Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s14622" xml:space="preserve">
              <pb o="312" file="342" n="342" rhead="GEOMETR. PRACT."/>
            corpus circa ſphęram conicis ſuperficiebus contentum, quarum ſuperficierum
              <lb/>
            latera æqualia ſunt, nemp è eadem, quę figuræ, vt ab Archimede demonſtra-
              <lb/>
            tur propoſ. </s>
            <s xml:id="echoid-s14623" xml:space="preserve">22. </s>
            <s xml:id="echoid-s14624" xml:space="preserve">& </s>
            <s xml:id="echoid-s14625" xml:space="preserve">27. </s>
            <s xml:id="echoid-s14626" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14627" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14628" xml:space="preserve">de ſphęra & </s>
            <s xml:id="echoid-s14629" xml:space="preserve">cylindro. </s>
            <s xml:id="echoid-s14630" xml:space="preserve">Sit iam ſphæra N, Iſoperi-
              <lb/>
            metra corpori EFGHIKLM, circa ſphęram A B C D, deſcripto. </s>
            <s xml:id="echoid-s14631" xml:space="preserve">Dico ſphęram
              <lb/>
            N, dicto corpore eſſe maiorem. </s>
            <s xml:id="echoid-s14632" xml:space="preserve">Quoniam enim ambitus ſolidi EF GHIKLM,
              <lb/>
            maior eſt (per propoſ. </s>
            <s xml:id="echoid-s14633" xml:space="preserve">27. </s>
            <s xml:id="echoid-s14634" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14635" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14636" xml:space="preserve">Archimedis deſphęra & </s>
            <s xml:id="echoid-s14637" xml:space="preserve">cylindro) ambitu ſphę-
              <lb/>
            rę ABCD, erit quoque ambitus ſphęrę N, maior ambitu ſphęrę ABCD; </s>
            <s xml:id="echoid-s14638" xml:space="preserve">ideoq;
              <lb/>
            </s>
            <s xml:id="echoid-s14639" xml:space="preserve">ſemidiameter ſphęrę N, maior erit ſemidiametro ſphęrę ABCD. </s>
            <s xml:id="echoid-s14640" xml:space="preserve">Et quia ſuper-
              <lb/>
            ficies ſphęræ quadrupla eſt (per propoſ. </s>
            <s xml:id="echoid-s14641" xml:space="preserve">31. </s>
            <s xml:id="echoid-s14642" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14643" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14644" xml:space="preserve">Archimedis de ſphęra & </s>
            <s xml:id="echoid-s14645" xml:space="preserve">cy-
              <lb/>
            lindro) maximi circuli in ſphęra; </s>
            <s xml:id="echoid-s14646" xml:space="preserve">ſi ſumat circul
              <emph style="sub">9</emph>
            O P, quadrupl
              <emph style="sub">9</emph>
            circuli maximi
              <lb/>
            in ſphęra N; </s>
            <s xml:id="echoid-s14647" xml:space="preserve">(quod quidem facilè fiet, ſi diameter O P, dupla ſumatur diametri
              <lb/>
              <note symbol="a" position="left" xlink:label="note-342-01" xlink:href="note-342-01a" xml:space="preserve">2. duodec.</note>
            maximi circuli in ſphęra N. </s>
            <s xml:id="echoid-s14648" xml:space="preserve"> Quoniam enim vt circulus O P, ad circulum ma- ximum in ſphęra N, ita quadratum diametri O P, ad quadratum diametri circuli
              <lb/>
              <note symbol="b" position="left" xlink:label="note-342-02" xlink:href="note-342-02a" xml:space="preserve">20. ſexti.</note>
            maximi in ſphęra N; </s>
            <s xml:id="echoid-s14649" xml:space="preserve"> Eſt autem quadrati ad quadratum proportio duplica- ta proportionis laterum homologorum, erit quo que circulus O P, ad circulum
              <lb/>
            maximum in ſphęra N, in proportione duplicata proportionis diametri O P, ad
              <lb/>
            diametrum circuli maximi in ſphęra N. </s>
            <s xml:id="echoid-s14650" xml:space="preserve">Cum igitur diametri ponantur habere
              <lb/>
            proportionem duplam, habebunt circuli proportionem quadruplam; </s>
            <s xml:id="echoid-s14651" xml:space="preserve">qua-
              <lb/>
            drupla enim proportio duplicata eſt ꝓportionis duplæ, vt in his numeris appa-
              <lb/>
            ret. </s>
            <s xml:id="echoid-s14652" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14653" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14654" xml:space="preserve">4.) </s>
            <s xml:id="echoid-s14655" xml:space="preserve">erit circulus OP, ęqualis ſuperficiei ſphæræ N. </s>
            <s xml:id="echoid-s14656" xml:space="preserve">Accipiatur rurſus cir-
              <lb/>
            culus S T, æqualis circulo O P. </s>
            <s xml:id="echoid-s14657" xml:space="preserve">Statuatur deinde ſupra circulum S T, conus re-
              <lb/>
            ctus S T V, axem V X, æqualem habens ſemidiametro ſphæræ N: </s>
            <s xml:id="echoid-s14658" xml:space="preserve">item ſupra cir-
              <lb/>
            culum O P, alter conus N P Q, conſtruatur habens axem Q R, ęqualem ſemidia-
              <lb/>
              <figure xlink:label="fig-342-01" xlink:href="fig-342-01a" number="235">
                <image file="342-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/342-01"/>
              </figure>
            metro ſphęrę ABCD; </s>
            <s xml:id="echoid-s14659" xml:space="preserve">eritque maior altitudo coni S T V, quam coni O P Q. </s>
            <s xml:id="echoid-s14660" xml:space="preserve">at
              <lb/>
              <note symbol="c" position="left" xlink:label="note-342-03" xlink:href="note-342-03a" xml:space="preserve">14. duodec.</note>
            baſes ęquales erunt. </s>
            <s xml:id="echoid-s14661" xml:space="preserve">Quare conus S T V, maior erit cono O P Q; </s>
            <s xml:id="echoid-s14662" xml:space="preserve"> propterea quod coni æqualium baſium eaminter ſe habent proportionem, quam altitudi-
              <lb/>
            nes. </s>
            <s xml:id="echoid-s14663" xml:space="preserve">Quoniam verò ſphęra N, quadrupla eſt eius coni, qui baſem habet ęqua-
              <lb/>
            lem maximo in ſphęra N, circulo, & </s>
            <s xml:id="echoid-s14664" xml:space="preserve">altitudinem ęqualem ſemidiametro ſphęrę
              <lb/>
            N, vt demonſtrauit Archimedes lib. </s>
            <s xml:id="echoid-s14665" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14666" xml:space="preserve">de ſphęra & </s>
            <s xml:id="echoid-s14667" xml:space="preserve">cylindro propoſ. </s>
            <s xml:id="echoid-s14668" xml:space="preserve">32. </s>
            <s xml:id="echoid-s14669" xml:space="preserve">Huius
              <lb/>
            autem eiuſdem coni quadruplus eſt conus S T V, eo quod coni eandem
              <note symbol="d" position="left" xlink:label="note-342-04" xlink:href="note-342-04a" xml:space="preserve">11. duodec.</note>
            tes altitu dinem proportionem habent quam baſes; </s>
            <s xml:id="echoid-s14670" xml:space="preserve"> erit conus S T V,
              <note symbol="e" position="left" xlink:label="note-342-05" xlink:href="note-342-05a" xml:space="preserve">9. quinti.</note>
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