Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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            <s xml:id="echoid-s270" xml:space="preserve">
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            perficiem cadentes ſint æquales, ac proinde & </s>
            <s xml:id="echoid-s271" xml:space="preserve">earum quadrata æqualia; </s>
            <s xml:id="echoid-s272" xml:space="preserve">ſit au
              <lb/>
            tem tam quadratum ex G C, quadratis ex G H, H C, quàm quadratum ex
              <lb/>
              <note position="left" xlink:label="note-022-01" xlink:href="note-022-01a" xml:space="preserve">47. primi.</note>
            G E, quadratis ex G I, I E, æquale; </s>
            <s xml:id="echoid-s273" xml:space="preserve">erũt quadrata ex G H, H C, ſimul æqua-
              <lb/>
            lia quadratis ex G I, I E, ſimul. </s>
            <s xml:id="echoid-s274" xml:space="preserve">Demptis ergo æqualibus quadratis rectarum
              <lb/>
            G H, G I, (poſitæ enim ſunt hæ lineæ æquales) æqualia erunt reliqua quadra
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            ta rectarum H C, I E, ac proinde & </s>
            <s xml:id="echoid-s275" xml:space="preserve">rectæ H C, I E, æquales erunt: </s>
            <s xml:id="echoid-s276" xml:space="preserve">quæ cum
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            ſint ſemidiametri circulorum B C, F E, æquales erunt circuli ipſi B C, F E.</s>
            <s xml:id="echoid-s277" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s278" xml:space="preserve">QVOD ſi alter horũ circulorũ, nempe B C, longius à centro G, ponatur
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            diſtare, quàm alter F E, hoc eſt, perpẽdicularis G H, maior ponatur perpen-
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            diculari G I, oſtendemus eodem fere modo, circulum B C, minorem eſſe cir-
              <lb/>
            culo F E. </s>
            <s xml:id="echoid-s279" xml:space="preserve">Cum enim quadrata ex G H, H C, æqualia ſint demonſtrata qua-
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            dratis ex G I, I E; </s>
            <s xml:id="echoid-s280" xml:space="preserve">ſi auferantur quadrata inæqualia rectarum inæqualium
              <lb/>
              <figure xlink:label="fig-022-01" xlink:href="fig-022-01a" number="14">
                <image file="022-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/022-01"/>
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            G H, G I, quorum illud maius eſt,
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            (quòd & </s>
            <s xml:id="echoid-s281" xml:space="preserve">recta G H, maior ponatur
              <lb/>
            quàm recta G I,) erit reliquum qua
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            dratum rectæ H C, minus quadrato
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            reliquo rectæ I E; </s>
            <s xml:id="echoid-s282" xml:space="preserve">ac propterea & </s>
            <s xml:id="echoid-s283" xml:space="preserve">re
              <lb/>
            cta H C, minor erit, quàm recta I E.
              <lb/>
            </s>
            <s xml:id="echoid-s284" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s285" xml:space="preserve">circulus B C, circulo F E,
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            minor erit.</s>
            <s xml:id="echoid-s286" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s287" xml:space="preserve">SIT iam circulus omnium ma-
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            ximus A D. </s>
            <s xml:id="echoid-s288" xml:space="preserve">Dico eum per G, cen-
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            trum ſphæræ tranſire. </s>
            <s xml:id="echoid-s289" xml:space="preserve">Sienim non
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            tranſeat per centrũ, erit alius quiſ-
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            piam circulus per centrum G, tran
              <lb/>
            ſiens maior circulo A D, non per
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            centrũ tranſeũte, vt in hac propoſ,
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            demonſtratum eſt. </s>
            <s xml:id="echoid-s290" xml:space="preserve">Quare A D, non
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            eſt maximus circulus. </s>
            <s xml:id="echoid-s291" xml:space="preserve">Quod eſt ab-
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            ſurdum. </s>
            <s xml:id="echoid-s292" xml:space="preserve">Ponitur enim maximus. </s>
            <s xml:id="echoid-s293" xml:space="preserve">Tranſit ergo per G, centrum ſphæræ.</s>
            <s xml:id="echoid-s294" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s295" xml:space="preserve">DEINDE ſint æquales circuli B C, F E. </s>
            <s xml:id="echoid-s296" xml:space="preserve">Dico eos à centro G, æquali-
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            ter diſtare. </s>
            <s xml:id="echoid-s297" xml:space="preserve">Conſtructa enim figura, vt prius, erunt ſemidiametri H C, I E, æ-
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            quales. </s>
            <s xml:id="echoid-s298" xml:space="preserve">Et quoniam quadrata ex G H, H C, æqualia ſunt quadratis ex G I,
              <lb/>
              <note position="left" xlink:label="note-022-02" xlink:href="note-022-02a" xml:space="preserve">47. primi.</note>
            I E, vt demonſtratum eſt; </s>
            <s xml:id="echoid-s299" xml:space="preserve">ablatis æqualibus quadratis linearum æqualium
              <lb/>
            H C, I E, erunt reliqua quadrata rectarum G H, G I, æqualia; </s>
            <s xml:id="echoid-s300" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s301" xml:space="preserve">
              <lb/>
            lineæ G H, G I, æquales erunt. </s>
            <s xml:id="echoid-s302" xml:space="preserve">Quæ cum perpendiculares ſint, ex conſtru-
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            ctione, ad plana circulorum B C, F E, æqualiter à centro G, diſtabunt cir-
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            culi B C, F E, ex defin. </s>
            <s xml:id="echoid-s303" xml:space="preserve">6. </s>
            <s xml:id="echoid-s304" xml:space="preserve">huius lib.</s>
            <s xml:id="echoid-s305" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s306" xml:space="preserve">QVOD ſi alter circulorum B C, F E, nimirum circulus B C, minor po-
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            natur altero circulo F E, oſtendemus eodem ferè modo, perpendicularem
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            G H, maiorem eſſe perpendiculari G I. </s>
            <s xml:id="echoid-s307" xml:space="preserve">Cum enim quadrata ex G H, H C,
              <lb/>
            oſtenſa ſint æqualia quadratis ex G I, I E; </s>
            <s xml:id="echoid-s308" xml:space="preserve">ſit autem quadratum ex H C, mi-
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            nus quadrato ex I E; </s>
            <s xml:id="echoid-s309" xml:space="preserve">(quòd & </s>
            <s xml:id="echoid-s310" xml:space="preserve">ſemidiameter H C, circuli minoris minor ſit
              <lb/>
            ſemidiametro I E, circuli maioris) erit quadratum reliquum rectæ G H, reli
              <lb/>
            quo quadrato rectæ G I, maius; </s>
            <s xml:id="echoid-s311" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s312" xml:space="preserve">recta G H, maior erit, quàm
              <lb/>
            G I. </s>
            <s xml:id="echoid-s313" xml:space="preserve">Quare cum G H, G I, perpendiculares ſint, ex conſtructione, ad plana
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            circulorum, longius diſtabit, per defin. </s>
            <s xml:id="echoid-s314" xml:space="preserve">6. </s>
            <s xml:id="echoid-s315" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s316" xml:space="preserve">circulus B C, minor à cen
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            tro G, quàm circulus maior F E. </s>
            <s xml:id="echoid-s317" xml:space="preserve">Itaque circulorum, qui in ſphæra </s>
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