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

Table of figures

< >
[Figure 81]
Page: 833
[Figure 82]
Page: 834
[Figure 83]
Page: 836
[Figure 84]
Page: 837
[Figure 85]
Page: 839
[Figure 86]
Page: 842
[Figure 87]
Page: 843
[Figure 88]
Page: 845
[Figure 89]
Page: 846
[Figure 90]
Page: 848
[Figure 91]
Page: 849
[Figure 92]
Page: 850
[Figure 93]
Page: 851
[Figure 94]
Page: 852
[Figure 95]
Page: 852
[Figure 96]
Page: 854
[Figure 97]
Page: 856
[Figure 98]
Page: 856
[Figure 99]
Page: 857
[Figure 100]
Page: 858
[Figure 101]
Page: 859
[Figure 102]
Page: 860
[Figure 103]
Page: 860
[Figure 104]
Page: 861
[Figure 105]
Page: 862
[Figure 106]
Page: 863
[Figure 107]
Page: 863
[Figure 108]
Page: 864
[Figure 109]
Page: 865
[Figure 110]
Page: 866
< >
page |< < of 701 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="040/01/861.jpg" pagenum="168"/>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let the Horizontal Lines be A F the upper, and C D the low­
                <lb/>
              er; between which let the Perpendicular A C, and inclined
                <lb/>
              Plane D F, be cut in B; and let A R be a Mean-Proportional
                <lb/>
              between the whole Perpendicular C A, and the upper part A B; and
                <lb/>
              let F S be a Mean-proportional between the whole Inclined Plane D F,
                <lb/>
              and the upper part B F. </s>
              <s>I ſay, that the Time of the Fall along the
                <lb/>
              whole Perpendicular A C hath the ſame proportion to the Time along
                <lb/>
              its upper part A B, with the lower of the Plane, that is, with B D,
                <lb/>
              as A C hath to the Mean-proporti­
                <lb/>
              onal of the Perpendicular, that is
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.861.1.jpg" xlink:href="040/01/861/1.jpg" number="104"/>
                <lb/>
                <emph type="italics"/>
              A R, with S D, which is the ex­
                <lb/>
              ceſſe of the whole Plane D F above
                <lb/>
              its Mean-proportional F S. </s>
              <s>Let a
                <lb/>
              Line be drawn from R to S, which
                <lb/>
              ſhall be parallel to the two Horizon­
                <lb/>
              tal Lines. </s>
              <s>And becauſe the Time of
                <lb/>
              the Fall along all A C, is to the
                <lb/>
              Time along the part A B, as C A is
                <lb/>
              to the Mean proportional A R, if we ſuppoſe A C to be the Time of
                <lb/>
              the Fall along A C, A R ſhall be the Time of the Fall along A B,
                <lb/>
              and R C that along the remainder B C. </s>
              <s>For if the Time along A C
                <lb/>
              be ſuppoſed, as was done, to be A C it ſelf the Time along F D ſhall
                <lb/>
              be F D; and in like manner D S may be concluded to be the Time a­
                <lb/>
              long B D, after F B, or after A B. </s>
              <s>The Time therefore along the
                <lb/>
              whole A C, is A R, with R C; And the Time along the inflected
                <lb/>
              Plane A B D, ſhall be A R, with S D: Which was to be proved.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              The ſame happeneth, if inſtead of the Perpendicular, another
                <lb/>
              Plane were taken, as ſuppoſe N O; and the Demonstration is the
                <lb/>
              ſame.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>PROBL I. PROP. XIII.</s>
            </p>
            <p type="main">
              <s>A Perpendicular being given, to Inflect a Plane
                <lb/>
              unto it, along which, when it hath the ſame
                <lb/>
              Elevation with the ſaid Perpendicular, it may
                <lb/>
              make a Motion after its Fall along the Per­
                <lb/>
              pendicular in the ſame Time, as along the
                <lb/>
              ſame Perpendicular
                <emph type="italics"/>
              ex quiete.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let the Perpendicular given be A B, to which extended to C,
                <lb/>
              let the part B C be equal; and draw the Horizontal Lines
                <lb/>
              C E and A G. </s>
              <s>It is required from B to inflect a Plane reach­
                <lb/>
              ing to the Horizon C E, along which a Motion, after the Fall out
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum