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

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          <pb o="440" file="452" n="452" rhead=""/>
          <p style="it">
            <s xml:id="echoid-s15460" xml:space="preserve">SI fiat, vt ſinus totus ad ſinum arcus angulo recto oppoſiti, ita ſecans
              <lb/>
              <note position="left" xlink:label="note-452-01" xlink:href="note-452-01a" xml:space="preserve">@raxis.</note>
            complementi arcus circa rectum angulum dati ad aliud, producetur ſe-
              <lb/>
            cans complementi anguli quæſiti, qui dicto arcui opponitur. </s>
            <s xml:id="echoid-s15461" xml:space="preserve">Iam ex da-
              <lb/>
            tis duobus arcubus tertium inueniemus, vt in problemate propoſ. </s>
            <s xml:id="echoid-s15462" xml:space="preserve">43. </s>
            <s xml:id="echoid-s15463" xml:space="preserve">vel
              <lb/>
            in problemate propoſ. </s>
            <s xml:id="echoid-s15464" xml:space="preserve">53. </s>
            <s xml:id="echoid-s15465" xml:space="preserve">tradidimus. </s>
            <s xml:id="echoid-s15466" xml:space="preserve">Item ex arcu, qui recto angulo
              <lb/>
            opponitur, & </s>
            <s xml:id="echoid-s15467" xml:space="preserve">hoc arcu inuento, reperiemus reliquum angulum huic inuen
              <lb/>
            to arcui oppoſitum, vt dictum eſt in hoc problemate, vel certe, vt in pro-
              <lb/>
            blemate 1. </s>
            <s xml:id="echoid-s15468" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15469" xml:space="preserve">41. </s>
            <s xml:id="echoid-s15470" xml:space="preserve">oſtendimus.</s>
            <s xml:id="echoid-s15471" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15472" xml:space="preserve">AN vero quæſitus angulus
              <emph style="sc">B</emph>
            , acutus ſit, an obtuſus, docebit arcus
              <emph style="sc">AC</emph>
            , circa an-
              <lb/>
            gulum rectum datus, vt in problemate 1. </s>
            <s xml:id="echoid-s15473" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15474" xml:space="preserve">41. </s>
            <s xml:id="echoid-s15475" xml:space="preserve">præcepimus.</s>
            <s xml:id="echoid-s15476" xml:space="preserve"/>
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        <div xml:id="echoid-div1254" type="section" level="1" n="591">
          <head xml:id="echoid-head626" xml:space="preserve">THEOR. 54. PROPOS. 56.</head>
          <p>
            <s xml:id="echoid-s15477" xml:space="preserve">IN omni triangulo ſphærico rectangulo, cu-
              <lb/>
            ius arcus ſint omnes quadrante minores: </s>
            <s xml:id="echoid-s15478" xml:space="preserve">ſinus to-
              <lb/>
            tus ad ſinum complementi vtriuſlibet arcuum cir
              <lb/>
            ca rectum angulum eandem proportionem ha-
              <lb/>
            bet, quam ſecans anguli huic arcui oppoſiti ad ſe-
              <lb/>
            cantem complementi reliqui anguli non recti.</s>
            <s xml:id="echoid-s15479" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15480" xml:space="preserve">IN triangulo ſphærico ABC, angulum B, rectum habente, ſint omnes ar-
              <lb/>
            cus quadrante minores. </s>
            <s xml:id="echoid-s15481" xml:space="preserve">Dico ita eſſe ſinum totum ad ſinũ complementi ar-
              <lb/>
            cus BC, vt eſt ſecans anguli non recti A, ad ſecantem complementi anguli
              <lb/>
            C. </s>
            <s xml:id="echoid-s15482" xml:space="preserve">Repetita enim conſtructione figuræ propoſ. </s>
            <s xml:id="echoid-s15483" xml:space="preserve">47. </s>
            <s xml:id="echoid-s15484" xml:space="preserve">erunt anguli G, E, re-
              <lb/>
            cti, & </s>
            <s xml:id="echoid-s15485" xml:space="preserve">arcus BF, DF, CI, EH, GH, quadran-
              <lb/>
            tes, & </s>
            <s xml:id="echoid-s15486" xml:space="preserve">DE, arcus anguli A, & </s>
            <s xml:id="echoid-s15487" xml:space="preserve">GI, arcus anguli
              <lb/>
              <figure xlink:label="fig-452-01" xlink:href="fig-452-01a" number="313">
                <image file="452-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/452-01"/>
              </figure>
            C, vt ex demõſtratis in propoſ. </s>
            <s xml:id="echoid-s15488" xml:space="preserve">45. </s>
            <s xml:id="echoid-s15489" xml:space="preserve">& </s>
            <s xml:id="echoid-s15490" xml:space="preserve">47. </s>
            <s xml:id="echoid-s15491" xml:space="preserve">liquet.
              <lb/>
            </s>
            <s xml:id="echoid-s15492" xml:space="preserve">Igitur quia duo maximi in ſphæra circuli CG,
              <lb/>
              <note position="left" xlink:label="note-452-02" xlink:href="note-452-02a" xml:space="preserve">Theor 8.
                <lb/>
              ſcholij 40.
                <lb/>
              huius.</note>
            CI, ſe in C, interſecant, ductiq́; </s>
            <s xml:id="echoid-s15493" xml:space="preserve">ſunt ex pun-
              <lb/>
            ctis F, I, arcus CI, ad arcum CG, arcus perpen-
              <lb/>
            diculares FE, IG; </s>
            <s xml:id="echoid-s15494" xml:space="preserve">erit, vt ſinus totus quadran
              <lb/>
            tis CI, ad ſecantem complementi arcus FE, hoc
              <lb/>
            eſt, ad ſecantem arcus DE, anguli A, ita ſinus
              <lb/>
            arcus CF, qui complementum eſt arcus BC, ad ſecantem complementi arcus
              <lb/>
            GI, anguli C: </s>
            <s xml:id="echoid-s15495" xml:space="preserve">Et permutando, vt ſinus totus ad ſinum complementi arcus
              <lb/>
            BC, ita ſecans anguli A, ad ſecantem complementi anguli C. </s>
            <s xml:id="echoid-s15496" xml:space="preserve">Non ſecus o-
              <lb/>
            ſtendemus, ſi aliter conſtruatur figura, ita eſſe ſinum totum ad ſinum comple
              <lb/>
            menti arcus AB, vt eſt ſecans anguli C, ad ſecantem complementi anguli A.
              <lb/>
            </s>
            <s xml:id="echoid-s15497" xml:space="preserve">Quapropter in omni triangulo ſphærico rectangulo, &</s>
            <s xml:id="echoid-s15498" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15499" xml:space="preserve">Quod demonſtran-
              <lb/>
            dum erat.</s>
            <s xml:id="echoid-s15500" xml:space="preserve"/>
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        <div xml:id="echoid-div1256" type="section" level="1" n="592">
          <head xml:id="echoid-head627" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s15501" xml:space="preserve">INFERTVR hinc problema huiuſmodi.</s>
            <s xml:id="echoid-s15502" xml:space="preserve"/>
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