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

Table of figures

< >
[Figure 151]
Page: 916
[Figure 152]
Page: 917
[Figure 153]
Page: 919
[Figure 154]
Page: 922
[Figure 155]
Page: 923
[Figure 156]
Page: 924
[Figure 157]
Page: 926
[Figure 158]
Page: 927
[Figure 159]
Page: 927
[Figure 160]
Page: 928
[Figure 161]
Page: 929
[Figure 162]
Page: 930
[Figure 163]
Page: 932
[Figure 164]
Page: 938
[Figure 165]
Page: 941
[Figure 166]
Page: 942
[Figure 167]
Page: 944
[Figure 168]
Page: 945
[Figure 169]
Page: 948
[Figure 170]
Page: 949
[Figure 171]
Page: 950
[Figure 172]
Page: 952
[Figure 173]
Page: 953
[Figure 174]
Page: 955
[Figure 175]
Page: 956
[Figure 176]
Page: 958
[Figure 177]
Page: 959
[Figure 178]
Page: 961
[Figure 179]
Page: 962
[Figure 180]
Page: 970
< >
page |< < of 701 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/959.jpg" pagenum="266"/>
                <emph type="italics"/>
              of the Circumſcribed and inſcribed Figures: and that it's poſſible, that
                <lb/>
              there be a Line in the middle betwixt thoſe Centers that is leſs than any
                <lb/>
              Line aſſigned; it followeth that the ſame given Line be much leſs that
                <lb/>
              lyeth betwixt one of the ſaid Centers and the ſaid point that divides
                <lb/>
              the Axis.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>PROPOSITION.</s>
            </p>
            <p type="main">
              <s>The Center of Gravity divideth the Axis of any
                <lb/>
              Cone or Pyramid ſo, that the part next the
                <lb/>
              Vertex is triple to the remainder.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Let there be a Cone whoſe Axis is A B. </s>
              <s>And in C let it be divided,
                <lb/>
              ſo that A C be triple to the remaining part C B. </s>
              <s>It is to be proved,
                <lb/>
              that C is the Center of Gravity of the Cone. </s>
              <s>For if it be not, the
                <lb/>
              Cone's Center ſhall be either above or below the point C. </s>
              <s>Let it be firſt
                <lb/>
              beneath, and let it be E. </s>
              <s>And draw the Line L P, by it ſelf, equal to
                <lb/>
              C E; which divided at pleaſure in N. </s>
              <s>And as both B E and P N to­
                <lb/>
              gether are to P N, ſo let the Cone be to the Solid X: and inſcribe in the
                <lb/>
              Cone a Solid Figure of Cylinders that have equal Baſes, whoſe Center
                <lb/>
              of Gravity is leſs diſtant from the point C than is the Line L N, and
                <lb/>
              the exceſs of the Cone above it leſs than the Solid X. </s>
              <s>And that this
                <lb/>
              may be done is manifeſt from what hath been already demonſtrated.
                <lb/>
              </s>
              <s>Now let the inſcribed Figure be ſuch as
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.040.01.959.1.jpg" xlink:href="040/01/959/1.jpg" number="177"/>
                <lb/>
                <emph type="italics"/>
              was required, whoſe Center of Gravity
                <lb/>
              let be I. </s>
              <s>The Line I E therefore ſhall be
                <lb/>
              greater than N P together with L P. </s>
              <s>Let
                <lb/>
              C E and I C leſs L N be equal: And be­
                <lb/>
              cauſe both together B E and N P is to N P
                <lb/>
              as the Cone to X: and the exceſs by which
                <lb/>
              the Cone exceeds the inſcribed Figure is
                <lb/>
              leſs than the Solid X: Therefore the Cone
                <lb/>
              ſhall have greater proportion to the ſaid
                <lb/>
              X S than both B E and N P to N P: and, by
                <lb/>
              Diviſion, the inſcribed Figure ſhall have
                <lb/>
              greater proportion to the exceſs by which
                <lb/>
              the Cone exceeds it, than B E to N P: But B E hath leſs proportion to
                <lb/>
              E I than to N P with I E. </s>
              <s>Let N P be greater. </s>
              <s>Then the inſcribed Fi­
                <lb/>
              gure hath to the exceſs of the Cone above it much greater proportion
                <lb/>
              than B E to E I. </s>
              <s>Therefore as the inſcribed Figure is to the ſaid exceſs,
                <lb/>
              ſo ſhall a Line bigger than B E be to E I. </s>
              <s>Let that Line be M E. Becauſe,
                <lb/>
              therefore, M E is to E I as the inſcribed Figure is to the exceſs of the
                <lb/>
              Cone above the ſaid Figure, and D is the Center of Gravity of the
                <lb/>
              Cone, and I the Center of Gravity of the inſcribed Figure: Therefore
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum