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

Table of Notes

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          to lateri oppoſitus ſit acutus etiam, an vero
            <lb/>
          obtuſus.</head>
          <p>
            <s xml:id="echoid-s17811" xml:space="preserve">FIAT, vt latus datum angulo dato oppoſitum ad alterum latus da-
              <lb/>
              <note position="left" xlink:label="note-504-01" xlink:href="note-504-01a" xml:space="preserve">Propoſ. 13.
                <lb/>
              triang. re-
                <lb/>
              ctil.</note>
            tum, ita ſinus anguli dati ad aliud, reperieturq́ue ſinus anguli alteri dato la-
              <lb/>
            teri oppoſiti, qui ſi acutus fuerit, (ſemper autem acutus erit, ſi datus eſt ob-
              <lb/>
            tuſus) ex ipſo ſinu inuento notus fiet; </s>
            <s xml:id="echoid-s17812" xml:space="preserve">ſi vero obtuſus, ſinus inuentus dabit
              <lb/>
            angulum, qui ex duobus rectis ſubductus quæſitum angulum alteri dato la-
              <lb/>
            teri oppoſitum relinquet: </s>
            <s xml:id="echoid-s17813" xml:space="preserve">Summa autem ex dato angulo, & </s>
            <s xml:id="echoid-s17814" xml:space="preserve">inuento angulo
              <lb/>
            conflata, ſi ex duobus rectis ſubtrahatur, indicabit tertium angulum à datis
              <lb/>
            lateribus comprehenſum. </s>
            <s xml:id="echoid-s17815" xml:space="preserve">Fiat deinde, vt ſinus anguli dati ad ſinum huius ter
              <lb/>
            tij anguli inuenti, ita latus datum dato angulo oppoſitum ad aliud, gigne-
              <lb/>
            turq́; </s>
            <s xml:id="echoid-s17816" xml:space="preserve">tertium latus quæſitum.</s>
            <s xml:id="echoid-s17817" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17818" xml:space="preserve">SI data latera ſint æqualia, datus etiam erit angulus alteri dato lateri op-
              <lb/>
            poſitus, cum dato angulo vt æqualis. </s>
            <s xml:id="echoid-s17819" xml:space="preserve">Hinc tertius angulus, & </s>
            <s xml:id="echoid-s17820" xml:space="preserve">tertium latus
              <lb/>
            reperietur, vt prius.</s>
            <s xml:id="echoid-s17821" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1443" type="section" level="1" n="641">
          <head xml:id="echoid-head676" xml:space="preserve">TRIANGVLORVM SPHAERI-
            <lb/>
          CORVM RECTANGVLORVM
            <lb/>
          PROBLEMATA, ACPRAXES.</head>
          <note position="left" xml:space="preserve">Quæritur
            <lb/>
          angulus nõ
            <lb/>
          rectus.</note>
        </div>
        <div xml:id="echoid-div1444" type="section" level="1" n="642">
          <head xml:id="echoid-head677" xml:space="preserve">1. DATO arcu in triangulo rectangulo, qui
            <lb/>
          recto angulo opponitur, cum alterutro ar-
            <lb/>
          cuum circa rectum angulum, inuenire angu
            <lb/>
          lum huic arcui oppoſitum.</head>
          <p>
            <s xml:id="echoid-s17822" xml:space="preserve">FIAT, vt ſinus arcus dati recto angulo oppoſiti ad ſinum totum, ita ſi-
              <lb/>
              <note position="left" xlink:label="note-504-03" xlink:href="note-504-03a" xml:space="preserve">Probl. 1. pro
                <lb/>
              poſ. 41. tri-
                <lb/>
              ang. ſphær.</note>
            nus arcus dati circa angulum rectum ad aliud, inuenieturq́; </s>
            <s xml:id="echoid-s17823" xml:space="preserve">ſin us anguli huic
              <lb/>
            arcui oppoſiti, qui quæritur. </s>
            <s xml:id="echoid-s17824" xml:space="preserve">Hic autem angulus erit acutus, ſi datus ar-
              <lb/>
            cus ei oppoſitus circa rectum angulum fuerit quadrante minor; </s>
            <s xml:id="echoid-s17825" xml:space="preserve">obtuſus au-
              <lb/>
            tem, ſi maior.</s>
            <s xml:id="echoid-s17826" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1446" type="section" level="1" n="643">
          <head xml:id="echoid-head678" xml:space="preserve">Aliter.</head>
          <p>
            <s xml:id="echoid-s17827" xml:space="preserve">FIAT, vt ſinus totus ad ſinum arcus angulo recto oppoſiti, ita ſecans
              <lb/>
              <note position="left" xlink:label="note-504-04" xlink:href="note-504-04a" xml:space="preserve">Probl. pro-
                <lb/>
              poſ. 55. tri-
                <lb/>
              ang. ſphær.</note>
            complementi arcus circa rectum angulum dati ad aliud, produceturq́; </s>
            <s xml:id="echoid-s17828" xml:space="preserve">ſecans
              <lb/>
            complementi anguli quæſiti, qui huic arcui opponitur.</s>
            <s xml:id="echoid-s17829" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1448" type="section" level="1" n="644">
          <head xml:id="echoid-head679" xml:space="preserve">2. DATO arcu in triangulo rectangulo, </head>
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