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

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            <s xml:id="echoid-s2867" xml:space="preserve">
              <pb o="74" file="086" n="86" rhead=""/>
            arcus æqùales F G, G H; </s>
            <s xml:id="echoid-s2868" xml:space="preserve">& </s>
            <s xml:id="echoid-s2869" xml:space="preserve">per puncta F, G, H, perq́ue polum A, circuli ma-
              <lb/>
            ximi deſeribantur A I, A K, A L, ſecantes B D, in I, K, L. </s>
            <s xml:id="echoid-s2870" xml:space="preserve">Dico arcum K L,
              <lb/>
            maiorem eſſe arcu I K. </s>
            <s xml:id="echoid-s2871" xml:space="preserve">Deſcribantur enim per eadem puncta F, G, H, paral-
              <lb/>
              <figure xlink:label="fig-086-01" xlink:href="fig-086-01a" number="93">
                <image file="086-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/086-01"/>
              </figure>
              <note position="left" xlink:label="note-086-01" xlink:href="note-086-01a" xml:space="preserve">20. 1. huius</note>
            leli M N, O P, Q R, ſecantes A K,
              <lb/>
            in V, X. </s>
            <s xml:id="echoid-s2872" xml:space="preserve">Erit igitur arcus M O,
              <lb/>
              <note position="left" xlink:label="note-086-02" xlink:href="note-086-02a" xml:space="preserve">5. huius.</note>
            maior arcu O Q; </s>
            <s xml:id="echoid-s2873" xml:space="preserve">atque adeo, cũ
              <lb/>
              <note position="left" xlink:label="note-086-03" xlink:href="note-086-03a" xml:space="preserve">10. 2. huius</note>
            arcui M O, arcus V G, & </s>
            <s xml:id="echoid-s2874" xml:space="preserve">arcui O Q,
              <lb/>
            arcus G X, ſit æqualis; </s>
            <s xml:id="echoid-s2875" xml:space="preserve">erit & </s>
            <s xml:id="echoid-s2876" xml:space="preserve">V G,
              <lb/>
            maior, quàm G X. </s>
            <s xml:id="echoid-s2877" xml:space="preserve">Sumatur arcus
              <lb/>
            G Y, ipſi G X, æqualis, & </s>
            <s xml:id="echoid-s2878" xml:space="preserve">per Y,
              <lb/>
            parallelus deſcribatur S T, ſecans
              <lb/>
            circulum A I, in Z. </s>
            <s xml:id="echoid-s2879" xml:space="preserve">Quoniam igi-
              <lb/>
            tur arcus G Y, G X, æquales ſunt,
              <lb/>
            nec non G F, G H, erunt ductæ re-
              <lb/>
            ctæ H X, Y F, æquales. </s>
            <s xml:id="echoid-s2880" xml:space="preserve">Et quia cir-
              <lb/>
              <note position="left" xlink:label="note-086-04" xlink:href="note-086-04a" xml:space="preserve">3. huius.</note>
            culus maximus A I, per polum A,
              <lb/>
            ſecat cir culum S T, ad angulos re
              <lb/>
              <note position="left" xlink:label="note-086-05" xlink:href="note-086-05a" xml:space="preserve">15. 1. huius.</note>
            ctos, & </s>
            <s xml:id="echoid-s2881" xml:space="preserve">bifariam, erit communis
              <lb/>
            ſectio, nempe recta ex Z, ad alte-
              <lb/>
            ram ſectionem ducta diameter circuli S T, ſuper quam inſiſtit ſemicirculus
              <lb/>
            rectus ad circulum A I, nempe ſemicirculus à puncto Z, incipiens, & </s>
            <s xml:id="echoid-s2882" xml:space="preserve">per S, vſq;
              <lb/>
            </s>
            <s xml:id="echoid-s2883" xml:space="preserve">ad alteram ſectionem progrediens, (hoc eſt, ſegmentum circuli, quod ſemicir-
              <lb/>
            culo maius non eſt.) </s>
            <s xml:id="echoid-s2884" xml:space="preserve">aufertque recta illa ex circulo A I, ſegmentum ſemicir-
              <lb/>
            culo maius, quod nimirum à puucto Z, per I, vſque ad alteram ſectionem cum
              <lb/>
            cireulo S T, ducitur, atque eſt Y Z, arcus inſiſtentis ſemicirculi quadrante
              <lb/>
            minor, (propterea quòd arcus Ik, qui illi eſt ſimilis, quadrante quoque mi-
              <lb/>
              <note position="left" xlink:label="note-086-06" xlink:href="note-086-06a" xml:space="preserve">10. 2. huius</note>
            nor eſt. </s>
            <s xml:id="echoid-s2885" xml:space="preserve">quod ita oſtendi poteſt. </s>
            <s xml:id="echoid-s2886" xml:space="preserve">Quoniam circuli maximi B D, E C, recti ſunt
              <lb/>
            ad maximum circulum A B C D, erit hic viciſsim ad illos rectos, ac proinde
              <lb/>
              <note position="left" xlink:label="note-086-07" xlink:href="note-086-07a" xml:space="preserve">13. 1 huius.</note>
            per illorum polos tranſibit. </s>
            <s xml:id="echoid-s2887" xml:space="preserve">Quare eorum ſegmenta, quæ ſemicirculi ſunt, bi-
              <lb/>
              <note position="left" xlink:label="note-086-08" xlink:href="note-086-08a" xml:space="preserve">9. 2. huius.</note>
            fariam ſecabit, id eſt, in quadrantes. </s>
            <s xml:id="echoid-s2888" xml:space="preserve">Quadrans ergo eſt arcus circuli B D, po-
              <lb/>
            ſitus inter B, & </s>
            <s xml:id="echoid-s2889" xml:space="preserve">illud punctum, vbiſe mutuo ſecant circuli B D, E C, ideoque
              <lb/>
            I K, quadrante minor. </s>
            <s xml:id="echoid-s2890" xml:space="preserve">Nam circulus Ak, cadit inter puncta B, I, cum circu-
              <lb/>
            lum A B C D, ſecet in altero polo.) </s>
            <s xml:id="echoid-s2891" xml:space="preserve">atque adeo reliquus arcus ex ſemicirculo
              <lb/>
            inſiſtente interceptus inter Y, & </s>
            <s xml:id="echoid-s2892" xml:space="preserve">altetam ſectionem cum circulo A I, quadran-
              <lb/>
            te maior; </s>
            <s xml:id="echoid-s2893" xml:space="preserve">erit recta Y Z, omnium rectarum ex Y, cadẽtium in circunferentiam
              <lb/>
              <note position="left" xlink:label="note-086-09" xlink:href="note-086-09a" xml:space="preserve">1. huius.</note>
            Z P, minima; </s>
            <s xml:id="echoid-s2894" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s2895" xml:space="preserve">adeò minor quàm Y F, hoceſt, quàm H X, quam ęqualẽ oſten
              <lb/>
            ndimus eſſe rectæ Y F. </s>
            <s xml:id="echoid-s2896" xml:space="preserve">Quocirca cum eirculus Q R, minor ſit circulo S T, au-
              <lb/>
            feret recta H X, maior maiorem arcum ex ſuo circulo, quàm recta Y Z, minor
              <lb/>
            ex ſuo, vt mox oſtendemus. </s>
            <s xml:id="echoid-s2897" xml:space="preserve">Maior igitur eſt arcus H X, quàm vt ſimilis eſſe
              <lb/>
            poſsit arcui Y Z: </s>
            <s xml:id="echoid-s2898" xml:space="preserve">Eſt autem arcui H X, arcus kL, & </s>
            <s xml:id="echoid-s2899" xml:space="preserve">arcui Y Z, arcus Ik, ſimilis.
              <lb/>
            </s>
            <s xml:id="echoid-s2900" xml:space="preserve">
              <note position="left" xlink:label="note-086-10" xlink:href="note-086-10a" xml:space="preserve">10. 2. huius.</note>
            Igitur & </s>
            <s xml:id="echoid-s2901" xml:space="preserve">kL, maior eſt, quàm vt ſimilis fit ipſi Ik; </s>
            <s xml:id="echoid-s2902" xml:space="preserve">ac proinde, cum ſint in eo-
              <lb/>
            dem circulo, maior erit arcus kL, quàm Ik. </s>
            <s xml:id="echoid-s2903" xml:space="preserve">Quamobrem, ſi in circumferentia
              <lb/>
            maximi circuli ſit polus parallelorum, &</s>
            <s xml:id="echoid-s2904" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2905" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s2906" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div250" type="section" level="1" n="118">
          <head xml:id="echoid-head132" xml:space="preserve">LEMMA.</head>
          <p style="it">
            <s xml:id="echoid-s2907" xml:space="preserve">_QVOD_ autem recta _H X,_ maiorem arcum auferatex ſuo circulo quàm recta
              <lb/>
            Y Z, ex ſuo, perſpicuum fiet, ſi prius theorema, quod ſequitur, demonſtretur.</s>
            <s xml:id="echoid-s2908" xml:space="preserve"/>
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