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

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          <p>
            <s xml:id="echoid-s231" xml:space="preserve">
              <pb o="9" file="021" n="21" rhead=""/>
            dum. </s>
            <s xml:id="echoid-s232" xml:space="preserve">Dato enim plano, à puncto, quod in illo datum eſt, duæ rectæ lincæ ad
              <lb/>
              <note position="right" xlink:label="note-021-01" xlink:href="note-021-01a" xml:space="preserve">13. vndee.</note>
            rectos angulos non excitantur. </s>
            <s xml:id="echoid-s233" xml:space="preserve">Quare ſi ſphæra planum tangat, quod ipſam
              <lb/>
            non ſecet, &</s>
            <s xml:id="echoid-s234" xml:space="preserve">c. </s>
            <s xml:id="echoid-s235" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s236" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div36" type="section" level="1" n="28">
          <head xml:id="echoid-head39" xml:space="preserve">THEOREMA 5. PROPOS. 6.</head>
          <note position="right" xml:space="preserve">6.</note>
          <note position="right" xml:space="preserve">7.</note>
          <p>
            <s xml:id="echoid-s237" xml:space="preserve">CIRCVLORVM, qui in ſphæra ſunt, ma-
              <lb/>
            ximi ſunt, qui per ſphærę centrum ducuntui: </s>
            <s xml:id="echoid-s238" xml:space="preserve">alio-
              <lb/>
            rum autem illi inter ſe æquales ſunt, qui æqualiter
              <lb/>
            à centro diſtát: </s>
            <s xml:id="echoid-s239" xml:space="preserve">qui vero longius à centro diſtant,
              <lb/>
            minores ſunt. </s>
            <s xml:id="echoid-s240" xml:space="preserve">Et circuli in ſphæra maximi per
              <lb/>
            ſphæræ centrum tranſeunt: </s>
            <s xml:id="echoid-s241" xml:space="preserve">aliorum autem æqua-
              <lb/>
            les à centro æqualiter diſtant: </s>
            <s xml:id="echoid-s242" xml:space="preserve">minores verò lon-
              <lb/>
            gius à centro diſtant.</s>
            <s xml:id="echoid-s243" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s244" xml:space="preserve">IN ſphæra A B C D E F, cuius centrum G, tranſeat circulus A D, per
              <lb/>
            centrum G, & </s>
            <s xml:id="echoid-s245" xml:space="preserve">alij B C, F E, non per centrum. </s>
            <s xml:id="echoid-s246" xml:space="preserve">Dico A D, circulum eſſe om-
              <lb/>
            nium maximum, &</s>
            <s xml:id="echoid-s247" xml:space="preserve">c. </s>
            <s xml:id="echoid-s248" xml:space="preserve">Ducantur ex centro G, ad plana circulorum B C, F E,
              <lb/>
              <note position="right" xlink:label="note-021-04" xlink:href="note-021-04a" xml:space="preserve">11. vndec.
                <lb/>
              Coroll. 1.
                <lb/>
              huius.</note>
            perpendiculares G H, G I, quæ in ipſorum centra cadent; </s>
            <s xml:id="echoid-s249" xml:space="preserve">ita vt H, I, cen-
              <lb/>
            tra ſint circulorum B C, F E: </s>
            <s xml:id="echoid-s250" xml:space="preserve">Eſt autem G, centrũ ſphæræ, centrũ quoq; </s>
            <s xml:id="echoid-s251" xml:space="preserve">cir-
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              <figure xlink:label="fig-021-01" xlink:href="fig-021-01a" number="13">
                <image file="021-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/021-01"/>
              </figure>
              <note position="right" xlink:label="note-021-05" xlink:href="note-021-05a" xml:space="preserve">Coroll. 1.
                <lb/>
              huius.</note>
            culi A D, per centrum ſphæræ tra-
              <lb/>
            iecti. </s>
            <s xml:id="echoid-s252" xml:space="preserve">Si igitur ex G, H, I, ad ſuper-
              <lb/>
            ficiem ſphæræ rectæ ducantur G D,
              <lb/>
            H C, I E, erũt hæ ſemidiametri cir
              <lb/>
            culorum A D, B C, F E. </s>
            <s xml:id="echoid-s253" xml:space="preserve">Conne-
              <lb/>
            ctantur autem rectæ G C, G E. </s>
            <s xml:id="echoid-s254" xml:space="preserve">Quo
              <lb/>
            niam igitur in triangulo G H C, an
              <lb/>
            gulus H, rectus eſt, ex defin. </s>
            <s xml:id="echoid-s255" xml:space="preserve">3. </s>
            <s xml:id="echoid-s256" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s257" xml:space="preserve">11
              <lb/>
            Eucl. </s>
            <s xml:id="echoid-s258" xml:space="preserve">erit quadratum ex G C, æqua
              <lb/>
              <note position="right" xlink:label="note-021-06" xlink:href="note-021-06a" xml:space="preserve">47. primi.</note>
            le quadratis ex G H, H C. </s>
            <s xml:id="echoid-s259" xml:space="preserve">Dempto
              <lb/>
            ergo quadrato rectæ G H, maius e-
              <lb/>
            rit quadratum ex G C, quadrato ex
              <lb/>
            H C; </s>
            <s xml:id="echoid-s260" xml:space="preserve">atque adeò & </s>
            <s xml:id="echoid-s261" xml:space="preserve">recta G C, hoc
              <lb/>
            eſt, ſibi æqualis G D, (ducuntur em̃
              <lb/>
            G C, G D, ex centro ſphæræ ad ſu-
              <lb/>
            perficiem) maior erit, quàm recta
              <lb/>
            H C. </s>
            <s xml:id="echoid-s262" xml:space="preserve">Quare circulus A D, maiorẽ
              <lb/>
            habens ſemidiametrum, quàm circulus B C, maior erit circulo B C. </s>
            <s xml:id="echoid-s263" xml:space="preserve">Non ſe-
              <lb/>
            cus oſtendemus, circulum A D, quocunque alio, qui per centrum G, non
              <lb/>
            tranſeat, maiorem eſſe. </s>
            <s xml:id="echoid-s264" xml:space="preserve">Maximus eſt ergo circulus A D.</s>
            <s xml:id="echoid-s265" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s266" xml:space="preserve">DISTENT iam circuli B C, F E, à centro G, æqualiter, hoc eſt, per-
              <lb/>
            pendiculares G H, G I, æquales ſint, ex deſin. </s>
            <s xml:id="echoid-s267" xml:space="preserve">6. </s>
            <s xml:id="echoid-s268" xml:space="preserve">huius libri. </s>
            <s xml:id="echoid-s269" xml:space="preserve">Dico circulos
              <lb/>
            B C, F E, æquales eſſe. </s>
            <s xml:id="echoid-s270" xml:space="preserve">Cum enim rectæ G C, G E, à centro ſphæræ in eius </s>
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