Harriot, Thomas, Mss. 6786

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691
691 (346) 		692
692 (346v)
693
693 (347) 		694
694 (347v)
695
695 (348) 		696
696 (348v)
697
697 (349) 		698
698 (349v)
699
699 (350) 		700
700 (350v)
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page |< < (440) of 1122 > >|
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      <text xml:lang="eng" type="free">
        <div type="section" level="1" n="1">
          <pb file="add_6786_f440" o="440" n="879"/>
          <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">This sheet contains Harriot's exploration of Proposition 2, Lemma 4, from the
                <emph style="it">Sphaerica Menelai</emph>
              of Menelaus, as translated by Maurolico (1558). The text includes a supplement by Thabit ibn Qurra (see Add MS 6787
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/MAH52R5E&start=610&viewMode=image&pn=611"> f. </ref>
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/MAH52R5E&start=610&viewMode=image&pn=614"> f. </ref>
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/MAH52R5E&start=610&viewMode=image&pn=617"> f. </ref>
              ).
                <lb/>
              For Harriot's copy of Propositions 1 and 2 see Add MS
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/MAH52R5E&start=610&viewMode=image&pn=610"> f. </ref>
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/MAH52R5E&start=610&viewMode=image&pn=617"> f. </ref>
              . The pages relevant to Proposition 2, Lemma 4, are
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/MAH52R5E&start=610&viewMode=image&pn=612"> f. </ref>
              ,
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/MAH52R5E&start=610&viewMode=image&pn=613"> f. </ref>
              , and
                <ref target="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/MAH52R5E&start=610&viewMode=image&pn=614"> f. </ref>
              . </s>
              <s xml:space="preserve">]</s>
            </p>
          </div>
          <p xml:lang="lat">
            <s xml:space="preserve"> Si fuerint sex quantitates, quorum ratio primæ ad secundum: componatur ex rationibus,
              <lb/>
            tertia ad quartam, et quintæ ad sextam. Tum solidum sub prima quarta et sexta
              <lb/>
            contentum, æquale erit solido sub secundo tertia et quinta
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If there are six quantities, where the ratio of the first to the second is composed of the ratio of the third to the fourth and of the fifth to the sixth, then the solid content of the first, fourth, and sixth will be equal to the solid composed of the second, third, and fifth.</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Sex
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            The six ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Ergo solidum
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                  <mi>z</mi>
                  <mo>=</mo>
                  <mi>b</mi>
                  <mi>g</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Therefore the solid
              <math>
                <mstyle>
                  <mi>a</mi>
                  <mi>d</mi>
                  <mi>z</mi>
                  <mo>=</mo>
                  <mi>b</mi>
                  <mi>g</mi>
                  <mi>e</mi>
                </mstyle>
              </math>
            . </s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Varia transpositio utrinque
              <emph style="st">solilidi</emph>
            solidi
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Various transpositions of the terms of both ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Habitudines æqualium solidorum.
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Forms of equal ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Thebit ben Corat.
              <lb/>
            et Ma
              <emph style="super">u</emph>
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            Thabit ibn Qurra and ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve">
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> componentes rationes
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            components of the transposed ]</s>
          </p>
          <p xml:lang="lat">
            <s xml:space="preserve"> Si consequentes fiant antecedentes
              <lb/>
            et antecedentes consequentes; sunt alia
              <lb/>
            36
              <lb/>
            [
              <emph style="bf">Translation: </emph>
            If the consequents become antecedents and antecedents consequents, there are another 36 ]</s>
          </p>
        </div>
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    </echo>
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