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

Table of figures

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        <div xml:id="echoid-div862" type="section" level="1" n="467">
          <pb o="325" file="337" n="337" rhead=""/>
          <note position="right" xml:space="preserve">
            <lb/>
          C. # A. # # AB. # # BC.
            <lb/>
          59996. # 50779. # # 13? # fit # 11. # ferè.
            <lb/>
          # # Item.
            <lb/>
          C. # B. # # AB. # # AC.
            <lb/>
          59996. # 92310. # # 13? # fit # 20. # ferè.
            <lb/>
          # # Vel.
            <lb/>
          A. # B. # # BC. # # AC.
            <lb/>
          50779. # 92310. # # 11? # fit # 20. # ferè.
            <lb/>
          </note>
          <p style="it">
            <s xml:id="echoid-s10408" xml:space="preserve">ITAQVE, datis angulis omnibus, cum vno latere; </s>
            <s xml:id="echoid-s10409" xml:space="preserve">Si fiat, vt ſi-
              <lb/>
              <note position="right" xlink:label="note-337-02" xlink:href="note-337-02a" xml:space="preserve">Praxis.</note>
            nus anguli lateri dato oppoſiti ad ſinum vtriuſuis reliquorum angulorum,
              <lb/>
            ita latus datum ad aliud, inuenietur latus angulo illi, cuius ſinus acce-
              <lb/>
            ptus eſt, oppoſitum: </s>
            <s xml:id="echoid-s10410" xml:space="preserve">Et ſi rurſus fiat, vt ſinus anguli lateri dato oppo-
              <lb/>
            ſiti ad ſinum tertij anguli, ita datum latus ad aliud, reperietur latus ter
              <lb/>
            tio angulo oppoſitum, &</s>
            <s xml:id="echoid-s10411" xml:space="preserve">c.</s>
            <s xml:id="echoid-s10412" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quãdo triã
            <lb/>
          gulũ eſt Iſo
            <lb/>
          ſceles, vel ę-
            <lb/>
          quilaterũ:
            <lb/>
          aut quãdo
            <lb/>
          in ſcaleno
            <lb/>
          dãtur duo
            <lb/>
          latera cum
            <lb/>
          angulis.</note>
          <p>
            <s xml:id="echoid-s10413" xml:space="preserve">QVOD ſi triangulum fuerit Iſoſceles, & </s>
            <s xml:id="echoid-s10414" xml:space="preserve">dentur anguli: </s>
            <s xml:id="echoid-s10415" xml:space="preserve">Vel ſi fuerit ſca-
              <lb/>
            lenum, & </s>
            <s xml:id="echoid-s10416" xml:space="preserve">duo dentur latera cum angulis, vnius tantum lateris inuentione
              <lb/>
            opus eſt, vt patet. </s>
            <s xml:id="echoid-s10417" xml:space="preserve">In æquilatero autem triangulo, ſi detur vnum latus, erunt
              <lb/>
            & </s>
            <s xml:id="echoid-s10418" xml:space="preserve">reliqua data, vtpoteilli æqualia.</s>
            <s xml:id="echoid-s10419" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10420" xml:space="preserve">IAM verò ſi datæ ſint proportiones angulorum, cum vno latere, inue-
              <lb/>
            ſtigandæ erunt ex illis proportionibus magnitudines angulorum, vt in ſcho-
              <lb/>
            lio propoſ. </s>
            <s xml:id="echoid-s10421" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10422" xml:space="preserve">demonſtrauimus: </s>
            <s xml:id="echoid-s10423" xml:space="preserve">Deinde vero reliqua latera exploranda, vt
              <lb/>
              <note position="right" xlink:label="note-337-04" xlink:href="note-337-04a" xml:space="preserve">Quãdo dã-
                <lb/>
              rur propor
                <lb/>
              tiones an-
                <lb/>
              gulorũ, cũ
                <lb/>
              vno latere.</note>
            hic oſtenſum eſt.</s>
            <s xml:id="echoid-s10424" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10425" xml:space="preserve">INVENTIS autem lateribus, liquido conſtat, eorum proportiones
              <lb/>
            eſſe notas in numeris, in quibus ipſa cognita ſunt. </s>
            <s xml:id="echoid-s10426" xml:space="preserve">Datis ergo omnibus angu-
              <lb/>
            lis trianguli non rectanguli, &</s>
            <s xml:id="echoid-s10427" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10428" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s10429" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div868" type="section" level="1" n="468">
          <head xml:id="echoid-head500" xml:space="preserve">PROBL. 7. PROPOS. 11.</head>
          <p>
            <s xml:id="echoid-s10430" xml:space="preserve">DATIS omnibus trianguli non rectanguli
              <lb/>
              <note position="right" xlink:label="note-337-05" xlink:href="note-337-05a" xml:space="preserve">In triãgulo
                <lb/>
              ex notis la-
                <lb/>
              teribus, vel
                <lb/>
              ex eorũ pro
                <lb/>
              portionibꝰ
                <lb/>
              notis, angu
                <lb/>
              li inueniũ-
                <lb/>
              tur.</note>
            lateribus, vel eorum proportionibus, omnes an-
              <lb/>
            gulos notos efficere.</s>
            <s xml:id="echoid-s10431" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10432" xml:space="preserve">IN triangulo priori ABC, ſint data omnia
              <lb/>
              <figure xlink:label="fig-337-01" xlink:href="fig-337-01a" number="182">
                <image file="337-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/337-01"/>
              </figure>
            latera; </s>
            <s xml:id="echoid-s10433" xml:space="preserve">AB, 13. </s>
            <s xml:id="echoid-s10434" xml:space="preserve">AC, 20. </s>
            <s xml:id="echoid-s10435" xml:space="preserve">& </s>
            <s xml:id="echoid-s10436" xml:space="preserve">BC, 21. </s>
            <s xml:id="echoid-s10437" xml:space="preserve">Oporter ex
              <lb/>
            his inueſtigare angulos. </s>
            <s xml:id="echoid-s10438" xml:space="preserve">In maximum latus BC,
              <lb/>
            ex oppoſito angulo A, ducatur perpendicularis
              <lb/>
            AD, quę neceſlario intra triangulum cadet. </s>
            <s xml:id="echoid-s10439" xml:space="preserve">Cum
              <lb/>
            enim latus BC, ſit maximum, erit & </s>
            <s xml:id="echoid-s10440" xml:space="preserve">angulus A,
              <lb/>
              <note position="right" xlink:label="note-337-06" xlink:href="note-337-06a" xml:space="preserve">19. primi.</note>
            ipſi oppoſitus, maximus: </s>
            <s xml:id="echoid-s10441" xml:space="preserve">ac propterea vterq; </s>
            <s xml:id="echoid-s10442" xml:space="preserve">B,
              <lb/>
              <note position="right" xlink:label="note-337-07" xlink:href="note-337-07a" xml:space="preserve">17. primi.</note>
            C, acutus. </s>
            <s xml:id="echoid-s10443" xml:space="preserve">Ex quo fit, perpendicularem AD, in-
              <lb/>
              <note position="right" xlink:label="note-337-08" xlink:href="note-337-08a" xml:space="preserve">Scholium</note>
            tra triangulum cadere. </s>
            <s xml:id="echoid-s10444" xml:space="preserve">Primùm itaq; </s>
            <s xml:id="echoid-s10445" xml:space="preserve">inquiran-
              <lb/>
              <note position="right" xlink:label="note-337-09" xlink:href="note-337-09a" xml:space="preserve">13. ſecundi.</note>
            tur rectæ BD, CD. </s>
            <s xml:id="echoid-s10446" xml:space="preserve">Inuenietur BD, 5. </s>
            <s xml:id="echoid-s10447" xml:space="preserve">& </s>
            <s xml:id="echoid-s10448" xml:space="preserve">CD,
              <lb/>
              <note position="right" xlink:label="note-337-10" xlink:href="note-337-10a" xml:space="preserve">9. huius.</note>
            16. </s>
            <s xml:id="echoid-s10449" xml:space="preserve">Quia ergo, poſito ſinu toto AB, recta BD,
              <lb/>
            ſinus eſt anguli BAD, vt in tractatione ſinuum
              <lb/>
            oſtendimus, dicemus per auream regulam. </s>
            <s xml:id="echoid-s10450" xml:space="preserve">Si </s>
          </p>
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    </echo>
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