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

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        <div xml:id="echoid-div250" type="section" level="1" n="118">
          <p style="it">
            <s xml:id="echoid-s2943" xml:space="preserve">
              <pb o="76" file="088" n="88" rhead=""/>
            contineat, ſint{quam} ambo arcus in eandẽ partem caui, at{quam} eadem extrema pun
              <lb/>
            cta habeant, vt vult Archimedes in ſuppoſitionibus ante lib. </s>
            <s xml:id="echoid-s2944" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2945" xml:space="preserve">deſphæra
              <lb/>
            & </s>
            <s xml:id="echoid-s2946" xml:space="preserve">cylindro. </s>
            <s xml:id="echoid-s2947" xml:space="preserve">Neque vero arcus C E D, arcui F G B, congruet, aut imra ip-
              <lb/>
              <figure xlink:label="fig-088-01" xlink:href="fig-088-01a" number="95">
                <image file="088-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/088-01"/>
              </figure>
            ſum cadet. </s>
            <s xml:id="echoid-s2948" xml:space="preserve">Nam ſi dicatur congruere,
              <lb/>
            congruet etiam tota circumferentia
              <lb/>
            circuli C E D, toti circumferentiæ cir-
              <lb/>
            culi F G B, atque adeo æquales erunt
              <lb/>
            circuli. </s>
            <s xml:id="echoid-s2949" xml:space="preserve">quod eſt abſurdum, cum inæquæ
              <lb/>
            les ponantur: </s>
            <s xml:id="echoid-s2950" xml:space="preserve">Si vero arcus C E D, di-
              <lb/>
            catur cadere intra arcum F G B, cu-
              <lb/>
            inſmodi eſt arcus C A D, quoniam vt
              <lb/>
            paulo ante in hoc lemmate ostenſum
              <lb/>
            eſt, arcus C E D, id eſt, C A D, maior
              <lb/>
            eſt, quàm vt ſimilis ſit arcui F G B, ſu-
              <lb/>
            matur arcus H F B, arcui C A D, ſimilis, atque adeo maior arcu F G B:
              <lb/>
            </s>
            <s xml:id="echoid-s2951" xml:space="preserve">Aſſumpto autem in arcu C A D, puncto A, vtcunque, ducantur rectæ
              <lb/>
            A F, A B; </s>
            <s xml:id="echoid-s2952" xml:space="preserve">productaque recta F A, donec arcum F G B, ſecet in G,
              <lb/>
            ducantur rectæ G H, G B. </s>
            <s xml:id="echoid-s2953" xml:space="preserve">Itaque quoniam arcus C A D, H F B, ſimiles
              <lb/>
            ſunt, erunt anguli C A D, H G B, inillis fegmentis exiſtentes, æquales. </s>
            <s xml:id="echoid-s2954" xml:space="preserve">Quia
              <lb/>
            vero angulus C A D, angulo C G B, maior eſt, externus interno; </s>
            <s xml:id="echoid-s2955" xml:space="preserve">& </s>
            <s xml:id="echoid-s2956" xml:space="preserve">angulus
              <lb/>
              <note position="left" xlink:label="note-088-01" xlink:href="note-088-01a" xml:space="preserve">16. primi.</note>
            C G B, angulo H G B, maior quoque, totum parte; </s>
            <s xml:id="echoid-s2957" xml:space="preserve">erit multò maior angulus
              <lb/>
            C A D, angulo H G B. </s>
            <s xml:id="echoid-s2958" xml:space="preserve">quod eſt abſurdũ. </s>
            <s xml:id="echoid-s2959" xml:space="preserve">Oſtenſus enim eſt æqualis. </s>
            <s xml:id="echoid-s2960" xml:space="preserve">Non ergo
              <lb/>
            arcus C E D, cadet intra arcũ F G B: </s>
            <s xml:id="echoid-s2961" xml:space="preserve">ſed neq; </s>
            <s xml:id="echoid-s2962" xml:space="preserve">ei congruit, vt demõſtratũ eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s2963" xml:space="preserve">Cadet ergo extra, atq; </s>
            <s xml:id="echoid-s2964" xml:space="preserve">adeo maior erit arcus C E D, arcu F G B, vt dictũ eſ.</s>
            <s xml:id="echoid-s2965" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s2966" xml:space="preserve">_HINC_ etiam liquido constat, multo magis maiorem lineam ex cir-
              <lb/>
            culo minore auferre arcum maiorem ſimpliciter eo, quem minor linea ex
              <lb/>
            circulo maiore aufert.</s>
            <s xml:id="echoid-s2967" xml:space="preserve"/>
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        <div xml:id="echoid-div254" type="section" level="1" n="119">
          <head xml:id="echoid-head133" xml:space="preserve">THEOR. 7. PROPOS. 7.</head>
          <note position="left" xml:space="preserve">5.</note>
          <p>
            <s xml:id="echoid-s2968" xml:space="preserve">SI in ſphæra maximus circulus tãgat aliquem
              <lb/>
            ſphæræ circulum, alius autem maximus circulus
              <lb/>
            ad parallelos obliquus ſit, tangatq́; </s>
            <s xml:id="echoid-s2969" xml:space="preserve">circulos maio-
              <lb/>
            res illis, quos tangit maximus circulus primo poſi-
              <lb/>
            tus, fuerintq́; </s>
            <s xml:id="echoid-s2970" xml:space="preserve">eorum contactus in maximo circu-
              <lb/>
            lo primo poſito, & </s>
            <s xml:id="echoid-s2971" xml:space="preserve">ſumanturà circulo obliquo </s>
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