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

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            <s xml:id="echoid-s3413" xml:space="preserve">
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            culus maximus I K. </s>
            <s xml:id="echoid-s3414" xml:space="preserve">Quoniam igitur arcus continui F I, I E, æquales ſunt, erit
              <lb/>
            H K, maior quàm K G; </s>
            <s xml:id="echoid-s3415" xml:space="preserve">atque adeo H K, maior erit dimidio ipſius H G, Qua-
              <lb/>
              <note position="left" xlink:label="note-100-01" xlink:href="note-100-01a" xml:space="preserve">6. huius.</note>
            re maior erit proportio H K, ad F I, quàm arcus dimidij ipſius H G, ad F I:
              <lb/>
            </s>
            <s xml:id="echoid-s3416" xml:space="preserve">
              <note position="left" xlink:label="note-100-02" xlink:href="note-100-02a" xml:space="preserve">8. quinti.</note>
            Sed vt dimidium arcus H G, ad F I, dimidium arcus F E, ita eſt totus arcus
              <lb/>
              <note position="left" xlink:label="note-100-03" xlink:href="note-100-03a" xml:space="preserve">15. quinti.</note>
            H G, ad totum arcum F E, Igitur maior erit proportio H K, ad F I, quam H G,
              <lb/>
            ad F E: </s>
            <s xml:id="echoid-s3417" xml:space="preserve">Ponitur autem, vt H G, ad F E, ita B H, ad C F. </s>
            <s xml:id="echoid-s3418" xml:space="preserve">Igitur maior erit quo-
              <lb/>
            que proportio H K, ad F I, quàm B H, ad C F; </s>
            <s xml:id="echoid-s3419" xml:space="preserve">atque adeo arcus H K, ad ar-
              <lb/>
            cum arcu F I, maiorem erit, vt B H, ad C F. </s>
            <s xml:id="echoid-s3420" xml:space="preserve">Quod eſt abſurdum. </s>
            <s xml:id="echoid-s3421" xml:space="preserve">Demonſtra-
              <lb/>
              <note position="left" xlink:label="note-100-04" xlink:href="note-100-04a" xml:space="preserve">10. quinti.</note>
            tum enim proxime ſuit in ſecunda figura, non poſſe eſſe, vt eſt arcus B H, ad
              <lb/>
            C F, ita arcum H K, ad arcum arcu F I, maiorem. </s>
            <s xml:id="echoid-s3422" xml:space="preserve">Non ergo eſt, vt B H, ad
              <lb/>
            C F, ita H G, ad F E: </s>
            <s xml:id="echoid-s3423" xml:space="preserve">ſed neque, vt B H, ad C F, ita eſt H G, ad arcum arcu
              <lb/>
            F E, maiorem, vt demonſtratum eſt. </s>
            <s xml:id="echoid-s3424" xml:space="preserve">Igitur erit, vt B H, ad C F, ita H G, ad
              <lb/>
            arcum arcu F E, minorem. </s>
            <s xml:id="echoid-s3425" xml:space="preserve">Quare ſi polus parallelorum ſit in circunferentia,
              <lb/>
            &</s>
            <s xml:id="echoid-s3426" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3427" xml:space="preserve">Quod oſtendendum erat.</s>
            <s xml:id="echoid-s3428" xml:space="preserve"/>
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        <div xml:id="echoid-div280" type="section" level="1" n="129">
          <head xml:id="echoid-head143" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s3429" xml:space="preserve">HINC ſit, maiorem eſſe proportionem arcus B H, ad atcum C F, quàm arcus H G, ad
              <lb/>
            arcum F E. </s>
            <s xml:id="echoid-s3430" xml:space="preserve">Cum enim ſit, vt B H, ad C F, ita H G, ad atcum arcu F E, minorem: </s>
            <s xml:id="echoid-s3431" xml:space="preserve">Sit autem
              <lb/>
              <note position="left" xlink:label="note-100-05" xlink:href="note-100-05a" xml:space="preserve">10. huius.</note>
            maior proportio arcus H G, ad arcum arcu F E, minorem, quàm ad F E; </s>
            <s xml:id="echoid-s3432" xml:space="preserve">erit quoque maior
              <lb/>
              <note position="left" xlink:label="note-100-06" xlink:href="note-100-06a" xml:space="preserve">8. quinti.</note>
            proportio B H, ad C F, quàm H G, ad F E.</s>
            <s xml:id="echoid-s3433" xml:space="preserve"/>
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        <div xml:id="echoid-div282" type="section" level="1" n="130">
          <head xml:id="echoid-head144" xml:space="preserve">THEOR. 11. PROPOS. 11.</head>
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            <s xml:id="echoid-s3434" xml:space="preserve">SI polus parallelorum ſit in circunferentia ma
              <lb/>
            ximi circuli, quem duo alij maximi circuli ad an-
              <lb/>
            gulos rectos ſecent, quorum alter ſit vnus paralle-
              <lb/>
            lorum, alter vero ſit obliquus ad parallelos; </s>
            <s xml:id="echoid-s3435" xml:space="preserve">alius
              <lb/>
            autem maximus circulus per polos parallelorum
              <lb/>
            tranſiens obliquum circulũ ſecet inter maximum
              <lb/>
            parallelorum, & </s>
            <s xml:id="echoid-s3436" xml:space="preserve">eum, quem obliquus circulus tan
              <lb/>
            git: </s>
            <s xml:id="echoid-s3437" xml:space="preserve">Diameter ſphæræ ad diametrum eius circuli,
              <lb/>
            quem tãgit obliquus circulus, maiorem rationem
              <lb/>
            habet, quàm circunferentia maximi parallelorum
              <lb/>
            intercepta inter maximum circulum primo poſi-
              <lb/>
            tum, & </s>
            <s xml:id="echoid-s3438" xml:space="preserve">maximum circulum per polos parallelo-
              <lb/>
            rum tranſeuntem, ad circunferentiam obliqui cir-
              <lb/>
            culi inter eoſdem circulos interceptam.</s>
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