Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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            <p type="main">
              <s>
                <pb xlink:href="040/01/222.jpg" pagenum="204"/>
              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
                <emph type="italics"/>
              v. </s>
              <s>g.
                <emph.end type="italics"/>
              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. </s>
              <s>I know that I have but obſcurely
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              expreſſed my ſelf, and I wiſh I may be underſtood.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg406"/>
                <emph type="italics"/>
              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.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>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. </s>
              <s>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
                <emph type="italics"/>
              v. </s>
              <s>g.
                <emph.end type="italics"/>
              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.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>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. </s>
              <s>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, [
                <emph type="italics"/>
              in Fig.
                <emph.end type="italics"/>
              8.] taking in the </s>
            </p>
          </chap>
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