Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of handwritten notes

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              <pb o="104" file="140" n="141" rhead="Comment. in I. Cap. Sphæræ"/>
            V X, æqualem habens ſemidiametro ſphæræ N: </s>
            <s xml:id="echoid-s4978" xml:space="preserve">Item ſupra circulum O P, al-
              <lb/>
            ter conus O P Q, conſtruatur habens axem Q R, ęqualem ſemidiametro ſphæ
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            rę A B C D; </s>
            <s xml:id="echoid-s4979" xml:space="preserve">eritq́ue maior altitudo coni S T V, quàm coni O P Q; </s>
            <s xml:id="echoid-s4980" xml:space="preserve">at baſes ęqua
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            les erunt. </s>
            <s xml:id="echoid-s4981" xml:space="preserve">Quare conus S T V, maior erit cono O P Q, propterea quòd coni
              <lb/>
            æqualium baſium eam inter ſe habent proportionem, quàm altitudines,
              <lb/>
            Quoniam uero ſphæra N, quadrupla eſt eius coni, qui baſim habet æqualẽ ma
              <lb/>
              <note position="left" xlink:label="note-140-01" xlink:href="note-140-01a" xml:space="preserve">14. duod.</note>
            ximo in ſphæra N, circulo, & </s>
            <s xml:id="echoid-s4982" xml:space="preserve">altitudinem æqualem ſemidiametro ſphæræ N,
              <lb/>
              <figure xlink:label="fig-140-01" xlink:href="fig-140-01a" number="41">
                <image file="140-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/140-01"/>
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            ut demonſtrauit Archimedes lib. </s>
            <s xml:id="echoid-s4983" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4984" xml:space="preserve">de ſphæra & </s>
            <s xml:id="echoid-s4985" xml:space="preserve">cylindro propoſ. </s>
            <s xml:id="echoid-s4986" xml:space="preserve">32. </s>
            <s xml:id="echoid-s4987" xml:space="preserve">Huius au
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            tem eiu ſdem coni quadruplus eſt conus S T V, eo quòd coni eandem haben-
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            tes alt itudinem proportionem habent, quam baſes; </s>
            <s xml:id="echoid-s4988" xml:space="preserve">erit conus S T V, ſphęræ
              <lb/>
              <note position="left" xlink:label="note-140-02" xlink:href="note-140-02a" xml:space="preserve">11. duod.</note>
            N, æqualis. </s>
            <s xml:id="echoid-s4989" xml:space="preserve">Eodem pacto, quia baſis coni O P Q, æqualis eſt ambitui corporis
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            E F G H I K L M, quia & </s>
            <s xml:id="echoid-s4990" xml:space="preserve">ęqualis ſuperſiciei ſphæræ N, quæ corpori illi iſo-
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            perim etra eſt: </s>
            <s xml:id="echoid-s4991" xml:space="preserve">altitudo uero æqualis ſemidiametro ſphæræ A B C D, erit ſo-
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            lido E F G H I K L M, æqualis conus O P Q, per ea, quæ Archimedes libro
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            1. </s>
            <s xml:id="echoid-s4992" xml:space="preserve">de ſphæra, & </s>
            <s xml:id="echoid-s4993" xml:space="preserve">cylindro propoſ. </s>
            <s xml:id="echoid-s4994" xml:space="preserve">29. </s>
            <s xml:id="echoid-s4995" xml:space="preserve">demonſtrauit. </s>
            <s xml:id="echoid-s4996" xml:space="preserve">Quamobrem & </s>
            <s xml:id="echoid-s4997" xml:space="preserve">ſphæra N,
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            mai or erit ſolido E F G H I K L M, conicis ſuperficiebus contento. </s>
            <s xml:id="echoid-s4998" xml:space="preserve">Sphæra igi-
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            tur omnibus corporibus ſibi iſoperimetris, & </s>
            <s xml:id="echoid-s4999" xml:space="preserve">circa alias ſphæras circumſcripti
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            bilibus, &</s>
            <s xml:id="echoid-s5000" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5001" xml:space="preserve">maior eſt, quod demonſtrandum erat.</s>
            <s xml:id="echoid-s5002" xml:space="preserve"/>
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            <s xml:id="echoid-s5003" xml:space="preserve">
              <emph style="sc">Haec</emph>
            ſunt, quæ mihi dicenda uidebantur de figuris Iſoperimetris. </s>
            <s xml:id="echoid-s5004" xml:space="preserve">Copio-
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            ſiorem autem tractationem eadem de re, Deo volente, alio in loco edemus
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            Nunc ad propoſitam ſphærę expoſitionem reuertamur.</s>
            <s xml:id="echoid-s5005" xml:space="preserve"/>
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              <emph style="sc">Necessitas</emph>
            , quoniam ſi mundus eſset alterius formæ, quàm ro-
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              <note position="left" xlink:label="note-140-03" xlink:href="note-140-03a" xml:space="preserve">Cælum eſſe
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              ro tundum
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              pro batur à
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              neceſſitate.</note>
            tundæ, ſcilicet trilateræ, uel quadrilateræ, uel multilateræ, ſequerentur
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            duo impoſſibilia, ſcilicet quòd aliquis locus eſset uacuus, & </s>
            <s xml:id="echoid-s5007" xml:space="preserve">corpus ſine </s>
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