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

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        <div xml:id="echoid-div1435" type="section" level="1" n="637">
          <pb o="491" file="503" n="503" rhead=""/>
          <note position="right" xml:space="preserve">Quærũtur
            <lb/>
          anguli.</note>
        </div>
        <div xml:id="echoid-div1437" type="section" level="1" n="638">
          <head xml:id="echoid-head673" xml:space="preserve">11. DATIS omnibus lateribus trianguli non
            <lb/>
          rectanguli, reperire omnes eius angulos.</head>
          <p>
            <s xml:id="echoid-s17784" xml:space="preserve">DVCTA ad maximum latus perpẽdiculari ex angulo oppoſito, (vt per-
              <lb/>
              <note position="right" xlink:label="note-503-02" xlink:href="note-503-02a" xml:space="preserve">Propoſ. 11.
                <lb/>
              triang. re-
                <lb/>
              ctil.</note>
            pendicularis ſemper intra triangulum cadat) inueniãtur, per antecedens pro-
              <lb/>
            blema, rectæ inter perpendicularem, & </s>
            <s xml:id="echoid-s17785" xml:space="preserve">duos angulos maximi lateris poſitæ.
              <lb/>
            </s>
            <s xml:id="echoid-s17786" xml:space="preserve">Deinde fiat, vt minimum latus ad ſinum totum, ita minus ſegmentum baſis ad
              <lb/>
            aliud, gigneturq́; </s>
            <s xml:id="echoid-s17787" xml:space="preserve">ſinus, cuius arcus complementum dabit angulum baſis mini-
              <lb/>
            mo lateri adiacentem. </s>
            <s xml:id="echoid-s17788" xml:space="preserve">Rurſus fiat, vt medium latus ad ſinum totum, ita ma-
              <lb/>
            ius ſegmentum baſis ad aliud, procreabiturq́; </s>
            <s xml:id="echoid-s17789" xml:space="preserve">ſinus, cuius arcus complemen-
              <lb/>
            tum dabit angulum baſis medio lateri adiacentem. </s>
            <s xml:id="echoid-s17790" xml:space="preserve">Tertius vero angulus ma-
              <lb/>
            ximo lateri oppoſitus conflabitur ex duobus arcubus duorum ſinuum inuen-
              <lb/>
            torum: </s>
            <s xml:id="echoid-s17791" xml:space="preserve">Vel certe relinquetur poſt detractionem duorum angulorum inuen-
              <lb/>
            torum ex duobus rectis.</s>
            <s xml:id="echoid-s17792" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17793" xml:space="preserve">SI triangulum ſit Iſoſceles, ducenda erit perpendicularis ad baſim, quam
              <lb/>
            bifariam ſecabit. </s>
            <s xml:id="echoid-s17794" xml:space="preserve">Nam ſi tunc fiat, vt vnum æqualium laterum ad ſinum to-
              <lb/>
            tum, ita dimidium baſis ad aliud, reperietur ſinus, cuius arcus complementum
              <lb/>
            dabit vnum æqualium angulorum ſupra baſim, ac proinde & </s>
            <s xml:id="echoid-s17795" xml:space="preserve">alterum. </s>
            <s xml:id="echoid-s17796" xml:space="preserve">Ter-
              <lb/>
            tius ex his duobus elicietur.</s>
            <s xml:id="echoid-s17797" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17798" xml:space="preserve">IN æquilatero dabuntur anguli, etiam ſi latera non dentur, cum quilibet
              <lb/>
            ſit tertia pars duorum rectorum, vel duæ tertiæ vnius recti.</s>
            <s xml:id="echoid-s17799" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quæritur
            <lb/>
          latus, cum
            <lb/>
          eius angu-
            <lb/>
          lis duobus.</note>
        </div>
        <div xml:id="echoid-div1439" type="section" level="1" n="639">
          <head xml:id="echoid-head674" xml:space="preserve">12. DATIS duobus lateribus trianguli non
            <lb/>
          rectanguli, cum angulo ab ipſis comprehen
            <lb/>
          ſo, inuenire tertiũ latus, & reliquos angulos.</head>
          <p>
            <s xml:id="echoid-s17800" xml:space="preserve">SVBDVCTO angulo dato ex duobus rectis, vt aggregatum aliorum
              <lb/>
              <note position="right" xlink:label="note-503-04" xlink:href="note-503-04a" xml:space="preserve">Propoſ. 12.
                <lb/>
              triang. re-
                <lb/>
              ctil.</note>
            duorum habeatur, inueniatur, per 6. </s>
            <s xml:id="echoid-s17801" xml:space="preserve">problema triang. </s>
            <s xml:id="echoid-s17802" xml:space="preserve">rectil. </s>
            <s xml:id="echoid-s17803" xml:space="preserve">ex hoc aggrega-
              <lb/>
            to, & </s>
            <s xml:id="echoid-s17804" xml:space="preserve">proportione laterum da torum eis oppoſitorum, (quæ eadem eſt, quæ
              <lb/>
            inter ſinus eorum reperitur) vterque eorum. </s>
            <s xml:id="echoid-s17805" xml:space="preserve">Deinde fiat, vt ſinus vtriusvis
              <lb/>
            horum angulorum inuẽtorum ad ſinum anguli in principio dati, ita latus in-
              <lb/>
            uento angulo, qui in aurea regula acceptus fuerit, oppoſitum ad aliud, inue-
              <lb/>
            nieturq́; </s>
            <s xml:id="echoid-s17806" xml:space="preserve">tertium latus.</s>
            <s xml:id="echoid-s17807" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17808" xml:space="preserve">QVOD ſi data duo latera ſint æqualia, ablato angulo dato ex duobus
              <lb/>
            rectis, dabit ſemiſsis reſidui vtrumque angulorum æqualium: </s>
            <s xml:id="echoid-s17809" xml:space="preserve">Et ſi fiat, vt ſi-
              <lb/>
            nus vnius illorum ad ſinum anguli dati, ita vnum laterum æqualium ad aliud,
              <lb/>
            prodibit tertium latus.</s>
            <s xml:id="echoid-s17810" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quærũtur
            <lb/>
          duo angu-
            <lb/>
          li, cum vno
            <lb/>
          latere.</note>
        </div>
        <div xml:id="echoid-div1441" type="section" level="1" n="640">
          <head xml:id="echoid-head675" xml:space="preserve">13. DATIS duobus lateribus trianguli non
            <lb/>
          rectanguli, cum angulo, qui vni eorum oppo
            <lb/>
          nitur, inueſtigare reliquos angulos, & ter-
            <lb/>
          tium latus: ſi modo, quando datus angulus
            <lb/>
          eſt acutus, conſtet, num angulus alteri </head>
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