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

Page concordance

< >
Scan Original
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
< >
page |< < of 701 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/195.jpg" pagenum="177"/>
              deſcending groweth leſs & leſs in it, the nearer it is to the firſt term
                <lb/>
              of its deſcent; that is, to the ſtate of reſt; as is manifeſt from that
                <lb/>
              which you declare unto us, demonſtrating that the deſcending grave
                <lb/>
              body departing from reſt, ought to paſſe thorow all the degrees of
                <lb/>
              tardity comprehended between the ſaid reſt, & any aſſigned degree
                <lb/>
              of velocity, the which grow leſs and leſs
                <emph type="italics"/>
              in infinitum.
                <emph.end type="italics"/>
              To which may
                <lb/>
              be added, that the ſaid velocity and propenſion to motion, doth for
                <lb/>
              another reaſon diminiſh to infinity; and it is becauſe the gravity of
                <lb/>
              the ſaid moveable may infinitely diminiſh. </s>
              <s>So that the cauſes which
                <lb/>
              diminiſh the propenſion of aſcending, and conſequently favour
                <lb/>
              the projection, are two; that is, the levity of the moveable, and its
                <lb/>
              vicinity to the ſtate of reſt; both which are augmentable
                <emph type="italics"/>
              in infinit.
                <emph.end type="italics"/>
                <lb/>
              and theſe two on the contrary being to contract but with one ſole
                <lb/>
              cauſe of making the projection, I cannot conceive how it alone,
                <lb/>
              though it alſo do admit of infinite augmentation, ſhould be able to
                <lb/>
              remain invincible againſt the union & confederacy of the others, w^{ch}
                <lb/>
              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
                <emph type="italics"/>
              Sagredus
                <emph.end type="italics"/>
              ; and to explain it ſo as
                <lb/>
              that we may more cleerly apprehend it, for that you ſay that you
                <lb/>
              your ſelf have but a confuſed
                <emph type="italics"/>
              Idea
                <emph.end type="italics"/>
              of it, we will diſtinguiſh of the
                <lb/>
              ſame by reducing it into figure; which may alſo perhaps afford us
                <lb/>
              ſome caſe in reſolving the ſame. </s>
              <s>Let us therefore [
                <emph type="italics"/>
              in Fig.
                <emph.end type="italics"/>
              4.] draw
                <lb/>
              a perpendicular line towards the centre, and let it be AC, and to it
                <lb/>
              at right angles let there be drawn the Horizontal line A
                <emph type="italics"/>
              B,
                <emph.end type="italics"/>
              upon
                <lb/>
              which the motion of the projection ought to be made; now the
                <lb/>
              ject would continue to move along the ſame with an even motion, if
                <lb/>
              ſo be its gravity did not incline it downwards. </s>
              <s>Let us ſuppoſe from
                <lb/>
              the point A a right line to be drawn, that may make any angle at
                <lb/>
              pleaſure with the line A B; which let be A E, and upon A
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              let us
                <lb/>
              mark ſome equal ſpaces AF, FH, HK, and from them let us let fall
                <lb/>
              the perpendiculars FG, HI, K L, as far as AE. </s>
              <s>And becauſe, as al
                <lb/>
              ready hath been ſaid, the deſcending grave body departing from reſt,
                <lb/>
              goeth from time to time acquiring a greater degree of velocity,
                <lb/>
              according as the ſaid time doth ſucceſſively encreaſe; we may
                <lb/>
              ceive the ſpaces AF, FH, HK, to repreſent unto us equal times; and
                <lb/>
              the perpendiculars FG, HI, KL, degrees of velocity acquired in the
                <lb/>
              ſaid times; ſo that the degree of velocity acquired in the whole time
                <lb/>
              A K, is as the line K L, in reſpect to the degree H I, acquired in the
                <lb/>
              time AH, and the degree FG in the time AF; the which degrees KL,
                <lb/>
              HI, FG, are (as is manifeſt) the ſame in proportion, as the times K A,
                <lb/>
              HA, F A, and if other perpendiculars were drawn from the points
                <lb/>
              marked at pleaſure in the line F A, one might ſucceſſively find
                <lb/>
              grees leſſe and leſſe
                <emph type="italics"/>
              in infinitum,
                <emph.end type="italics"/>
              proceeding towards the point A,
                <lb/>
              repreſenting the firſt inſtant of time, and the firſt ſtate of reſt. </s>
              <s>And
                <lb/>
              this retreat towards A, repreſenteth the firſt propenſion to the </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum