D H, as far as to
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E I, and ſo ſuppoſing it to have grown greater in the ſucceeding
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times, according to the increaſe of the lines F K, G L,
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&c.
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but
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becauſe the acceleration is made continually from moment to
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ment, and not disjunctly from one certain part of time to another;
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the point A being put for the loweſt moment of velocity, that is,
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for the ſtate of reſt, and A D for the firſt inſtant of time
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ing; it is manifeſt, that before the acquiſt of the degree of velocity
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D H, made in the time A D, the moveable muſt have paſt by
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infinite other leſſer and leſſer degrees gained in the infinite inſtants
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that are in the time D A, anſwering the infinite points that are in
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the line D A; therefore to repreſent unto us the infinite degrees
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of velocity that precede the degree D H, it is neceſſary to imagine
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infinite lines ſucceſſively leſſer and leſſer, which are ſuppoſed to
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be drawn by the infinite points of the line D A, and parallels to
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D H, the which infinite lines repreſent unto us the ſuperficies of
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the Triangle A H D, and thus we may imagine any ſpace paſſed
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by the moveable, with a motion which begining at reſt, goeth
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formly accelerating, to have ſpent and made uſe of infinite degrees
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of velocity, increaſing according to the infinite lines that
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ing from the point A, are ſuppoſed to be drawn parallel to the
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line H D, and to the reſt I E, K F, L G, the motion continuing as
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far as one will.</s>
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<s>
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The acceleration
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of grave bodies
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turally deſcendent,
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increaſeth from
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moment to moment.
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<s>Now let us compleat the whole Parallelogram A M B C, and let
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us prolong as far as to the ſide thereof B M, not onely the Parallels
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marked in the Triangle, but thoſe infinite others imagined to be
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drawn from all the points of the ſide A C; and like as B C, was
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the greateſt of thoſe infinite parallels of the Triangle,
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ing unto us the greateſt degree of velocity acquired by the
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able in the accelerate motion, and the whole ſuperficies of the ſaid
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Triangle, was the maſs and ſum of the whole velocity, wherewith
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in the time A C it paſſed ſuch a certain ſpace, ſo the parallelogram
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is now a maſs and aggregate of a like number of degrees of
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locity, but each equal to the greateſt B C, the which maſs of
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locities will be double to the maſs of the increaſing velocities in
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the Triangle, like as the ſaid Parallelogram is double to the
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angle: and therefore if the moveable, that falling did make uſe </s>
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