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

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          <p>
            <s xml:id="echoid-s4525" xml:space="preserve">
              <pb o="118" file="130" n="130" rhead=""/>
            ctæ FH, æqualis, ob parallelogrammum FI. </s>
            <s xml:id="echoid-s4526" xml:space="preserve">Quare GK, differentia erit ſi-
              <lb/>
              <note position="left" xlink:label="note-130-01" xlink:href="note-130-01a" xml:space="preserve">34. primi.</note>
            nuum FH, GI. </s>
            <s xml:id="echoid-s4527" xml:space="preserve">Dico hanc differentiam GK, æqualem eſſe ſinui FL, vel GL.
              <lb/>
            </s>
            <s xml:id="echoid-s4528" xml:space="preserve">Ducta enim recta BE, quæ latus hexagoni eſt, ac propterea, ex coroll propoſ. </s>
            <s xml:id="echoid-s4529" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-130-01" xlink:href="fig-130-01a" number="127">
                <image file="130-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/130-01"/>
              </figure>
            15. </s>
            <s xml:id="echoid-s4530" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4531" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4532" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s4533" xml:space="preserve">ſemidiametro DE, æqualis; </s>
            <s xml:id="echoid-s4534" xml:space="preserve">ſecetur
              <lb/>
            BD, bifariã in M, iungaturq́ recta EM. </s>
            <s xml:id="echoid-s4535" xml:space="preserve">Quoniã igi-
              <lb/>
            tur latera DM, ME, lateribus BM, ME, æqualia
              <lb/>
            ſunt, & </s>
            <s xml:id="echoid-s4536" xml:space="preserve">baſis DE, baſi BE, æqualis, erunt anguli ad
              <lb/>
              <note position="left" xlink:label="note-130-02" xlink:href="note-130-02a" xml:space="preserve">8. primi.</note>
            M, ęquales, atque adeo recti. </s>
            <s xml:id="echoid-s4537" xml:space="preserve">Completo autem ſe-
              <lb/>
            micirculo ABC, & </s>
            <s xml:id="echoid-s4538" xml:space="preserve">productis rectis GI, EM, ad
              <lb/>
            N, O, erit arcus NO, arcui GE, hoc eſt, arcui EF,
              <lb/>
            æqualis, ex ſcholio propoſ. </s>
            <s xml:id="echoid-s4539" xml:space="preserve">27. </s>
            <s xml:id="echoid-s4540" xml:space="preserve">li b. </s>
            <s xml:id="echoid-s4541" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4542" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s4543" xml:space="preserve">propterea
              <lb/>
            quod rectæ GN, EO, parallelæ ſunt, ob rectos angu
              <lb/>
              <note position="left" xlink:label="note-130-03" xlink:href="note-130-03a" xml:space="preserve">28. primi.</note>
            los I, M. </s>
            <s xml:id="echoid-s4544" xml:space="preserve">Addito ergo communi arcu FO, erit ar-
              <lb/>
            cus FN, arcui EO, æqualis: </s>
            <s xml:id="echoid-s4545" xml:space="preserve">Sed arcus EO, duplus
              <lb/>
            eſt arcus BE. </s>
            <s xml:id="echoid-s4546" xml:space="preserve">(Nam recta DB, rectam EO, ſecans ad
              <lb/>
              <note position="left" xlink:label="note-130-04" xlink:href="note-130-04a" xml:space="preserve">3. tertij.</note>
            angulos rectos ſecat eandem bifariam: </s>
            <s xml:id="echoid-s4547" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s4548" xml:space="preserve">
              <lb/>
            arcum EO, bifariam, ex ſcholio in definitionibus
              <lb/>
            poſito) Igitur & </s>
            <s xml:id="echoid-s4549" xml:space="preserve">arcus FN, eiuſdem arcus BE, du-
              <lb/>
            plus erit. </s>
            <s xml:id="echoid-s4550" xml:space="preserve">Quare ductis rectis DF, DN, erit quoque
              <lb/>
            angulus FDN, anguli EDB, duplus: </s>
            <s xml:id="echoid-s4551" xml:space="preserve">Eſt autem idem angulus FDN, in cen
              <lb/>
              <note position="left" xlink:label="note-130-05" xlink:href="note-130-05a" xml:space="preserve">33. ſexti.</note>
            tro anguli FGN, in circunferentia duplus. </s>
            <s xml:id="echoid-s4552" xml:space="preserve">Igitur æquales ſunt anguli EDM,
              <lb/>
              <note position="left" xlink:label="note-130-06" xlink:href="note-130-06a" xml:space="preserve">20.tertij.</note>
            FGK: </s>
            <s xml:id="echoid-s4553" xml:space="preserve">Suntautem & </s>
            <s xml:id="echoid-s4554" xml:space="preserve">recti M, K, æquales. </s>
            <s xml:id="echoid-s4555" xml:space="preserve">Aequiangula ergo ſunt triangula
              <lb/>
            EDM,
              <emph style="sc">F</emph>
            GK: </s>
            <s xml:id="echoid-s4556" xml:space="preserve">atque idcirco erit vt ED, ad DM, ita FG, ad GK. </s>
            <s xml:id="echoid-s4557" xml:space="preserve">Cum ergo
              <lb/>
              <note position="left" xlink:label="note-130-07" xlink:href="note-130-07a" xml:space="preserve">4. ſexti.</note>
            ED, dupla ſit ipſius DM, (ſecta enim eſt DB, ipſi DE, æqualis, bifariam in
              <lb/>
            M.) </s>
            <s xml:id="echoid-s4558" xml:space="preserve">erit & </s>
            <s xml:id="echoid-s4559" xml:space="preserve">FG, ipſius GK, dupla: </s>
            <s xml:id="echoid-s4560" xml:space="preserve">Eſt autem & </s>
            <s xml:id="echoid-s4561" xml:space="preserve">FG, ipſius FL, vel GL, du-
              <lb/>
            pla. </s>
            <s xml:id="echoid-s4562" xml:space="preserve">Igitur recta GK, differentia ſinuum FH, GI, æqualis eſt rectæ FL, ſi-
              <lb/>
            nui arcus EF, vel rectæ GL, ſinui arcus EG. </s>
            <s xml:id="echoid-s4563" xml:space="preserve">Differentia ergo ſinuum duo-
              <lb/>
            rum arcuum quadrantis, &</s>
            <s xml:id="echoid-s4564" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4565" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s4566" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div378" type="section" level="1" n="165">
          <head xml:id="echoid-head191" xml:space="preserve">COROLLARIVM.</head>
          <note position="left" xml:space="preserve">Duo ſinus
            <lb/>
          duorum ar
            <lb/>
          cuũ confi-
            <lb/>
          cientium
            <lb/>
          grad. 60. ſi-
            <lb/>
          mul æqua-
            <lb/>
          les ſunt ſi-
            <lb/>
          nui arcus
            <lb/>
          compoſiti
            <lb/>
          ex arcu
            <lb/>
          grad. 60. &
            <lb/>
          arcu mino
            <lb/>
          re illorum
            <lb/>
          duorum.</note>
          <p>
            <s xml:id="echoid-s4567" xml:space="preserve">HINC ſequitur, ſi duorum arcuum conficientium grad. </s>
            <s xml:id="echoid-s4568" xml:space="preserve">60. </s>
            <s xml:id="echoid-s4569" xml:space="preserve">ſinus ſimul componantur,
              <lb/>
            effici ſinum arcus cõpoſiti ex arcu grad. </s>
            <s xml:id="echoid-s4570" xml:space="preserve">60. </s>
            <s xml:id="echoid-s4571" xml:space="preserve">& </s>
            <s xml:id="echoid-s4572" xml:space="preserve">arcu minore illorũ duorũ, ſi inæquales ſunt.
              <lb/>
            </s>
            <s xml:id="echoid-s4573" xml:space="preserve">Ita enim vides in ſigura poſterioris demonſtrationis huius propoſ. </s>
            <s xml:id="echoid-s4574" xml:space="preserve">ſinus rectos FH, FL, ar-
              <lb/>
            cuum BF, FE, conſicientium grad. </s>
            <s xml:id="echoid-s4575" xml:space="preserve">60. </s>
            <s xml:id="echoid-s4576" xml:space="preserve">ſimul ſumptos æquari ſinui recto GI, arcus BEG,
              <lb/>
            compoſiti ex arcu BE, grad. </s>
            <s xml:id="echoid-s4577" xml:space="preserve">60. </s>
            <s xml:id="echoid-s4578" xml:space="preserve">& </s>
            <s xml:id="echoid-s4579" xml:space="preserve">arcu EG, qui minori EF, æqualis eſt: </s>
            <s xml:id="echoid-s4580" xml:space="preserve">propterea quòd,
              <lb/>
            vt demonſtratum eſt, differentia GK, inter ſinus FH, GI, æqualis eſt ſinui FL.</s>
            <s xml:id="echoid-s4581" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div379" type="section" level="1" n="166">
          <head xml:id="echoid-head192" xml:space="preserve">PROBL. 3. PROP. 9.</head>
          <p>
            <s xml:id="echoid-s4582" xml:space="preserve">SINVS rectos omnium arcuum quadrantis
              <lb/>
              <note position="left" xlink:label="note-130-09" xlink:href="note-130-09a" xml:space="preserve">Qua rõne
                <lb/>
              omniũ ar-
                <lb/>
              cuum ſinus
                <lb/>
              recti ſuppu
                <lb/>
              tentur.</note>
            ſeſe ordine ſuperantium vno Minuto, in partibus
              <lb/>
            Sinus totius in quotcunque particulas diſſributi,
              <lb/>
            ſupputare.</s>
            <s xml:id="echoid-s4583" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4584" xml:space="preserve">PRIMVM omnium ſupputabimus ſinus rectos arcuum ſeſe 15. </s>
            <s xml:id="echoid-s4585" xml:space="preserve"/>
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