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

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          <p>
            <s xml:id="echoid-s8559" xml:space="preserve">
              <pb o="201" file="213" n="213" rhead=""/>
            eum EF, atq; </s>
            <s xml:id="echoid-s8560" xml:space="preserve">adeo abſcindere arcum minorem arcu DE, nempe partem arcus EF. </s>
            <s xml:id="echoid-s8561" xml:space="preserve">Eademq́;
              <lb/>
            </s>
            <s xml:id="echoid-s8562" xml:space="preserve">ratio eſt de alijs.</s>
            <s xml:id="echoid-s8563" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8564" xml:space="preserve">RVRSVS quia demonſtratum eſt, ſecantem AG, minorem eſſe, quàm AH; </s>
            <s xml:id="echoid-s8565" xml:space="preserve">fit, vt
              <lb/>
            ablatis femidiametris æqualibus AD, AE, ſegmentum DG, ſeliquum minus ſit ſegmen-
              <lb/>
            to reliquo EH, &</s>
            <s xml:id="echoid-s8566" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8567" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div583" type="section" level="1" n="268">
          <head xml:id="echoid-head295" xml:space="preserve">THEOR. 16. PROPOS. 24.</head>
          <p>
            <s xml:id="echoid-s8568" xml:space="preserve">TANGENS arcus maioris ad tangentem
              <lb/>
              <note position="right" xlink:label="note-213-01" xlink:href="note-213-01a" xml:space="preserve">Arcuu inę-
                <lb/>
              qualiú tan-
                <lb/>
              gens maio-
                <lb/>
              ris ad tan-
                <lb/>
              gentem mi
                <lb/>
              noris pro-
                <lb/>
              portionem
                <lb/>
              habet maio
                <lb/>
              rem, quam
                <lb/>
              fecans ma-
                <lb/>
              ioris ad ſe-
                <lb/>
              cantem mi
                <lb/>
              noris.</note>
            minoris arcus maioré proportionem habet, quá
              <lb/>
            ſecans maioris eiuſdem arcus ad ſecantem eiuſdé
              <lb/>
            minoris.</s>
            <s xml:id="echoid-s8569" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8570" xml:space="preserve">REPETATVR figura pręcedentis propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s8571" xml:space="preserve">
              <figure xlink:label="fig-213-01" xlink:href="fig-213-01a" number="157">
                <image file="213-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/213-01"/>
              </figure>
            Dico maiorem eſſe proportionem tágentis CI,
              <lb/>
            ad tangentem CH, quàm ſecantis AI, ad ſecan
              <lb/>
            tem AH. </s>
            <s xml:id="echoid-s8572" xml:space="preserve">Quoniam enim eſt, vt AF, ad FM,
              <lb/>
              <note position="right" xlink:label="note-213-02" xlink:href="note-213-02a" xml:space="preserve">4. fexti.</note>
            ita AI, ad IC: </s>
            <s xml:id="echoid-s8573" xml:space="preserve">Item vt AE, ad EN, ita AH,
              <lb/>
            ad HC. </s>
            <s xml:id="echoid-s8574" xml:space="preserve">Eſt autem minor proportio ſemidia-
              <lb/>
              <note position="right" xlink:label="note-213-03" xlink:href="note-213-03a" xml:space="preserve">8. quinti.</note>
            metri AF, ad FM, quàm ſemidiametri AE ad,
              <lb/>
            EN; </s>
            <s xml:id="echoid-s8575" xml:space="preserve">quòd ſinus FM, maioris arcus CF, ma-
              <lb/>
            ior ſit ſinu EN, minoris arcus CE, vt in ex-
              <lb/>
            poſitione definitionum dictum eſt. </s>
            <s xml:id="echoid-s8576" xml:space="preserve">Igitur minor
              <lb/>
            quoq; </s>
            <s xml:id="echoid-s8577" xml:space="preserve">erit proportio AI, ad IC, quàm AH,
              <lb/>
            ad HC: </s>
            <s xml:id="echoid-s8578" xml:space="preserve">Et permutando, minor etiam propor-
              <lb/>
              <note position="right" xlink:label="note-213-04" xlink:href="note-213-04a" xml:space="preserve">ſchol. 27. 5.</note>
            tio AI, ad AH, quàm IC, ad HC; </s>
            <s xml:id="echoid-s8579" xml:space="preserve">hoc eſt, tan
              <lb/>
            gens CI, ad tangentem CH, habebit maiorem
              <lb/>
            proportionem, quàm ſecans AI, ad ſecantem AH. </s>
            <s xml:id="echoid-s8580" xml:space="preserve">Quocirca Tangensar-
              <lb/>
            cus maioris ad tangentem minoris arcus, &</s>
            <s xml:id="echoid-s8581" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8582" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s8583" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div586" type="section" level="1" n="269">
          <head xml:id="echoid-head296" style="it" xml:space="preserve">SEQVVNTVR TABVLAE TANGEN-
            <lb/>
          tium atque ſecantium.</head>
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