Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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              <pb o="100" file="136" n="137" rhead="Comment. in I. Cap. Sphæræ"/>
            des (nempe corpus A B C D, ex illis compoſitum) æquales ſolido rectangu-
              <lb/>
            lo L R. </s>
            <s xml:id="echoid-s4838" xml:space="preserve">Quamobrem area cuiuſlibet corporis planis ſuperficiebus contenti,
              <lb/>
            &</s>
            <s xml:id="echoid-s4839" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4840" xml:space="preserve">quod demonſtrandum erat.</s>
            <s xml:id="echoid-s4841" xml:space="preserve"/>
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        <div xml:id="echoid-div265" type="section" level="1" n="91">
          <head xml:id="echoid-head95" style="it" xml:space="preserve">THEOR. 14. PROPOS. 16.</head>
          <p style="it">
            <s xml:id="echoid-s4842" xml:space="preserve">
              <emph style="sc">Area</emph>
            cuiuslibet ſphærę æqualis eſt ſolido rectangulo comprehenſo
              <lb/>
              <note position="left" xlink:label="note-136-01" xlink:href="note-136-01a" xml:space="preserve">Sphę ra q̃li
                <lb/>
              bet cui pa-
                <lb/>
              rallel epipe
                <lb/>
              do ſit ęqua
                <lb/>
              lis.</note>
            ſub ſemidiametro ſphæræ, & </s>
            <s xml:id="echoid-s4843" xml:space="preserve">tertia parte ambitus ſphæræ.</s>
            <s xml:id="echoid-s4844" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4845" xml:space="preserve">
              <emph style="sc">Esto</emph>
            ſphæra A B C, cuius centrum D, ſemidiameter A D: </s>
            <s xml:id="echoid-s4846" xml:space="preserve">Solidum au-
              <lb/>
            tem rectangulum E, contentum ſub ſemidiametro A D, & </s>
            <s xml:id="echoid-s4847" xml:space="preserve">tertia parte ambi-
              <lb/>
            tus ſpæræ A B C. </s>
            <s xml:id="echoid-s4848" xml:space="preserve">Dico corpus E, ſphæræ A B C, eſſe æquale. </s>
            <s xml:id="echoid-s4849" xml:space="preserve">Nam ſi non eſt
              <lb/>
            æquale; </s>
            <s xml:id="echoid-s4850" xml:space="preserve">ſit, ſi fieri poteſt, primum maius, ſitq́ue exceſfus corporis E, ſupra
              <lb/>
            ſphęram A B C, quantitas F. </s>
            <s xml:id="echoid-s4851" xml:space="preserve">Intelligatur circa ccntrum D, deſcripta ſphæ-
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            ra GHK, maior quàm ſphæra A B C, ita tamen, ut exceſſus ſphęrę G H K,
              <lb/>
            ſupra ſphęram A B C, non ſit maior quantitate F, ſed uel æqualis, uel mi-
              <lb/>
            nor, hoc eſt, vt ſphæra G H K, ſit uel ęqualis ſolido E, quando nimirum
              <lb/>
              <figure xlink:label="fig-136-01" xlink:href="fig-136-01a" number="38">
                <image file="136-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/136-01"/>
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            ipſa excedit ſphæram A B C, præciſe
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            quantitate F; </s>
            <s xml:id="echoid-s4852" xml:space="preserve">uel minor, ſi nimirum
              <lb/>
            ipſa excedit ſphęram A B C, mino-
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            ri quantitate, quàm F. </s>
            <s xml:id="echoid-s4853" xml:space="preserve">Neceſlario
              <lb/>
            enim aliqua ſphæra erit, quæ uel
              <lb/>
            æqualis ſit magnitudini E, atque
              <lb/>
            adeo maior, quàm ſphæra A B C;
              <lb/>
            </s>
            <s xml:id="echoid-s4854" xml:space="preserve">uel maior quidem quã ſphęra A B C,
              <lb/>
            minor vero quàm magnitudo E, quæ
              <lb/>
            maior ponitur, quàm ſphæra A B C. </s>
            <s xml:id="echoid-s4855" xml:space="preserve">
              <lb/>
            Inſcribatur deinde intra ſphæram
              <lb/>
            G H K, corpus, quod non tangat
              <lb/>
            ſphæram A B C, ita ut unaquæque
              <lb/>
              <note position="left" xlink:label="note-136-02" xlink:href="note-136-02a" xml:space="preserve">37. duod.</note>
            perpendicularium ex centro D, ad
              <lb/>
            baſes iſtius corporis eductarum ma-
              <lb/>
            ior fit ſemidiametro A D. </s>
            <s xml:id="echoid-s4856" xml:space="preserve">Si igitur
              <lb/>
            à centro D, ad omnes angulos di-
              <lb/>
            cti corporis ducantur lineæ rectæ,
              <lb/>
            ut totum corpus in pyramides di-
              <lb/>
            uidatur, quarum baſes ſunt eædem,
              <lb/>
            quæ corporis G H K, uertex au-
              <lb/>
            tem communis centrum D; </s>
            <s xml:id="echoid-s4857" xml:space="preserve">erit quæ
              <lb/>
            libet pyramis (per 14. </s>
            <s xml:id="echoid-s4858" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4859" xml:space="preserve">hu-
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            ius) æqualis ſolido rectangulo contento ſub eius perpendiculari, & </s>
            <s xml:id="echoid-s4860" xml:space="preserve">tertia
              <lb/>
            parte baſis; </s>
            <s xml:id="echoid-s4861" xml:space="preserve">A tque idcirco ſolidum rectangulum contentum ſub ſemidiame-
              <lb/>
            tro A D & </s>
            <s xml:id="echoid-s4862" xml:space="preserve">tertia parte baſis cuiuſlibet pyramidis, minus ipſa pyramide
              <lb/>
            erit. </s>
            <s xml:id="echoid-s4863" xml:space="preserve">Et quoniam omnia ſolida rectangula contenta ſub ſingulis perpendi-
              <lb/>
            cularibus ex centro D, ad baſes corporis dicti protractis, & </s>
            <s xml:id="echoid-s4864" xml:space="preserve">ſingulis ter-
              <lb/>
            tijs partibus baſium, ſimul ęqualia ſunt toti corpori, efficiunt autem om-
              <lb/>
            @es tertiæ partes baſium ſimul tertiam partem ambitus corporis, erit </s>
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