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

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              <s>
                <pb xlink:href="040/01/195.jpg" pagenum="177"/>
              deſcending groweth leſs & leſs in it, the nearer it is to the firſt term
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              of its deſcent; that is, to the ſtate of reſt; as is manifeſt from that
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              which you declare unto us, demonſtrating that the deſcending grave
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              body departing from reſt, ought to paſſe thorow all the degrees of
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              tardity comprehended between the ſaid reſt, & any aſſigned degree
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              of velocity, the which grow leſs and leſs
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              in infinitum.
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              To which may
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              be added, that the ſaid velocity and propenſion to motion, doth for
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              another reaſon diminiſh to infinity; and it is becauſe the gravity of
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              the ſaid moveable may infinitely diminiſh. </s>
              <s>So that the cauſes which
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              diminiſh the propenſion of aſcending, and conſequently favour
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              the projection, are two; that is, the levity of the moveable, and its
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              vicinity to the ſtate of reſt; both which are augmentable
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              in infinit.
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              and theſe two on the contrary being to contract but with one ſole
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              cauſe of making the projection, I cannot conceive how it alone,
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              though it alſo do admit of infinite augmentation, ſhould be able to
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              remain invincible againſt the union & confederacy of the others, w^{ch}
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              are two, and are in like manner capable of infinite augmentation.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>This is a doubt worthy of
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              Sagredus
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              ; and to explain it ſo as
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              that we may more cleerly apprehend it, for that you ſay that you
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              your ſelf have but a confuſed
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              Idea
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              of it, we will diſtinguiſh of the
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              ſame by reducing it into figure; which may alſo perhaps afford us
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              ſome caſe in reſolving the ſame. </s>
              <s>Let us therefore [
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              in Fig.
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              4.] draw
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              a perpendicular line towards the centre, and let it be AC, and to it
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              at right angles let there be drawn the Horizontal line A
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              B,
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              upon
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              which the motion of the projection ought to be made; now the
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              ject would continue to move along the ſame with an even motion, if
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              ſo be its gravity did not incline it downwards. </s>
              <s>Let us ſuppoſe from
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              the point A a right line to be drawn, that may make any angle at
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              pleaſure with the line A B; which let be A E, and upon A
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              B
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              let us
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              mark ſome equal ſpaces AF, FH, HK, and from them let us let fall
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              the perpendiculars FG, HI, K L, as far as AE. </s>
              <s>And becauſe, as al
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              ready hath been ſaid, the deſcending grave body departing from reſt,
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              goeth from time to time acquiring a greater degree of velocity,
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              according as the ſaid time doth ſucceſſively encreaſe; we may
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              ceive the ſpaces AF, FH, HK, to repreſent unto us equal times; and
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              the perpendiculars FG, HI, KL, degrees of velocity acquired in the
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              ſaid times; ſo that the degree of velocity acquired in the whole time
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              A K, is as the line K L, in reſpect to the degree H I, acquired in the
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              time AH, and the degree FG in the time AF; the which degrees KL,
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              HI, FG, are (as is manifeſt) the ſame in proportion, as the times K A,
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              HA, F A, and if other perpendiculars were drawn from the points
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              marked at pleaſure in the line F A, one might ſucceſſively find
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              grees leſſe and leſſe
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              in infinitum,
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              proceeding towards the point A,
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              repreſenting the firſt inſtant of time, and the firſt ſtate of reſt. </s>
              <s>And
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              this retreat towards A, repreſenteth the firſt propenſion to the </s>
            </p>
          </chap>
        </body>
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