Harriot, Thomas, Mss. 6784

List of thumbnails

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611
611 (306) 		612
612 (306v)
613
613 (307) 		614
614 (307v)
615
615 (308) 		616
616 (308v)
617
617 (309) 		618
618 (309v)
619
619 (310) 		620
620 (310v)
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page |< < (328) of 862 > >|
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      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6784_f328" o="328" n="655"/>
          <div type="page_commentary" level="0" n="0">
            <p>
              <s xml:space="preserve">[
                <emph style="bf">Commentary:</emph>
              </s>
            </p>
            <p>
              <s xml:space="preserve"> The references on this folio are to pages 148, 256, 258 of Commandino's edition of
                <emph style="it">Mathematicae collectiones</emph>
                <ref id="pappus_1588"> (Pappus </ref>
              . Page 148 contains Proposition 54. </s>
              <lb/>
              <quote xml:lang="lat">
                <s xml:space="preserve"> Theorema LIIII. Propositio LIIII.
                  <lb/>
                Circulo positione dato, & dato puncto in plano circuli intra circumferentiam ipsius, visui locum invenire, a quo circulus ellipsis videatur, centrum habens intra circumferentiam datum.</s>
              </quote>
              <lb/>
              <quote>
                <s xml:space="preserve"> Given a circle in position, and a given point in the plane of the circle inside its circumference, to find the looking place from which the circle appears as an ellipse having its centre inside the given circumference.</s>
              </quote>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <head xml:space="preserve"> 2.) pappus. pag. 148 et 256. </head>
          <p xml:lang="lat">
            <s xml:space="preserve"> effectio igitur talis:
              <lb/>
            dividatur
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            bisariam in
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
              <lb/>
            et centro
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            intervallo
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            describatur periferia
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
              <lb/>
            sit perpendicularis
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            ad
              <lb/>
            lineam
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            :
              <lb/>
            connectantur puncta
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            ,
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            .
              <lb/>
            & a linea
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            , erigatur
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
              <lb/>
            perpendicularis
              <lb/>
            quæ secabit
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            productum in
              <math>
                <mstyle>
                  <mi>h</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The construction is thus:
              <lb/>
            Divide
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            in half at
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            .
              <lb/>
            With centre
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            and radius
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            draw the circumference
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>c</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Let
              <math>
                <mstyle>
                  <mi>f</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            be perpendicular to the line
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Connect the points
              <math>
                <mstyle>
                  <mi>e</mi>
                </mstyle>
              </math>
            and
              <math>
                <mstyle>
                  <mi>c</mi>
                </mstyle>
              </math>
            and from the line
              <math>
                <mstyle>
                  <mi>e</mi>
                  <mi>c</mi>
                </mstyle>
              </math>
            erect the perpendicular
              <math>
                <mstyle>
                  <mi>c</mi>
                  <mi>h</mi>
                </mstyle>
              </math>
            , which will cut
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            extended at
              <math>
                <mstyle>
                  <mi>h</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> effectio optime
              <lb/>
            sumatur quodvis punctum
              <lb/>
              <math>
                <mstyle>
                  <mi>p</mi>
                </mstyle>
              </math>
            , et ducatur
              <math>
                <mstyle>
                  <mi>r</mi>
                  <mi>f</mi>
                  <mi>o</mi>
                </mstyle>
              </math>
              <lb/>
            sit
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>q</mi>
                  <mo>=</mo>
                  <mi>b</mi>
                  <mi>p</mi>
                </mstyle>
              </math>
              <lb/>
            ducatur
              <math>
                <mstyle>
                  <mi>q</mi>
                  <mi>o</mi>
                </mstyle>
              </math>
            & continuet
              <lb/>
            et secabit
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            producta
              <lb/>
            in
              <math>
                <mstyle>
                  <mi>h</mi>
                </mstyle>
              </math>
            ; ita ut:
              <lb/>
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>f</mi>
                  <mo>,</mo>
                  <mi>f</mi>
                  <mi>d</mi>
                  <mo>:</mo>
                  <mi>b</mi>
                  <mi>h</mi>
                  <mo>,</mo>
                  <mi>h</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Vide pappum: pag:
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The best construction
              <lb/>
            Take any point
              <math>
                <mstyle>
                  <mi>p</mi>
                </mstyle>
              </math>
            and draw
              <math>
                <mstyle>
                  <mi>r</mi>
                  <mi>f</mi>
                  <mi>o</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Let
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>q</mi>
                  <mo>=</mo>
                  <mi>b</mi>
                  <mi>p</mi>
                </mstyle>
              </math>
            .
              <lb/>
            Draw
              <math>
                <mstyle>
                  <mi>q</mi>
                  <mi>o</mi>
                </mstyle>
              </math>
            and continue it, and it will cut
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            extended at
              <math>
                <mstyle>
                  <mi>h</mi>
                </mstyle>
              </math>
            ; so that
              <math>
                <mstyle>
                  <mi>b</mi>
                  <mi>f</mi>
                  <mo>:</mo>
                  <mi>f</mi>
                  <mi>d</mi>
                  <mo>=</mo>
                  <mi>b</mi>
                  <mi>h</mi>
                  <mo>:</mo>
                  <mi>h</mi>
                  <mi>d</mi>
                </mstyle>
              </math>
            .
              <lb/>
            See Pappus, page ]</s>
          </p>
        </div>
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    </echo>
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