Harriot, Thomas, Mss. 6785

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page |< < (182) of 882 > >|
    <echo version="1.0RC">
      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6785_f182" o="182" n="363"/>
          <head xml:space="preserve"/>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sphæram solidam bisecare
              <lb/>
            secundum datam
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            To bisect a solid sphere in a given ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sit
              <math>
                <mstyle>
                  <mi>Y</mi>
                </mstyle>
              </math>
            centrum sphæræ
              <lb/>
            et axis
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            , quæ dividatur
              <lb/>
            in puncto
              <math>
                <mstyle>
                  <mi>C</mi>
                </mstyle>
              </math>
            secundum datam
              <lb/>
            rationem
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            ad
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Let
              <math>
                <mstyle>
                  <mi>Y</mi>
                </mstyle>
              </math>
            be the centre of the sphere, and the axis
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            , which is divided at the point
              <math>
                <mstyle>
                  <mi>C</mi>
                </mstyle>
              </math>
            in the given ratio
              <math>
                <mstyle>
                  <mi>d</mi>
                </mstyle>
              </math>
            to
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Secet axim
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            , linea
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            ad angulos rectos in puncto
              <math>
                <mstyle>
                  <mi>C</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Manifestum est quod planum circuli cuius diameter
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            dividit
              <lb/>
            superficiem sphæræ secundum rationem
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The line
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            cuts the axis
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            at right angles in the point
              <math>
                <mstyle>
                  <mi>C</mi>
                </mstyle>
              </math>
            .
              <lb/>
            It is clear that the plane of the circle whose diameter is
              <math>
                <mstyle>
                  <mi>D</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            divides the surface of the sphere in the given ratio. </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Pro divisione soliditatus ita agendum:
              <lb/>
            Fiat
              <math>
                <mstyle>
                  <mi>E</mi>
                  <mi>F</mi>
                  <mo>=</mo>
                  <mn>2</mn>
                  <mi>Y</mi>
                  <mi>C</mi>
                  <mo>=</mo>
                  <mi>C</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            . Et dividetur arcus
              <math>
                <mstyle>
                  <mi>F</mi>
                  <mi>U</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            in tres
              <lb/>
            æquales partes, et subtensæ unius partis fiat æqualis
              <math>
                <mstyle>
                  <mi>Y</mi>
                  <mi>K</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Et per punctum
              <math>
                <mstyle>
                  <mi>K</mi>
                </mstyle>
              </math>
            agatur
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>K</mi>
                  <mi>L</mi>
                </mstyle>
              </math>
            ad angulus rectus cum
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Dico quod:
              <lb/>
            Planum circuli cuius diameter
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>K</mi>
                  <mi>L</mi>
                </mstyle>
              </math>
            bisecet solidum sphæram
              <lb/>
            secundum datam rationem.
              <lb/>
            vel, ita:
              <lb/>
            fiat:
              <math>
                <mstyle>
                  <mi>Y</mi>
                  <mi>K</mi>
                </mstyle>
              </math>
            sinus duplus tertiæ partis arcus illius, cuius
              <math>
                <mstyle>
                  <mi>Y</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            est sinus.
              <lb/>
            et per punctum
              <math>
                <mstyle>
                  <mi>K</mi>
                </mstyle>
              </math>
            fit divisio secundum datam rationem;
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>m</mi>
                  <mi>p</mi>
                  <mo>;</mo>
                  <mi>c</mi>
                  <mo>.</mo>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            For the division of solidity, it is to be done thus:
              <lb/>
            Construct
              <math>
                <mstyle>
                  <mi>E</mi>
                  <mi>F</mi>
                  <mo>=</mo>
                  <mn>2</mn>
                  <mi>Y</mi>
                  <mi>C</mi>
                  <mo>=</mo>
                  <mi>C</mi>
                  <mi>G</mi>
                </mstyle>
              </math>
            , and divide the arc
              <math>
                <mstyle>
                  <mi>F</mi>
                  <mi>U</mi>
                  <mi>E</mi>
                </mstyle>
              </math>
            into three equal parts; and the chore of one part is equal to
              <math>
                <mstyle>
                  <mi>Y</mi>
                  <mi>K</mi>
                </mstyle>
              </math>
            . And through the point
              <math>
                <mstyle>
                  <mi>K</mi>
                </mstyle>
              </math>
            is drawn
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>K</mi>
                  <mi>L</mi>
                </mstyle>
              </math>
            at right angles to
              <math>
                <mstyle>
                  <mi>A</mi>
                  <mi>B</mi>
                </mstyle>
              </math>
            .
              <lb/>
            I say that: the plane of the circle with diameter
              <math>
                <mstyle>
                  <mi>H</mi>
                  <mi>K</mi>
                  <mi>L</mi>
                </mstyle>
              </math>
            bisects the solid sphere in the given ratio.
              <lb/>
            Or, thus:
              <lb/>
            Construct
              <math>
                <mstyle>
                  <mi>Y</mi>
                  <mi>K</mi>
                </mstyle>
              </math>
            , twice the sine of the third part of that arc of which
              <math>
                <mstyle>
                  <mi>Y</mi>
                  <mi>C</mi>
                </mstyle>
              </math>
            is the sine; and through the point
              <math>
                <mstyle>
                  <mi>K</mi>
                </mstyle>
              </math>
            make the division in the given ratio, etc. </s>
          </p>
        </div>
      </text>
    </echo>
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