Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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            <s xml:id="echoid-s4943" xml:space="preserve">
              <pb o="103" file="139" n="140" rhead="Ioan. de Sacro Boſco."/>
            Ducaturq́. </s>
            <s xml:id="echoid-s4944" xml:space="preserve">ex angulo E, per centrum ad angulum I, recta E I. </s>
            <s xml:id="echoid-s4945" xml:space="preserve">Itaq; </s>
            <s xml:id="echoid-s4946" xml:space="preserve">ſi circa ma
              <lb/>
              <note position="right" xlink:label="note-139-01" xlink:href="note-139-01a" xml:space="preserve">quę conici@
                <lb/>
              upe@ficie-
                <lb/>
              bus conti-
                <lb/>
              @entur.</note>
            @entem rectam E I, immobilem circumuagatur planum, in quo eſt circulus
              <lb/>
            A B C D, & </s>
            <s xml:id="echoid-s4947" xml:space="preserve">figura E F G H I K L M, deſcribet circulus ſpheram, figura
              <lb/>
            uero corpus circa ſphæram conicis ſuperficiebus contentum, quarum ſuperfi-
              <lb/>
            cierum latera æqualia ſunt, nempe eadem, quæ figuræ, ut ab Archimede demõ
              <lb/>
            ſtratur propoſ. </s>
            <s xml:id="echoid-s4948" xml:space="preserve">22. </s>
            <s xml:id="echoid-s4949" xml:space="preserve">& </s>
            <s xml:id="echoid-s4950" xml:space="preserve">27. </s>
            <s xml:id="echoid-s4951" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4952" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4953" xml:space="preserve">de ſphæra, & </s>
            <s xml:id="echoid-s4954" xml:space="preserve">cylindro. </s>
            <s xml:id="echoid-s4955" xml:space="preserve">Sitiam ſphæra N, iſo-
              <lb/>
            perimetra corpori E F G H I K L M, circa ſphęram A B C D, deſcripto. </s>
            <s xml:id="echoid-s4956" xml:space="preserve">Di-
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              <figure xlink:label="fig-139-01" xlink:href="fig-139-01a" number="40">
                <image file="139-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/139-01"/>
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            co ſphæram N, dicto corpore eſſe maiorem. </s>
            <s xml:id="echoid-s4957" xml:space="preserve">Quoniam enim ambitus ſolidi
              <lb/>
            E F G H I K L M, maior eſt (per propoſ. </s>
            <s xml:id="echoid-s4958" xml:space="preserve">27. </s>
            <s xml:id="echoid-s4959" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4960" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4961" xml:space="preserve">Archimedis de ſphæra & </s>
            <s xml:id="echoid-s4962" xml:space="preserve">
              <lb/>
            cylindro) ambitu ſphæræ A B C D, erit quoque ambitus ſphæræ N, maior am
              <lb/>
            bitu ſphæræ A B C D, ideoq́ue ſemidiameter ſphæræ N, maior erit ſemidiame
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            tro ſphæræ A B C D. </s>
            <s xml:id="echoid-s4963" xml:space="preserve">Et quia ſuperſicies ſphæræ quadrupla eſt (per propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s4964" xml:space="preserve">31. </s>
            <s xml:id="echoid-s4965" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4966" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4967" xml:space="preserve">Archimedis de ſphæra, & </s>
            <s xml:id="echoid-s4968" xml:space="preserve">cylindro) maximi circuli in ſphæra, ſi ſu-
              <lb/>
            matur circulus O P, quadruplus circuli maximi in ſphæra N, (quod quidem
              <lb/>
            facile fiet, ſi diameter O P, dupla ſumatur diametri circuli maximi in ſphæra
              <lb/>
            N. </s>
            <s xml:id="echoid-s4969" xml:space="preserve">Quoniam enim, ut circulus O P, ad circulum maximum in ſphæra N, ita
              <lb/>
            quadratum diametri O P, ad quadratum diametri circuli maximi in ſphæra
              <lb/>
              <note position="right" xlink:label="note-139-02" xlink:href="note-139-02a" xml:space="preserve">2. duod.</note>
            N, Eſt autem quadrati ad quadratum proportio duplicata proporionis late-
              <lb/>
              <note position="right" xlink:label="note-139-03" xlink:href="note-139-03a" xml:space="preserve">20. ſexti.</note>
            rum homologorum, erit quoque circulus O P, ad circulum maximũ in ſphæ
              <lb/>
            ra N, in proportione duplicata proportionis diametri O P, ad diametrum cir
              <lb/>
            culi maximi in ſphæra N. </s>
            <s xml:id="echoid-s4970" xml:space="preserve">Cum igitur diametri ponantur habere proportionẽ
              <lb/>
            duplam, habebunt circuli proportionem quadruplam: </s>
            <s xml:id="echoid-s4971" xml:space="preserve">quadrupla enim propor
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            tio duplicata eſt proportionis duplæ, ut in his numeris apparet. </s>
            <s xml:id="echoid-s4972" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4973" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4974" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4975" xml:space="preserve">erit cir-
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            cul us O P, æqualis ſuperficiei ſphæræ N. </s>
            <s xml:id="echoid-s4976" xml:space="preserve">Accipiatur rurſus circulus S T, æqua
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            liscirculo O P. </s>
            <s xml:id="echoid-s4977" xml:space="preserve">Statuatur deinde ſupra circulum S T, conus rectus S T V, </s>
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