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

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          <p>
            <s xml:id="echoid-s2548" xml:space="preserve">
              <pb o="66" file="078" n="78" rhead=""/>
            tiore minor eſt. </s>
            <s xml:id="echoid-s2549" xml:space="preserve">Si verò recta linea ſubiectum circu
              <lb/>
            lum ſecans ſit eius diameter, & </s>
            <s xml:id="echoid-s2550" xml:space="preserve">reliqua omnia ea-
              <lb/>
            dem ſint, vt ſupra; </s>
            <s xml:id="echoid-s2551" xml:space="preserve">recta linea ſubtendens mino-
              <lb/>
            rem partem circunferentiæ ſegmenti inſiſtentis,
              <lb/>
            minima eſt rectarum ductarum ab illo eodem
              <lb/>
            puncto ad primi, & </s>
            <s xml:id="echoid-s2552" xml:space="preserve">ſubiecti circuli circunferen-
              <lb/>
            tiam; </s>
            <s xml:id="echoid-s2553" xml:space="preserve">ea verò, quæ maiorem partem circunferen-
              <lb/>
            tiæ ſegmenti inſiſtentis ſubtendit, maxima eſt.</s>
            <s xml:id="echoid-s2554" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2555" xml:space="preserve">RECTA linea A B, ſecet circulum A C B D, cuius centrum E, in partes
              <lb/>
              <figure xlink:label="fig-078-01" xlink:href="fig-078-01a" number="87">
                <image file="078-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/078-01"/>
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            inæquales, quarum maior ſit A C B: </s>
            <s xml:id="echoid-s2556" xml:space="preserve">Inſiſtat
              <lb/>
            autem ipſi A B, rectum circuli ſegmentum
              <lb/>
            A F B, ſemicirculonó maius, quod in partes in-
              <lb/>
            æquales diuidatur in F; </s>
            <s xml:id="echoid-s2557" xml:space="preserve">ſitque minor pars B F:
              <lb/>
            </s>
            <s xml:id="echoid-s2558" xml:space="preserve">Ex F, demittatur in circulum A C B D, per-
              <lb/>
              <note position="left" xlink:label="note-078-01" xlink:href="note-078-01a" xml:space="preserve">11. vndec.</note>
            pendicularis F L, quæ in A B, communem ſe-
              <lb/>
              <note position="left" xlink:label="note-078-02" xlink:href="note-078-02a" xml:space="preserve">38. vndec.</note>
            ctionem cadet: </s>
            <s xml:id="echoid-s2559" xml:space="preserve">Per E, autem, & </s>
            <s xml:id="echoid-s2560" xml:space="preserve">L, diameter
              <lb/>
            agatur C D; </s>
            <s xml:id="echoid-s2561" xml:space="preserve">& </s>
            <s xml:id="echoid-s2562" xml:space="preserve">ex F, in circunferentiam A C B,
              <lb/>
            maioris ſegmenti circuli A C B D, plurimę
              <lb/>
            rectæ cadãt F B, F G, F H, F C, F A, F I, F K.
              <lb/>
            </s>
            <s xml:id="echoid-s2563" xml:space="preserve">Dico omnium minimam eſſe F B, & </s>
            <s xml:id="echoid-s2564" xml:space="preserve">F G, mino-
              <lb/>
            rem, quàm F H; </s>
            <s xml:id="echoid-s2565" xml:space="preserve">Omnium autem maximam eſ
              <lb/>
            ſe F C. </s>
            <s xml:id="echoid-s2566" xml:space="preserve">Item F A, eſſe omnium minimam, quæ
              <lb/>
            ex F, in portioncm A C, cadent; </s>
            <s xml:id="echoid-s2567" xml:space="preserve">& </s>
            <s xml:id="echoid-s2568" xml:space="preserve">F I, minorem, quàm F K. </s>
            <s xml:id="echoid-s2569" xml:space="preserve">Ducantur ex L,
              <lb/>
            lineæ rectę L G, L H, L I, L K; </s>
            <s xml:id="echoid-s2570" xml:space="preserve">eruntq́ue ex defin. </s>
            <s xml:id="echoid-s2571" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2572" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2573" xml:space="preserve">11. </s>
            <s xml:id="echoid-s2574" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s2575" xml:space="preserve">omnes an-
              <lb/>
            guli ad L, quos recta F L, facit, recti. </s>
            <s xml:id="echoid-s2576" xml:space="preserve">Quoniam igitur recta L D, eſt omnium
              <lb/>
            rectarum ex L, cadentium minima, & </s>
            <s xml:id="echoid-s2577" xml:space="preserve">L B, minor, quàm L G, L H, L C, L K,
              <lb/>
              <note position="left" xlink:label="note-078-03" xlink:href="note-078-03a" xml:space="preserve">7. tertij.</note>
            L I, L A; </s>
            <s xml:id="echoid-s2578" xml:space="preserve">erunt quadrata ex F L, L B, minora quadratis ex F L, L G: </s>
            <s xml:id="echoid-s2579" xml:space="preserve">Eſt au-
              <lb/>
            tem tam quadratum ex F B, quadratis ex F L, L B, quàm quadratum ex F G,
              <lb/>
              <note position="left" xlink:label="note-078-04" xlink:href="note-078-04a" xml:space="preserve">47. primi.</note>
            quadratis ex F L, L G,æquale. </s>
            <s xml:id="echoid-s2580" xml:space="preserve">Igitur erit quoq; </s>
            <s xml:id="echoid-s2581" xml:space="preserve">quadratum ex F B, minus qua-
              <lb/>
            drato ex F G; </s>
            <s xml:id="echoid-s2582" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s2583" xml:space="preserve">adeo & </s>
            <s xml:id="echoid-s2584" xml:space="preserve">recta F B, minor erit quàm F G. </s>
            <s xml:id="echoid-s2585" xml:space="preserve">Nõ aliter oſtẽdemus,
              <lb/>
            rectá F B, minoré eſſe, quàm F H, F C, F K, F I, F A. </s>
            <s xml:id="echoid-s2586" xml:space="preserve">Quare F B, omniũ minima eſt.</s>
            <s xml:id="echoid-s2587" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2588" xml:space="preserve">RVRSVS quia L G, minor eſt, quàm L H, erunt quadrata ex F L, L G,
              <lb/>
              <note position="left" xlink:label="note-078-05" xlink:href="note-078-05a" xml:space="preserve">7. tertij.</note>
            minora quadratis ex F L, L H: </s>
            <s xml:id="echoid-s2589" xml:space="preserve">Eſt autem tam quadratum ex F G, quadratis
              <lb/>
            ex F L, L G, quàm quadratum ex F H, quadratis ex F L, L H, æquale. </s>
            <s xml:id="echoid-s2590" xml:space="preserve">Igitur
              <lb/>
              <note position="left" xlink:label="note-078-06" xlink:href="note-078-06a" xml:space="preserve">47. primi.</note>
            & </s>
            <s xml:id="echoid-s2591" xml:space="preserve">quadratum ex F G, quadrato ex F H, minus erit; </s>
            <s xml:id="echoid-s2592" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s2593" xml:space="preserve">adeo & </s>
            <s xml:id="echoid-s2594" xml:space="preserve">recta F G, mi-
              <lb/>
            nor erit, quàm recta F H.</s>
            <s xml:id="echoid-s2595" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2596" xml:space="preserve">AMPLIVS quia L C, omnium ex L, cadentium maxima eſt;</s>
            <s xml:id="echoid-s2597" xml:space="preserve">erunt qua-
              <lb/>
              <note position="left" xlink:label="note-078-07" xlink:href="note-078-07a" xml:space="preserve">7. tertij.</note>
            drata ex F L, L C, maiora quadratis ex F L, L K: </s>
            <s xml:id="echoid-s2598" xml:space="preserve">Eſt autem tam quadratum
              <lb/>
            ex F C, quadratis ex F L, L C, quàm quadratum ex Fk, quadratis ex F L, Lk,
              <lb/>
              <note position="left" xlink:label="note-078-08" xlink:href="note-078-08a" xml:space="preserve">47. primi.</note>
            æquale. </s>
            <s xml:id="echoid-s2599" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s2600" xml:space="preserve">qua dratum ex F C, maius erit quadrato ex F K;</s>
            <s xml:id="echoid-s2601" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s2602" xml:space="preserve">
              <lb/>
            recta F C, maior erit, quàm recta F K. </s>
            <s xml:id="echoid-s2603" xml:space="preserve">Non aliter demonſtrabimus, rectam F C,
              <lb/>
            maiorem eſſe, quàm F I, & </s>
            <s xml:id="echoid-s2604" xml:space="preserve">F A. </s>
            <s xml:id="echoid-s2605" xml:space="preserve">Eſt ergo recta F C, omnium maxima.</s>
            <s xml:id="echoid-s2606" xml:space="preserve"/>
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