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

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        <div xml:id="echoid-div772" type="section" level="1" n="451">
          <p style="it">
            <s xml:id="echoid-s8741" xml:space="preserve">
              <pb o="299" file="311" n="311" rhead=""/>
            tam in ſemicirculo CAE, reliquus arcus AE, quam in ſemicirculo
              <lb/>
            ACD, reliquus arcus CD, quadrans: </s>
            <s xml:id="echoid-s8742" xml:space="preserve">Eodemq́, modo in ſemicirculo
              <lb/>
            AED, vel CDE, reliquus arcus DE, quadrans erit; </s>
            <s xml:id="echoid-s8743" xml:space="preserve">& </s>
            <s xml:id="echoid-s8744" xml:space="preserve">proinde qua-
              <lb/>
            tuor anguliad B, quatuor quadrantibus æqualibus inſiſtentes erunt æqua-
              <lb/>
              <note position="right" xlink:label="note-311-01" xlink:href="note-311-01a" xml:space="preserve">27. tertij.</note>
            les, & </s>
            <s xml:id="echoid-s8745" xml:space="preserve">recti. </s>
            <s xml:id="echoid-s8746" xml:space="preserve">Reliqua, vt prius, oſtendentur.</s>
            <s xml:id="echoid-s8747" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div778" type="section" level="1" n="452">
          <head xml:id="echoid-head484" xml:space="preserve">SCHOLIVM.</head>
          <note position="right" xml:space="preserve">Datis duo-
            <lb/>
          bus angulis
            <lb/>
          tirãguli re-
            <lb/>
          ctilinei, da-
            <lb/>
          tus etiã erit
            <lb/>
          tertius. Itẽ
            <lb/>
          in triãgulo
            <lb/>
          rectangulo,
            <lb/>
          ſi detur vnꝰ
            <lb/>
          angulus a-
            <lb/>
          cutus, datus
            <lb/>
          quoq; erit
            <lb/>
          acutus reli-
            <lb/>
          quus.</note>
          <p style="it">
            <s xml:id="echoid-s8748" xml:space="preserve">_IN_ materia porro triangulorum rectilineorum, cum dantur duo anguli noti, ter
              <lb/>
            tius illico notus quoq; </s>
            <s xml:id="echoid-s8749" xml:space="preserve">erit, cum ſit complementum duorum rectorum: </s>
            <s xml:id="echoid-s8750" xml:space="preserve">Item cum in
              <lb/>
            triangulo rectãgulo datur vnus acutus angulus, notus etiã erit reliquus acutus, quod
              <lb/>
            ſit complementum vnius recti. </s>
            <s xml:id="echoid-s8751" xml:space="preserve">Itaq; </s>
            <s xml:id="echoid-s8752" xml:space="preserve">detractis duobus angulis notis ſimul ex grad. </s>
            <s xml:id="echoid-s8753" xml:space="preserve">180.
              <lb/>
            </s>
            <s xml:id="echoid-s8754" xml:space="preserve">reliquus erit tertius notus. </s>
            <s xml:id="echoid-s8755" xml:space="preserve">Item in triangulo rectangulo, ſi detrahatur acutus no@
              <lb/>
            tus ex grad. </s>
            <s xml:id="echoid-s8756" xml:space="preserve">90. </s>
            <s xml:id="echoid-s8757" xml:space="preserve">remanebit alter acutus notus. </s>
            <s xml:id="echoid-s8758" xml:space="preserve">Quod ſemel monuiſſe ſatis ſit.</s>
            <s xml:id="echoid-s8759" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div779" type="section" level="1" n="453">
          <head xml:id="echoid-head485" xml:space="preserve">THEOR. I. PROPOS. I.</head>
          <p>
            <s xml:id="echoid-s8760" xml:space="preserve">IN omni triangulo rectilineo latera quæuis
              <lb/>
              <note position="right" xlink:label="note-311-03" xlink:href="note-311-03a" xml:space="preserve">Latera triã-
                <lb/>
              guli rectili-
                <lb/>
              nei ſunt ſi-
                <lb/>
              nubus an-
                <lb/>
              gulotũ op-
                <lb/>
              poſitorum
                <lb/>
              proportio-
                <lb/>
              nalia.</note>
            duo eandem proportionem habent, quam ſinus
              <lb/>
            angulorum illis oppoſitorum.</s>
            <s xml:id="echoid-s8761" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8762" xml:space="preserve">SIT primum triangulum rectangulum ABC, cuius angulus rectus B.
              <lb/>
            </s>
            <s xml:id="echoid-s8763" xml:space="preserve">Dico eſſe AB, ad AC, vt eſt ſinus anguli C, ad ſinum anguli B. </s>
            <s xml:id="echoid-s8764" xml:space="preserve">Item
              <lb/>
            AB, ad BC, vt eſt ſinus anguli C, ad ſinum angu-
              <lb/>
              <figure xlink:label="fig-311-01" xlink:href="fig-311-01a" number="160">
                <image file="311-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/311-01"/>
              </figure>
            li A, &</s>
            <s xml:id="echoid-s8765" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8766" xml:space="preserve">Quoniam enim, vt in definitionibus ſi-
              <lb/>
            nuum oſtendimus, ſi AC, ponatur ſinus totus, latus
              <lb/>
            AB, eſt ſinus anguli C; </s>
            <s xml:id="echoid-s8767" xml:space="preserve">& </s>
            <s xml:id="echoid-s8768" xml:space="preserve">BC, ſinus anguli A: </s>
            <s xml:id="echoid-s8769" xml:space="preserve">liquido
              <lb/>
            conſtat, ita eſſe latus AB, ad latus AC, vt eſt AB, ſinus
              <lb/>
            anguli C, ad AC, ſinum totum anguli recti B: </s>
            <s xml:id="echoid-s8770" xml:space="preserve">Vel ita
              <lb/>
            eſſe latus AC, ad latus AB, vt eſt AC, ſinus totus re-
              <lb/>
            cti anguli B, ad AB, ſinum anguli C; </s>
            <s xml:id="echoid-s8771" xml:space="preserve">cum ipſa latera
              <lb/>
            ſint ſinus angulorum oppoſitorum, ac proinde vtro-
              <lb/>
            biq; </s>
            <s xml:id="echoid-s8772" xml:space="preserve">ſit identitatis proportio. </s>
            <s xml:id="echoid-s8773" xml:space="preserve">Eadem ratione erit, vt latus AC, ad latus BC,
              <lb/>
            ita AC, ſinus totus anguli recti B, ad BC, ſinum anguli A: </s>
            <s xml:id="echoid-s8774" xml:space="preserve">Vel vt latus BC,
              <lb/>
            ad latus AC, ita BC, ſinus anguli A, ad AC, ſinum totum recti anguli B.
              <lb/>
            </s>
            <s xml:id="echoid-s8775" xml:space="preserve">Item vt latus AB, ad latus BC, ita AB, ſinus anguli C, ad BC, ſinum an-
              <lb/>
            guli A: </s>
            <s xml:id="echoid-s8776" xml:space="preserve">Vel vt latus BC, ad latus AB, ita BC, ſinus anguli A, ad AB, ſi-
              <lb/>
            num anguli C.</s>
            <s xml:id="echoid-s8777" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8778" xml:space="preserve">SIT deinde triangulum ABC, non rectangulum. </s>
            <s xml:id="echoid-s8779" xml:space="preserve">Dico rurſus eſſe la-
              <lb/>
            tus AB, ad latus AC, vt eſt ſinus anguli C, ad ſinum anguli B, &</s>
            <s xml:id="echoid-s8780" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s8781" xml:space="preserve">Aut enim latera aſſumpta AB, AC, æqualia ſunt, autinæqualia. </s>
            <s xml:id="echoid-s8782" xml:space="preserve">Siæqua-
              <lb/>
            lia, erunt quoq; </s>
            <s xml:id="echoid-s8783" xml:space="preserve">anguli C, B, æquales; </s>
            <s xml:id="echoid-s8784" xml:space="preserve">ac proinde, vt in definitionibus ſi-
              <lb/>
              <note position="right" xlink:label="note-311-04" xlink:href="note-311-04a" xml:space="preserve">5. primi.</note>
            nuum docuimus, eorum ſinus æquales. </s>
            <s xml:id="echoid-s8785" xml:space="preserve">Quare erit, vt latus AB, ad latus
              <lb/>
            AC, ita ſinus anguli C, ad ſinum anguli B: </s>
            <s xml:id="echoid-s8786" xml:space="preserve">Vel vt latus AC, ad latus AB, ita
              <lb/>
            ſinus anguli B, ad ſinum anguli C; </s>
            <s xml:id="echoid-s8787" xml:space="preserve">cum ſemper ſit proportio æqualitatis. </s>
            <s xml:id="echoid-s8788" xml:space="preserve"/>
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