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

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            <s xml:id="echoid-s2909" xml:space="preserve">ÆQVALES rectæ lineæ ex circulis inæqualibus auferunt ar-
              <lb/>
            cus inæquales, maiorq́ue eſt arcus minoris circuli, quàm vt ſimilis
              <lb/>
            ſit arcui maioris circuli.</s>
            <s xml:id="echoid-s2910" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2911" xml:space="preserve">_SINT_ circuli inæquales A B, C D, circa idem centrum E, deſcripti:
              <lb/>
            </s>
            <s xml:id="echoid-s2912" xml:space="preserve">ducantur autem ex E, duærectę vtcunque E A, E B, ſecantes circulum
              <lb/>
            C D, in punctis C, D: </s>
            <s xml:id="echoid-s2913" xml:space="preserve">erunt{quam} arcus A B, C D, ſimiles, cum illis idem an-
              <lb/>
              <note position="right" xlink:label="note-087-01" xlink:href="note-087-01a" xml:space="preserve">ſchol. 33.
                <lb/>
              ſexti.</note>
            gulus E, inſiſtat ad centrum. </s>
            <s xml:id="echoid-s2914" xml:space="preserve">Et quoniam rectæ E A, E B, proportiona-
              <lb/>
              <figure xlink:label="fig-087-01" xlink:href="fig-087-01a" number="94">
                <image file="087-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/087-01"/>
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            liter ſunt ſectæ in punctis C, D, quòd E A,
              <lb/>
            E B, æquales ſint, nec non E C, E D; </s>
            <s xml:id="echoid-s2915" xml:space="preserve">erunt re-
              <lb/>
              <note position="right" xlink:label="note-087-02" xlink:href="note-087-02a" xml:space="preserve">2. ſexti.</note>
            etæ ductæ A B, C D, parallelæ; </s>
            <s xml:id="echoid-s2916" xml:space="preserve">atque adeo
              <lb/>
            triangula E A B, E C D, ſimilia, habentia
              <lb/>
              <note position="right" xlink:label="note-087-03" xlink:href="note-087-03a" xml:space="preserve">Coroll. 4.
                <lb/>
              ſexti.</note>
            angulos E A B, E C D, inter ſe æquales, nec
              <lb/>
            non & </s>
            <s xml:id="echoid-s2917" xml:space="preserve">angulos E B A, E D C, & </s>
            <s xml:id="echoid-s2918" xml:space="preserve">angulũ E,
              <lb/>
              <note position="right" xlink:label="note-087-04" xlink:href="note-087-04a" xml:space="preserve">4. ſexti.</note>
            communem. </s>
            <s xml:id="echoid-s2919" xml:space="preserve">Quare erit, vt E A, ad A B,
              <lb/>
            ita E C, ad C D: </s>
            <s xml:id="echoid-s2920" xml:space="preserve">Eſt autem E A, maior quam
              <lb/>
            E C. </s>
            <s xml:id="echoid-s2921" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s2922" xml:space="preserve">A B, maior erit, quàm C D.
              <lb/>
            </s>
            <s xml:id="echoid-s2923" xml:space="preserve">
              <note position="right" xlink:label="note-087-05" xlink:href="note-087-05a" xml:space="preserve">14. quinti.</note>
            Accommodetur igitur ipſi C D, in circulo
              <lb/>
              <note position="right" xlink:label="note-087-06" xlink:href="note-087-06a" xml:space="preserve">1. quarti.</note>
            A B, æqualis B F; </s>
            <s xml:id="echoid-s2924" xml:space="preserve">erit{quam} arcus A B, maior, quàm F B. </s>
            <s xml:id="echoid-s2925" xml:space="preserve">Quare cum ar-
              <lb/>
              <note position="right" xlink:label="note-087-07" xlink:href="note-087-07a" xml:space="preserve">Schol. 28.
                <lb/>
              tertij.</note>
            cus C D, arcui A B, ſit ſimilis; </s>
            <s xml:id="echoid-s2926" xml:space="preserve">erit arcus C D, maior, quàm vt ſimilis ſit
              <lb/>
            ipſi F B. </s>
            <s xml:id="echoid-s2927" xml:space="preserve">Aequales igitur rectæ F B, C D, ex circulis inæqualibus A B,
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            C D, inæquales arcus auferunt, maior{quam} eſt arcus C D, circuli minoris,
              <lb/>
            quàm vt ſimilis ſit arcui F B, circuli minoris. </s>
            <s xml:id="echoid-s2928" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s2929" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2930" xml:space="preserve">HINC perſpicuum eſt, multo magis maiorem lineam ex circulo mi-
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            nore auferre arcum maiorem, quàm vt ſimilis ſit ei, quem ex circulo ma-
              <lb/>
            iore aufert linea minor. </s>
            <s xml:id="echoid-s2931" xml:space="preserve">Cum enim recta C D, æqualis ipſi F B, auferat arcũ
              <lb/>
            C D, maiorem, quàm vt ſimilis ſit arcui F B; </s>
            <s xml:id="echoid-s2932" xml:space="preserve">multo magis linea maior quàm
              <lb/>
            C D, auferet maiorem arcum, quàm vt ſimilis ſit arcui F B; </s>
            <s xml:id="echoid-s2933" xml:space="preserve">cum illa maior
              <lb/>
              <note position="right" xlink:label="note-087-08" xlink:href="note-087-08a" xml:space="preserve">Schol. 28.
                <lb/>
              tertij.</note>
            maiorem arcum abſcindat, quam C D. </s>
            <s xml:id="echoid-s2934" xml:space="preserve">Quare in propoſ. </s>
            <s xml:id="echoid-s2935" xml:space="preserve">hac ſexta etiam
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            recta H X, maior exiſtens, quàm recta Y Z, auferet ex circulo minore
              <lb/>
            Q R, arcum H X, maiorem, quàm vt ſimilis ſit arcui Y Z, quem recta
              <lb/>
            Y Z, aufert ex S T, circulo maiore.</s>
            <s xml:id="echoid-s2936" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2937" xml:space="preserve">HOC autem lemmate demonſtrato, facile etiam oſtendemus, æquales
              <lb/>
            rectas lineas ex circulis inæqualibus auferre arcus inæquales ſimpliciter,
              <lb/>
            ita vt arcus minoris circuli ſimpliciter maior ſit arcu circuli maioris, & </s>
            <s xml:id="echoid-s2938" xml:space="preserve">
              <lb/>
            nθn ſolũ maior, quàm vt ſimilis ſit. </s>
            <s xml:id="echoid-s2939" xml:space="preserve">Sint enim rectæ lineæ C D, B F, æquales,
              <lb/>
            auferat{quam} C D, arcum minoris circuli C E D, & </s>
            <s xml:id="echoid-s2940" xml:space="preserve">F B, arcum circuli maioris
              <lb/>
            F G B. </s>
            <s xml:id="echoid-s2941" xml:space="preserve">Dico ſimpliciter arcum C E D, maiorem eſſe arcu F G B. </s>
            <s xml:id="echoid-s2942" xml:space="preserve">Congruente
              <lb/>
            enim recta C D, rectæ F B, cadet neceſſario arcus C E D, extra arcũ F G B;
              <lb/>
            </s>
            <s xml:id="echoid-s2943" xml:space="preserve">at que adeo arcus C E D, maior erit arcu F G B, cum ille hunc totum intra </s>
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