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

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        <div xml:id="echoid-div105" type="section" level="1" n="60">
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            <s xml:id="echoid-s964" xml:space="preserve">
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            racirculum _A B C,_ qui maximus erit, cum per centrum ſphæræ tranſeat. </s>
            <s xml:id="echoid-s965" xml:space="preserve">Secet au
              <lb/>
              <figure xlink:label="fig-038-01" xlink:href="fig-038-01a" number="37">
                <image file="038-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/038-01"/>
              </figure>
              <note position="left" xlink:label="note-038-01" xlink:href="note-038-01a" xml:space="preserve">6. huius.</note>
            tem circulus _A B C,_ circulum _B C,_ in punctis
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            _B, C._ </s>
            <s xml:id="echoid-s966" xml:space="preserve">Non cadet ergo recta _A E,_ in puncta _B, C._
              <lb/>
            </s>
            <s xml:id="echoid-s967" xml:space="preserve">cum ponatur non cadere in circunferentiam cir
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            culi _B C._ </s>
            <s xml:id="echoid-s968" xml:space="preserve">Ducta igitur recta _A B,_ erit hæc, ex
              <lb/>
            defin. </s>
            <s xml:id="echoid-s969" xml:space="preserve">poli, rectæ _A D,_ atque adeo rectæ _A E,_
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            æqualis. </s>
            <s xml:id="echoid-s970" xml:space="preserve">Et quia vtraque _A B, A E,_ minor eſt
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            diametro maximi circuli _A B C,_ vt dictum eſt,
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            erunt areus _A B, A E,_ cum ſint ſegmenta ſemi-
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            circulo minora, æquales, pars & </s>
            <s xml:id="echoid-s971" xml:space="preserve">totum. </s>
            <s xml:id="echoid-s972" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-038-02" xlink:href="note-038-02a" xml:space="preserve">28. tertij.</note>
            Quod eſt abſurdum. </s>
            <s xml:id="echoid-s973" xml:space="preserve">Cadet ergo recta _A E,_ in
              <lb/>
            circunferentiam circuli _B C._ </s>
            <s xml:id="echoid-s974" xml:space="preserve">Quod eſt pros
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            poſitum.</s>
            <s xml:id="echoid-s975" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div108" type="section" level="1" n="61">
          <head xml:id="echoid-head72" xml:space="preserve">PROBL. 4. PROP. 20.</head>
          <note position="left" xml:space="preserve">31.</note>
          <p>
            <s xml:id="echoid-s976" xml:space="preserve">PER duo puncta data in ſphærica ſuperficie
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            maximum circulum deſcribere.</s>
            <s xml:id="echoid-s977" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s978" xml:space="preserve">IN ſphærica ſuperficie data ſint duo pũcta A, B, per quæ deſcribere opor
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            teat circulum maximum. </s>
            <s xml:id="echoid-s979" xml:space="preserve">Si ergo puncta A, B, ſint oppoſita ex diametro
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            ſphęræ, certum eſt, inſinitos circulos maximos per ipſa duci poſſe, ductis ni-
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            mirum inſinitis planis per diametrum ſphæræ puncta illa connectentem. </s>
            <s xml:id="echoid-s980" xml:space="preserve">Si
              <lb/>
              <figure xlink:label="fig-038-02" xlink:href="fig-038-02a" number="38">
                <image file="038-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/038-02"/>
              </figure>
            autem puncta A, B, non ſint in ſphæræ dia-
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            metro, deſcribatur ex A, polo, & </s>
            <s xml:id="echoid-s981" xml:space="preserve">interual-
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            lo quod lateri quadrati in maximo circulo
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            deſcripti æquale ſit, circulus C D, qui ma-
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            ximus erit, cum recta ex A, polo ad eius cir
              <lb/>
              <note position="left" xlink:label="note-038-04" xlink:href="note-038-04a" xml:space="preserve">17. huius.</note>
            cunferentiam ducta æqualis ſit lateri qua-
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            drati in circulo maximo deſcripti, propter
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            interuallum, quo circulus C D, deſeriptus
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            eſt. </s>
            <s xml:id="echoid-s982" xml:space="preserve">Similiter ex B, polo, & </s>
            <s xml:id="echoid-s983" xml:space="preserve">interuallo eodẽ,
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            quo prius, circulus deſcribatur E F, qui rur
              <lb/>
              <note position="left" xlink:label="note-038-05" xlink:href="note-038-05a" xml:space="preserve">17. huius.</note>
            ſus erit maximus. </s>
            <s xml:id="echoid-s984" xml:space="preserve">Secet autem hic priorem
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            in puncto G, a quo ad polos A, B, rectæ du
              <lb/>
            cantur G A, G B; </s>
            <s xml:id="echoid-s985" xml:space="preserve">quarum vtraque, ex con
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            ſtructione, æqualis erit lateri quadrati in
              <lb/>
            maximo circulo deſcripti. </s>
            <s xml:id="echoid-s986" xml:space="preserve">Tanto enim interuallo ex polis A, B, circuli C D,
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            E F, deſcripti ſunt. </s>
            <s xml:id="echoid-s987" xml:space="preserve">Aequales ergo ſunt G A, G B. </s>
            <s xml:id="echoid-s988" xml:space="preserve">Iam ex G, polo, & </s>
            <s xml:id="echoid-s989" xml:space="preserve">inter-
              <lb/>
            uallo G A, circulus deſcribatur A E D F C B, qui maximus erit; </s>
            <s xml:id="echoid-s990" xml:space="preserve">cum recta
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              <note position="left" xlink:label="note-038-06" xlink:href="note-038-06a" xml:space="preserve">17. huius.</note>
            G A, ex G, polo ad eius circunferentiam ducta æqualis ſit lateri quadrati in
              <lb/>
            maximo circulo inſcripti, vt demonſtratum eſt. </s>
            <s xml:id="echoid-s991" xml:space="preserve">Quoniam vero recta G B, æ-
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            qualis ipſi G A, ducta ad ſuperficiem ſphæræ cadit in circunferentiam circu-
              <lb/>
              <note position="left" xlink:label="note-038-07" xlink:href="note-038-07a" xml:space="preserve">Schol. 19.
                <lb/>
              huius.</note>
            li A E D F C B, deſcriptus propterea erit circulus maximus A E D F C B,
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            per data duo puncta A, B, in ſuperficie ſphæræ. </s>
            <s xml:id="echoid-s992" xml:space="preserve">Per duo ergo puncta data in
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            ſphærica ſuperſicie maximum circulum deſcripſimus, Quod faciendum erat.</s>
            <s xml:id="echoid-s993" xml:space="preserve"/>
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