Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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204
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had in the centre, ſucceſſively until it come to total extinction,
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do carry the moveable in ſuch a time ſuch a certain ſpace, as it had
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gone in ſuch a like quantity of time, by the acquiſt of velocity
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from the total privation of it until it came to that its greateſt degree;
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it ſeemeth very reaſonable, that if it ſhould move always with the
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ſaid greateſt degree of velocity it would paſs, in ſuch another
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quantity of time, both thoſe ſpaces: For if we do but in our
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mind ſucceſſively divide thoſe velocities into riſing and falling
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degrees, as
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v. </
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<
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>g.
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theſe numbers in the margine; ſo that the
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firſt ſort unto 10 be ſuppoſed the increaſing velocities, and the
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others unto 1, be the decreaſing; and let thoſe of the time
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of the deſcent, and the others of the time of the aſcent being
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added all together, make as many, as if one of the two ſums of
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them had been all of the greateſt degrees, and therefore the
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whole ſpace paſſed by all the degrees of the increaſing
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ties, and decreaſing, (which put together is the whole
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ter) ought to be equal to the ſpace paſſed by the greateſt
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cities, that are in number half the aggregate of the increaſing
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and decreaſing velocities. </
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<
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>I know that I have but obſcurely
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expreſſed my ſelf, and I wiſh I may be underſtood.</
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If the Terreſtrial
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Globe were
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rated, a grave
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dy deſcending by
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that bore, would
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paß and aſcend as
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far beyond the
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tre, as it did
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ſcend.
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<
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>SAGR. </
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<
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>I think I underſtand you very well; and alſo that I
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can in a few words ſhew, that I do underſtand you. </
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<
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>You had
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a mind to ſay, that the motion begining from reſt, and all the
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way increaſing the velocity with equal augmentations, ſuch as
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are thoſe of continuate numbers begining at 1, rather at 0,
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which repreſenteth the ſtate of reſt, diſpoſed as in the margine:
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and continued at pleaſure, ſo as that the leaſt degree may be 0,
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and the greateſt
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v. </
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<
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5, all theſe degrees of velocity wherewith
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the moveable is moved, make the ſum of 15; but if the
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moveable ſhould move with as many degrees in number as
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theſe are, and each of them equal to the biggeſt, which is 5, the
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aggregate of all theſe laſt velocities would be double to the
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others, namely 30. And therefore the moveable moving with
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a like time, but with uniform velocity, which is that of the
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higheſt degree 5, ought to paſs a ſpace double to that which it
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paſſeth in the accelerate time, which beginneth at the ſtate of reſt.</
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<
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>SALV. </
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<
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>According to your quick and piercing way of
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hending things, you have explained the whole buſineſs with more
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plainneſs than I my ſelf; and put me alſo in mind of adding
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thing more: for in the accelerate motion, the augmentation
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ing continual, you cannot divide the degrees of velocity, which
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continually increaſe, into any determinate number, becauſe
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ging every moment, they are evermore infinite. </
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<
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>Therefore we
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ſhall be the better able to exemplifie our intentions by deſcribing
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a Triangle, which let be this A B C, [
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in Fig.
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8.] taking in the </
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