Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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        <div xml:id="echoid-div97" type="section" level="1" n="56">
          <head xml:id="echoid-head67" xml:space="preserve">LEMMA.</head>
          <p>
            <s xml:id="echoid-s850" xml:space="preserve">IN omni circulo quadratum ſemidiametri dimidium eſt qua-
              <lb/>
            drati in ipſo circulo deſcripti.</s>
            <s xml:id="echoid-s851" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s852" xml:space="preserve">_IN_ circulo, cuius centrum E, ductæ ſint duæ diametri A C, B D,
              <lb/>
              <figure xlink:label="fig-035-01" xlink:href="fig-035-01a" number="32">
                <image file="035-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/035-01"/>
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            ſeſe ad angulos rectos ſecantes in E, cen-
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            tro. </s>
            <s xml:id="echoid-s853" xml:space="preserve">lunctis igitur rectis A B, B C, C D,
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            _D A,_ quadratum erit A B C D, in circu
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            lo inſcriptum, vt conſtat ex propoſ. </s>
            <s xml:id="echoid-s854" xml:space="preserve">6. </s>
            <s xml:id="echoid-s855" xml:space="preserve">lib.
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            </s>
            <s xml:id="echoid-s856" xml:space="preserve">4. </s>
            <s xml:id="echoid-s857" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s858" xml:space="preserve">Quoniam vero quadrata ex ſemi-
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            diametris æqualibus E A, E B, æqualia
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            inter ſe, æqualia ſimul ſunt quadrato ex
              <lb/>
            A B; </s>
            <s xml:id="echoid-s859" xml:space="preserve">dimidium erit quadratum ſemidia
              <lb/>
              <note position="right" xlink:label="note-035-01" xlink:href="note-035-01a" xml:space="preserve">47. primi.</note>
            metri E A, quadrati ex A B, quod in cir
              <lb/>
            culo deſcribitur. </s>
            <s xml:id="echoid-s860" xml:space="preserve">Quod eſt propoſitum. </s>
            <s xml:id="echoid-s861" xml:space="preserve">Ex
              <lb/>
            quo conſtat, in ſuperiorifigura, quadratum ſemidiametri B E, dimidium
              <lb/>
            eſſe quadrati ex C B, quod æquale ponitur ei, quod in circulo A B, in-
              <lb/>
            ſcribitur.</s>
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        <div xml:id="echoid-div99" type="section" level="1" n="57">
          <head xml:id="echoid-head68" xml:space="preserve">THEOR. 16. PROPOS. 17.</head>
          <note position="right" xml:space="preserve">27.</note>
          <p>
            <s xml:id="echoid-s863" xml:space="preserve">SI in ſphæra ſit circulus, à cuius polo in ipſius
              <lb/>
            circunferentiam ducta recta linea æqualis ſit late-
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            ri quadrati in ſcripti in maximo circulo, ipſe circu
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            lus maximus erit.</s>
            <s xml:id="echoid-s864" xml:space="preserve"/>
          </p>
          <figure number="33">
            <image file="035-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/035-02"/>
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          <p>
            <s xml:id="echoid-s865" xml:space="preserve">IN ſphæra ſit circulus A B, à cuius polo
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            C, ad eius circunferentiam recta ducta C A,
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            æqualis ſit lateri quadrati in maximo circulo
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            ſphæræ deſcripti. </s>
            <s xml:id="echoid-s866" xml:space="preserve">Dico A B, circulum eſſe ma
              <lb/>
            ximum. </s>
            <s xml:id="echoid-s867" xml:space="preserve">Per rectam enim A C, & </s>
            <s xml:id="echoid-s868" xml:space="preserve">centrũ ſphæ
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            ræ planum ducatur, faciens in ſphæra circulũ
              <lb/>
              <note position="right" xlink:label="note-035-03" xlink:href="note-035-03a" xml:space="preserve">1. huius.</note>
            A C B, qui maximus erit, cum per ſphæræ cen
              <lb/>
              <note position="right" xlink:label="note-035-04" xlink:href="note-035-04a" xml:space="preserve">6. huius.</note>
            trum ducatur. </s>
            <s xml:id="echoid-s869" xml:space="preserve">Ducatur quoq; </s>
            <s xml:id="echoid-s870" xml:space="preserve">ex C, recta li-
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            nea C B, ad B, punctũ, in quo circulus maxi-
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            mus A C B, circulũ A B, ſecat; </s>
            <s xml:id="echoid-s871" xml:space="preserve">eritq́; </s>
            <s xml:id="echoid-s872" xml:space="preserve">per deſi
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            nit. </s>
            <s xml:id="echoid-s873" xml:space="preserve">poli, recta C B, rectæ C A, æqualis. </s>
            <s xml:id="echoid-s874" xml:space="preserve">Cũ
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            ergo A C, ponatur latus quadrati in maximo circulo A C B, deſcripti, erit
              <lb/>
            quoque C B, latus eiuſdem quadrati; </s>
            <s xml:id="echoid-s875" xml:space="preserve">atque adeò duo arcus A C, C B, qua-
              <lb/>
            drantes erunt conſicientes ſemicirculũ A C B, quòd quatuor latera quadra-
              <lb/>
            ti æqualia ſubtendãt quatuor circuli arcus æquales. </s>
            <s xml:id="echoid-s876" xml:space="preserve">Recta igitur A B, com-
              <lb/>
              <note position="right" xlink:label="note-035-05" xlink:href="note-035-05a" xml:space="preserve">28. tertij.</note>
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