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

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          <p>
            <s xml:id="echoid-s8476" xml:space="preserve">
              <pb o="199" file="211" n="211" rhead=""/>
            gens arcus CD, ad CG, tangentem arcus CF, ita BH, tangens complemen-
              <lb/>
            ti arcus poſterioris CF, ad BI, tangentem complementi prioris arcus CD.
              <lb/>
            </s>
            <s xml:id="echoid-s8477" xml:space="preserve">Tangens igitur cuiuſuis arcus eſt ad tangentem alterius, &</s>
            <s xml:id="echoid-s8478" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8479" xml:space="preserve">Quod oſtenden-
              <lb/>
            dum erat.</s>
            <s xml:id="echoid-s8480" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div574" type="section" level="1" n="265">
          <head xml:id="echoid-head292" xml:space="preserve">THEOR. 14. PROPOS. 22.</head>
          <p>
            <s xml:id="echoid-s8481" xml:space="preserve">SECANS cuiuſuis arcus eſt ad Secantem al-
              <lb/>
              <note position="right" xlink:label="note-211-01" xlink:href="note-211-01a" xml:space="preserve">Secãtes du@
                <lb/>
              rũ arcuum
                <lb/>
              quorũlibet
                <lb/>
              sũt recipro-
                <lb/>
              ce pportio
                <lb/>
              nales cũ fi-
                <lb/>
              nubus com
                <lb/>
              plemẽto rũ
                <lb/>
              arcuum eo
                <lb/>
              rundem.</note>
            terius arcus cuiuſlibet, vt ſinus complementi po
              <lb/>
            ſterioris arcus ad ſinum complementi prioris.</s>
            <s xml:id="echoid-s8482" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8483" xml:space="preserve">IN quadrante ABC, ſit AD, ſecans arcus CE, & </s>
            <s xml:id="echoid-s8484" xml:space="preserve">AF, ſecans arcus CG: </s>
            <s xml:id="echoid-s8485" xml:space="preserve">& </s>
            <s xml:id="echoid-s8486" xml:space="preserve">
              <lb/>
            EH, ſinus complementi arcus CE, at GI, ſinus complementi arcus CG. </s>
            <s xml:id="echoid-s8487" xml:space="preserve">Di-
              <lb/>
            coita eſſe ſecantem AD, arcus CE, ad AF, ſecantem arcus CG, vt eſt GI,
              <lb/>
            ſinus complementi poſterioris arcus CG, ad EH,
              <lb/>
              <figure xlink:label="fig-211-01" xlink:href="fig-211-01a" number="155">
                <image file="211-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/211-01"/>
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            ſinum complementi arcus prioris CE. </s>
            <s xml:id="echoid-s8488" xml:space="preserve">Quoniam
              <lb/>
            enim ſinus totus eſt medius proportionalis tã in-
              <lb/>
              <note position="right" xlink:label="note-211-02" xlink:href="note-211-02a" xml:space="preserve">18. huius.</note>
            ter ſecantem AD, arcus CE, & </s>
            <s xml:id="echoid-s8489" xml:space="preserve">EH, ſinum com-
              <lb/>
            plementi eiuſdem arcus CE, quàm inter AF, ſe-
              <lb/>
            cantem arcus CG, & </s>
            <s xml:id="echoid-s8490" xml:space="preserve">GI, ſinum complementi eiu-
              <lb/>
            ſdem arcus CG; </s>
            <s xml:id="echoid-s8491" xml:space="preserve">erit tam rectangulum ſub AD,
              <lb/>
            EH, quàm rectangulum ſub AF, GI, quadrato
              <lb/>
              <note position="right" xlink:label="note-211-03" xlink:href="note-211-03a" xml:space="preserve">17. fexti.</note>
            ſinus totius æquale: </s>
            <s xml:id="echoid-s8492" xml:space="preserve">ac proinde rectangulum illud
              <lb/>
            huic æquale. </s>
            <s xml:id="echoid-s8493" xml:space="preserve">Quare erit vt AD, prima ad AF, ſe-
              <lb/>
              <note position="right" xlink:label="note-211-04" xlink:href="note-211-04a" xml:space="preserve">16. fexti.</note>
            cundam, ita GI, tertia ad EH, quartam; </s>
            <s xml:id="echoid-s8494" xml:space="preserve">hoc eſt,
              <lb/>
            vt AD, ſecans arcus CE, ad AF, ſecantem arcus CG, ita GI, ſinus comple-
              <lb/>
            menti arcus poſterioris CG, ad EH, ſinum complementi arcus prioris CE.
              <lb/>
            </s>
            <s xml:id="echoid-s8495" xml:space="preserve">Secans igitur cuiuſuis arcus eſt ad ſecantem alterius arcus, &</s>
            <s xml:id="echoid-s8496" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8497" xml:space="preserve">Quod demon-
              <lb/>
            ſtrandum erat.</s>
            <s xml:id="echoid-s8498" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div577" type="section" level="1" n="266">
          <head xml:id="echoid-head293" xml:space="preserve">THEOR. 15. PROPOS. 23.</head>
          <p>
            <s xml:id="echoid-s8499" xml:space="preserve">SI plures ſint arcus æquali exceſſu progredien
              <lb/>
              <note position="right" xlink:label="note-211-05" xlink:href="note-211-05a" xml:space="preserve">Tangentes
                <lb/>
              & ſecantes
                <lb/>
              arcuũ ęqna
                <lb/>
              liter creſcẽ
                <lb/>
              tiũ augent
                <lb/>
              femper dif-
                <lb/>
              ferentias.</note>
            tes, habebunt tam tangentes, quàm Secantes ma-
              <lb/>
            iorum arcuum maiorem differentiam, quàm mi-
              <lb/>
            norum:</s>
            <s xml:id="echoid-s8500" xml:space="preserve">ita vt in tabula differentiæ tam tangentiũ,
              <lb/>
            quàm ſecantium ſemper creſcant vſque ad finem
              <lb/>
            quadrantis.</s>
            <s xml:id="echoid-s8501" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8502" xml:space="preserve">IN quadrante ABC, ſintarcus CD, CE, CF, quorum differentiæ DE,
              <lb/>
            EF, æquales ſint, & </s>
            <s xml:id="echoid-s8503" xml:space="preserve">eorumdem tangentes ſint CG, CH, CI; </s>
            <s xml:id="echoid-s8504" xml:space="preserve">ſecantes </s>
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