Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s14521" xml:space="preserve">
              <pb o="309" file="339" n="339" rhead="LIBER SEPTIMVS."/>
            ABC. </s>
            <s xml:id="echoid-s14522" xml:space="preserve">Dico corpus E, ſphæræ ABC, eſſe æquale. </s>
            <s xml:id="echoid-s14523" xml:space="preserve">Nam ſi non eſt æquale: </s>
            <s xml:id="echoid-s14524" xml:space="preserve">ſit, ſi
              <lb/>
            fieri poteſt, primum maius, ſitque exceſſus corporis E, ſupra ſphæram A B C,
              <lb/>
            quantitas F. </s>
            <s xml:id="echoid-s14525" xml:space="preserve">Intelligatur circa centrum D, deſcripta ſphæra GHK, maior quam
              <lb/>
            ſphæra ABC, ita tamen, vt exceſſus ſphæræ GHK, ſupra ſphęram ABC, non ſit
              <lb/>
            maior quantitate F, ſed vel æqualis, vel minor, hoc eſt, vt ſphæra GHK, ſit vel ę-
              <lb/>
            qualis ſolido E, quando nimirum ipſa excedit ſphærã A B C, præciſè quantitate
              <lb/>
            F; </s>
            <s xml:id="echoid-s14526" xml:space="preserve">vel minor, ſi nimirum ipſa excedit ſphæram A B C, minori quãtitate, quam F.
              <lb/>
            </s>
            <s xml:id="echoid-s14527" xml:space="preserve">Neceſſario enim aliqua ſphæra erit, quæ vel æqualis ſit magnitudini E, atq; </s>
            <s xml:id="echoid-s14528" xml:space="preserve">ad-
              <lb/>
            eo maior quam ſphæra ABC; </s>
            <s xml:id="echoid-s14529" xml:space="preserve">vel maior quidem quam ſphæra ABC, minor verò
              <lb/>
              <note symbol="a" position="right" xlink:label="note-339-01" xlink:href="note-339-01a" xml:space="preserve">17. duodec.</note>
            quam magnitudo E, quæ maior ponitur, quam ſphæra ABC. </s>
            <s xml:id="echoid-s14530" xml:space="preserve"> Inſcribatur de- inde intra ſphæram GHK, corpus, quod non tangat ſphæram A B C, ita vt vna-
              <lb/>
            quæque perpendicularium ex centro D, ad baſes iſtius corporis eductarum ma-
              <lb/>
            ior ſit ſemidiametro A D. </s>
            <s xml:id="echoid-s14531" xml:space="preserve">Siigitur à centro D, ad omnes angulos dicti corporis
              <lb/>
            ducantur lineæ rectæ, vt to tum corpus in pyramides diuidatur, quarum baſes
              <lb/>
            ſunt eædem, quæ corporis G H K, vertex autem communis centrum D; </s>
            <s xml:id="echoid-s14532" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-339-02" xlink:href="note-339-02a" xml:space="preserve">14. hui{us}.</note>
            quælibet pyramis æqualis ſolido rectangulo contento ſub eius perpendiculari,
              <lb/>
            & </s>
            <s xml:id="echoid-s14533" xml:space="preserve">tertia parte baſis; </s>
            <s xml:id="echoid-s14534" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s14535" xml:space="preserve">idcirco ſolidum
              <lb/>
              <figure xlink:label="fig-339-01" xlink:href="fig-339-01a" number="231">
                <image file="339-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/339-01"/>
              </figure>
            rectangulum contentum ſub ſemidiame-
              <lb/>
            tro AD, & </s>
            <s xml:id="echoid-s14536" xml:space="preserve">tertia parte baſis cuiuslibet py-
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            ramidis, minus ipſa pyramide erit. </s>
            <s xml:id="echoid-s14537" xml:space="preserve">Et quo-
              <lb/>
            niam omnia ſolida rectangula cõtenta ſub
              <lb/>
            ſingulis perpendicularibus ex centro D, ad
              <lb/>
            baſes corporis dicti protractis, & </s>
            <s xml:id="echoid-s14538" xml:space="preserve">ſingulis
              <lb/>
            tertijs partibus baſium, ſimul æqualia ſunt
              <lb/>
            toti corpori; </s>
            <s xml:id="echoid-s14539" xml:space="preserve">efficiunt autem omnes tertiæ
              <lb/>
            partes baſium ſimul tertiam partem ambi-
              <lb/>
            tus corporis; </s>
            <s xml:id="echoid-s14540" xml:space="preserve">erit ſolidum rectangulũ con-
              <lb/>
            tẽtum ſub ſemidiametro AD, & </s>
            <s xml:id="echoid-s14541" xml:space="preserve">tertia par-
              <lb/>
            te ambitus præfati corporis inſcripti intra
              <lb/>
            ſphæram G H K, minus corpore inſcripto.
              <lb/>
            </s>
            <s xml:id="echoid-s14542" xml:space="preserve">Quoniam verò ambitus corporis inſcripti
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            maior eſt ambitu ſphęræ ABC, vt demon-
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            ſtrat Archimedes lib. </s>
            <s xml:id="echoid-s14543" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14544" xml:space="preserve">de ſphęra & </s>
            <s xml:id="echoid-s14545" xml:space="preserve">cylin-
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            dro propoſ. </s>
            <s xml:id="echoid-s14546" xml:space="preserve">27. </s>
            <s xml:id="echoid-s14547" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s14548" xml:space="preserve">tertia pars
              <lb/>
            ambitus dicti corporis maior tertia parte ambitus ſphęrę ABC: </s>
            <s xml:id="echoid-s14549" xml:space="preserve">erit ſolidum re-
              <lb/>
            ctangulum contentum ſub ſemidiametro AD, & </s>
            <s xml:id="echoid-s14550" xml:space="preserve">tertia parte ambitus ſphęrę A-
              <lb/>
            B C, hoc eſt, ſolidum E, multo minus corpore inſcripto intra ſphęram G H K: </s>
            <s xml:id="echoid-s14551" xml:space="preserve">
              <lb/>
            Poſita eſt autem ſphæra GHK, vel æqualis ſolido E, vel minor. </s>
            <s xml:id="echoid-s14552" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s14553" xml:space="preserve">ſphę-
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            ra G H K, minor erit corpore intra ipſam deſcripto, totum parte quod eſt ab-
              <lb/>
            ſurdum. </s>
            <s xml:id="echoid-s14554" xml:space="preserve">Quo circa ſolidum E, maius non erit ſphęra ABC.</s>
            <s xml:id="echoid-s14555" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s14556" xml:space="preserve">
              <emph style="sc">Sit</emph>
              <emph style="sc">Deinde</emph>
            , ſi fieri poteſt, ſolidum E, minus, quam ſphęra ABC, exce-
              <lb/>
            datur que à ſphęra ABC, quantitate F. </s>
            <s xml:id="echoid-s14557" xml:space="preserve">Intelligatur circa centrum D, ſphęra de-
              <lb/>
            ſcripta L M N, minor quàm ſphęra A B C, ita tamen vt exceſſus, quo ſphęra
              <lb/>
            LMN, ſuperatur à ſphęra ABC, non ſit maior quantitate F, ſed vel æqualis, vel
              <lb/>
            minor, hoc eſt, vt ſphęra LMN, ſit vel æqualis ſolido E, ſi nimirum ipſa exceda-
              <lb/>
            tur à ſphęra ABC, quantitate F, vel maior ſolido E, ſi videlicet ſphęra L M N, à
              <lb/>
            ſphęra ABC, ſuperetur minori quantitate, quam F. </s>
            <s xml:id="echoid-s14558" xml:space="preserve">Neceſſario enim aliqua </s>
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