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

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        <div xml:id="echoid-div476" type="section" level="1" n="240">
          <p style="it">
            <s xml:id="echoid-s6540" xml:space="preserve">
              <pb o="175" file="187" n="187" rhead=""/>
            recta gradus _20._ </s>
            <s xml:id="echoid-s6541" xml:space="preserve">
              <de:unknown code="022"/>
            . </s>
            <s xml:id="echoid-s6542" xml:space="preserve">_Q_uot autem gradus complectatur arcus _VC_, indicabit quadrans
              <lb/>
            in _90_. </s>
            <s xml:id="echoid-s6543" xml:space="preserve">gradus diuiſus.</s>
            <s xml:id="echoid-s6544" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6545" xml:space="preserve">_EODEM_ pacto omnia alia problemata _G_eometrice per ſinus abſoluemus, etiamſi
              <lb/>
            ſinubus verſis vti oportuerit aliquando, qui quidem eadem facilitate exdatis arcu-
              <lb/>
            bus inueniuntur, & </s>
            <s xml:id="echoid-s6546" xml:space="preserve">exipſis arcus, qua ſinus rectos, & </s>
            <s xml:id="echoid-s6547" xml:space="preserve">ſinus complemẽtorum reperi-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s6548" xml:space="preserve">_S_i enim arcus datus minor eſt quadrante, vt _AG;_ </s>
            <s xml:id="echoid-s6549" xml:space="preserve">ducta _GS_. </s>
            <s xml:id="echoid-s6550" xml:space="preserve">ad _AE_, perpendi-
              <lb/>
            culari, erit _AS_ ſinus verſus arcus _AG_. </s>
            <s xml:id="echoid-s6551" xml:space="preserve">_S_i vero datus arcus quadrante maior eſt, vt
              <lb/>
            _AV;_ </s>
            <s xml:id="echoid-s6552" xml:space="preserve">ducta _VT_, ad _EC_, perpendiculari, erit _AT_, ſinus verſus arcus _AV_, vt ex
              <lb/>
            definitione manifeſtum eſt.</s>
            <s xml:id="echoid-s6553" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6554" xml:space="preserve">_SED_ iam ad inquiſitionem chordarum _G_eometricam aggrediamur, ex quibus
              <lb/>
            rurſum ſinuum tabulam facili negotio componemus.</s>
            <s xml:id="echoid-s6555" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div492" type="section" level="1" n="241">
          <head xml:id="echoid-head268" xml:space="preserve">THEOR. 7. PROPOS. 10.</head>
          <p>
            <s xml:id="echoid-s6556" xml:space="preserve">IN circulo ſumptis duobus arcubus inæqua-
              <lb/>
              <note position="right" xlink:label="note-187-01" xlink:href="note-187-01a" xml:space="preserve">Maior eſt
                <lb/>
              proportio
                <lb/>
              maioris ar-
                <lb/>
              cꝰ in circu-
                <lb/>
              lo ad arcũ
                <lb/>
              minorẽ, q̃
                <lb/>
              chordæ ma
                <lb/>
              ioris arcus
                <lb/>
              ad chordã
                <lb/>
              minoris.</note>
            libus, quorum maioris chorda maior ſit, quam
              <lb/>
            chorda minoris; </s>
            <s xml:id="echoid-s6557" xml:space="preserve">maior eſt proportio arcus maio-
              <lb/>
            ris ad minorem, quam chordæ arcus maioris ad
              <lb/>
            chordam minoris arcus.</s>
            <s xml:id="echoid-s6558" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6559" xml:space="preserve">IN circulo ABCD, ſint inęquales arcus AB,
              <emph style="sc">Bc</emph>
            ; </s>
            <s xml:id="echoid-s6560" xml:space="preserve">ille maior, hic vero minor:
              <lb/>
            </s>
            <s xml:id="echoid-s6561" xml:space="preserve">quorum chordæ AB, BC; </s>
            <s xml:id="echoid-s6562" xml:space="preserve">illa maior, hæc vero minor. </s>
            <s xml:id="echoid-s6563" xml:space="preserve">Dico maiorem eſſe
              <lb/>
            proportionem arcus AB, ad arcum BC, quam chordæ AB, ad chordam BC. </s>
            <s xml:id="echoid-s6564" xml:space="preserve">
              <lb/>
            Contineant enim chordæ AB, BC, angulum ABC, ita vt arcus ſint conti-
              <lb/>
            nuati, minoreſq; </s>
            <s xml:id="echoid-s6565" xml:space="preserve">ſint tota circunferentia. </s>
            <s xml:id="echoid-s6566" xml:space="preserve">Nam ſi toti circunferentiæ forent
              <lb/>
            æquales, eſſet eadem chorda vtriuſq; </s>
            <s xml:id="echoid-s6567" xml:space="preserve">arcus: </s>
            <s xml:id="echoid-s6568" xml:space="preserve">ſi vero totam circunferentiam
              <lb/>
            excederent, eſſet chorda arcus minoris maior, quam maioris, vt patet in ſe-
              <lb/>
              <figure xlink:label="fig-187-01" xlink:href="fig-187-01a" number="137">
                <image file="187-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/187-01"/>
              </figure>
            cunda figura, ſi minor arcus foret BAI. </s>
            <s xml:id="echoid-s6569" xml:space="preserve">Angulus porrò ABC, bifariam ſe-
              <lb/>
              <note position="right" xlink:label="note-187-02" xlink:href="note-187-02a" xml:space="preserve">9. primi.</note>
            cetur recta BD, connectãturq́; </s>
            <s xml:id="echoid-s6570" xml:space="preserve">rectæ AC, AD, CD, quarum AC, rectam BD,
              <lb/>
            ſecet in E. </s>
            <s xml:id="echoid-s6571" xml:space="preserve">Erunt autem rectæ AD, CD, æquales, propter arcus AD, CD,
              <lb/>
              <note position="right" xlink:label="note-187-03" xlink:href="note-187-03a" xml:space="preserve">29. tertij.</note>
            qui ſubten ſiangulis ABD, CBD, ex conſtructione æqualibus æqualesinter
              <lb/>
              <note position="right" xlink:label="note-187-04" xlink:href="note-187-04a" xml:space="preserve">26. tertij.</note>
            ſe ſunt. </s>
            <s xml:id="echoid-s6572" xml:space="preserve">Et quoniam in triangulo ABC, recta BE, angulum ABC, bifariam
              <lb/>
            ſecat; </s>
            <s xml:id="echoid-s6573" xml:space="preserve">erit, vt AB, ad BC, ita AE, ad EC: </s>
            <s xml:id="echoid-s6574" xml:space="preserve">Eſt autem recta AB, maior, quam
              <lb/>
              <note position="right" xlink:label="note-187-05" xlink:href="note-187-05a" xml:space="preserve">3. fextia</note>
            </s>
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