Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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              <pb o="101" file="137" n="138" rhead="Ioan. de Sacro Boſco."/>
            lidum rectangulum contentum ſub ſemidiametro A D, & </s>
            <s xml:id="echoid-s4865" xml:space="preserve">tertia parte ambit@
              <lb/>
            præfati corporis inſcripti intra ſphærã G H K, minus corpore inſcripto. </s>
            <s xml:id="echoid-s4866" xml:space="preserve">Quo-
              <lb/>
            niã vero ambitus corporis inſcripti maior eſt ambitu ſphæræ A B C, ut demon
              <lb/>
            ſtrat Archimedes lib. </s>
            <s xml:id="echoid-s4867" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4868" xml:space="preserve">de ſphæra, & </s>
            <s xml:id="echoid-s4869" xml:space="preserve">cylindro propoſ. </s>
            <s xml:id="echoid-s4870" xml:space="preserve">27. </s>
            <s xml:id="echoid-s4871" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s4872" xml:space="preserve">tertia
              <lb/>
            pars ambitus dicti corporis maior tertia parte ambitus ſphęræ A B C, erit ſo-
              <lb/>
            lidum rectangulum contentum ſub ſemidiametro A D, & </s>
            <s xml:id="echoid-s4873" xml:space="preserve">tertia parte ambitus
              <lb/>
            ſphærę A B C, hoc eſt, ſolidum E, multo minus corpore inſcripto intra ſphærã
              <lb/>
            G H K: </s>
            <s xml:id="echoid-s4874" xml:space="preserve">Poſita eſt autem ſphæra G H K, uel æqualis ſolido E, vel minor. </s>
            <s xml:id="echoid-s4875" xml:space="preserve">Igitur
              <lb/>
            & </s>
            <s xml:id="echoid-s4876" xml:space="preserve">ſphęra G H K, minor erit corpore intra ipſam deſcripto, totum parte, quod
              <lb/>
            eſt abſurdum. </s>
            <s xml:id="echoid-s4877" xml:space="preserve">Quocirca ſolidum E, maius non erit ſphæra A B C.</s>
            <s xml:id="echoid-s4878" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4879" xml:space="preserve">
              <emph style="sc">Sitdeinde</emph>
            , ſi fieri poteſt, ſolidum E, minus, quàm ſphæra A B C,
              <lb/>
            excedaturq́ue à ſphæra A B C, quantitate F. </s>
            <s xml:id="echoid-s4880" xml:space="preserve">Intelligatur circa centrum D,
              <lb/>
            ſphæra deſcripta L M N, minor, quàm ſphæia A B C, ita tamen, ut exceſſus,
              <lb/>
            quo ſphæra L M N, ſuperatur à ſphæra A B C, non ſit maior quantitate F,
              <lb/>
            ſed uel æqualis, uel minor, hoc eſt, ut ſphæra L M N, ſit uel ęqualis ſolido
              <lb/>
            E, ſi nimirum ipſa excedatur a ſphæra A B C, quantitate F, vel maior ſolido
              <lb/>
            E, ſi uidelicet ſphæra L M N, a ſphæra A B C, ſuperetur minori quantitate,
              <lb/>
            quam F. </s>
            <s xml:id="echoid-s4881" xml:space="preserve">Neceſſario enim aliqua ſphæra erit, quę uel æqualis ſit ſolido E, at-
              <lb/>
            que adeo minor, quàm ſphęra A B C; </s>
            <s xml:id="echoid-s4882" xml:space="preserve">uel minor quidem, quàm ſphęra A B C,
              <lb/>
            maior uerò, quàm magnitu
              <unsure/>
            do E, quæ minor ponitur, quàm ſphæra A B C. </s>
            <s xml:id="echoid-s4883" xml:space="preserve">De-
              <lb/>
            ſcribatur deinde intra ſphæram A B C, corpus, quod minime tangat ſphęram
              <lb/>
              <note position="right" xlink:label="note-137-01" xlink:href="note-137-01a" xml:space="preserve">17. duod.</note>
            L M N; </s>
            <s xml:id="echoid-s4884" xml:space="preserve">ita ut unaquæque perpendicularium ex centro D, ad baſes huius cor-
              <lb/>
            poris inſcripti cadentium minor ſit ſemidiametro A D. </s>
            <s xml:id="echoid-s4885" xml:space="preserve">Si igitur à centro D,
              <lb/>
            ad omnes eius angulos lineæ extendantur, ut totum corpus in pyramides re-
              <lb/>
            ſoluatur, quarum baſes ſunt eędem, quæ corporis A B C, uertex autem com-
              <lb/>
            munis centrum D; </s>
            <s xml:id="echoid-s4886" xml:space="preserve">erit quælibet pyramis æqualis (per 14. </s>
            <s xml:id="echoid-s4887" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4888" xml:space="preserve">huius) ſoli-
              <lb/>
            do rectangulo contento ſub eius perpendiculari, & </s>
            <s xml:id="echoid-s4889" xml:space="preserve">tertia parte baſis, Et ideo
              <lb/>
            ſolidum rectan gulum contentum ſub ſemidiametro A D, & </s>
            <s xml:id="echoid-s4890" xml:space="preserve">tertia baſis cuiuſ-
              <lb/>
            uis pyramidis, maius erit pyramide ipſa. </s>
            <s xml:id="echoid-s4891" xml:space="preserve">Et quoniam omnia ſolida rectangu-
              <lb/>
            la contenta ſub ſingulis perpendicularibus ex centro D, ad baſes corporis di-
              <lb/>
            cti protractis, & </s>
            <s xml:id="echoid-s4892" xml:space="preserve">ſingulis tertijs partibus baſium, ſimul ęqualia ſunt toti corpo-
              <lb/>
            ri, eſſiciunt autem omnes tertię partes baſium ſimul tertiam partem ambitus
              <lb/>
            corporis; </s>
            <s xml:id="echoid-s4893" xml:space="preserve">erit ſolidum rectangulum contentum ſub ſemidiametro A D, & </s>
            <s xml:id="echoid-s4894" xml:space="preserve">ter-
              <lb/>
            tia parte ambitus dicti corporis ſphærę A B C, inſcripti, maius corpore inſcri-
              <lb/>
            pto. </s>
            <s xml:id="echoid-s4895" xml:space="preserve">Cum igitur ambitus ſphærę A B C, maior ſit ambitu corporis ſibi in ſcripti
              <lb/>
            atque adeo & </s>
            <s xml:id="echoid-s4896" xml:space="preserve">tertia pars ambitus ſphæræ maior tertia parte ambitus dicti cor-
              <lb/>
            poris, erit ſolidum rectan gulum contentum ſub A D, ſemidiametro, & </s>
            <s xml:id="echoid-s4897" xml:space="preserve">tertia
              <lb/>
            parte ambitus ſphærę A B C, hoc eſt, ſolidum E, multo maius corpore inſcri-
              <lb/>
            pto intra ſphæram A B C: </s>
            <s xml:id="echoid-s4898" xml:space="preserve">Ponebatur autem ſphæra L M N, uel æqualis ſoli-
              <lb/>
            do E, uel maior. </s>
            <s xml:id="echoid-s4899" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s4900" xml:space="preserve">ſphęra L M N, maior erit corpore intra ſphęram
              <lb/>
            A B C, deſcripto, pars toto, quod eſt abſurdum. </s>
            <s xml:id="echoid-s4901" xml:space="preserve">Non igitur ſolidum E, minus
              <lb/>
            erit ſphęra A B C. </s>
            <s xml:id="echoid-s4902" xml:space="preserve">Cum ergo neque maius ſit oſtenſum, ęquale omnino erit.
              <lb/>
            </s>
            <s xml:id="echoid-s4903" xml:space="preserve">Ac propterea area cuiuslibet ſphæræ æqualis eſt ſolido rectangulo compre-
              <lb/>
            henſo ſub ſemidiametro ſphæræ, & </s>
            <s xml:id="echoid-s4904" xml:space="preserve">tertia parte ambitus ſphæræ, quod demon-
              <lb/>
            ſtrandum erat.</s>
            <s xml:id="echoid-s4905" xml:space="preserve"/>
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