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

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          <p>
            <s xml:id="echoid-s10234" xml:space="preserve">ALITER & </s>
            <s xml:id="echoid-s10235" xml:space="preserve">facilius. </s>
            <s xml:id="echoid-s10236" xml:space="preserve">Ex A, ad interuallum minoris lateris AB, circulus
              <lb/>
              <note position="left" xlink:label="note-334-01" xlink:href="note-334-01a" xml:space="preserve">Alia inuẽ-
                <lb/>
              tio ſegmẽ-
                <lb/>
              torum ba-
                <lb/>
              ſis. & fac@-
                <lb/>
              lior.</note>
            deſcribatur ſecans maius latus AC, in F, idemq́. </s>
            <s xml:id="echoid-s10237" xml:space="preserve">productum in G, & </s>
            <s xml:id="echoid-s10238" xml:space="preserve">latus BC,
              <lb/>
              <figure xlink:label="fig-334-01" xlink:href="fig-334-01a" number="179">
                <image file="334-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/334-01"/>
              </figure>
            ſi perpen dicularis intra trian
              <lb/>
            gulum cadit, vel certe, ſi ex-
              <lb/>
            tra cadit, ipſum productum in
              <lb/>
            E: </s>
            <s xml:id="echoid-s10239" xml:space="preserve">ſecabiturq́; </s>
            <s xml:id="echoid-s10240" xml:space="preserve">recta BE, bifa-
              <lb/>
              <note position="left" xlink:label="note-334-02" xlink:href="note-334-02a" xml:space="preserve">3. tertij.</note>
            riam in E. </s>
            <s xml:id="echoid-s10241" xml:space="preserve">Quia vero rectan-
              <lb/>
            gulum ſub BC, CE, rectan-
              <lb/>
              <note position="left" xlink:label="note-334-03" xlink:href="note-334-03a" xml:space="preserve">corol. 1. 36.
                <lb/>
              tertij.</note>
            gulo ſub GC, CF, æquale eſt;
              <lb/>
            </s>
            <s xml:id="echoid-s10242" xml:space="preserve">erit, vt BC, latus, in quod
              <lb/>
              <note position="left" xlink:label="note-334-04" xlink:href="note-334-04a" xml:space="preserve">16. ſexti.</note>
            perpendicularis ducitur, nem-
              <lb/>
            pe vt 21. </s>
            <s xml:id="echoid-s10243" xml:space="preserve">in priori triangulo,
              <lb/>
            vel vt 11. </s>
            <s xml:id="echoid-s10244" xml:space="preserve">in poſteriori, ad GC,
              <lb/>
            ſummam reliquorũ duorum
              <lb/>
            laterũ AC, AB, (quod AG,
              <lb/>
            ipſi AB, ſit æqualis) hoc eſt,
              <lb/>
            ad 33. </s>
            <s xml:id="echoid-s10245" xml:space="preserve">ita CF, differentia in-
              <lb/>
            ter eadem duo latera, id eſt,
              <lb/>
            ita 7. </s>
            <s xml:id="echoid-s10246" xml:space="preserve">ad CE. </s>
            <s xml:id="echoid-s10247" xml:space="preserve">Quare per
              <lb/>
            regulam auream inuenietur
              <lb/>
            C E, partium 11. </s>
            <s xml:id="echoid-s10248" xml:space="preserve">in triangulo
              <lb/>
            priori, in poſteriori autem 21.
              <lb/>
            </s>
            <s xml:id="echoid-s10249" xml:space="preserve">vt hic perſpicuum eſt.</s>
            <s xml:id="echoid-s10250" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          BC. # GC. # # CF. # # CE.
            <lb/>
          21. # 33. # # 7? # fit. # 11.
            <lb/>
          # # Item
            <lb/>
          11. # 33. # # 7? # fit. # 21.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10251" xml:space="preserve">Quòd ſi EC, inuenta partium 11. </s>
            <s xml:id="echoid-s10252" xml:space="preserve">in priori triangulo auferatur ex latere
              <lb/>
            BC, nempe ex 21. </s>
            <s xml:id="echoid-s10253" xml:space="preserve">remanebit BE, 10. </s>
            <s xml:id="echoid-s10254" xml:space="preserve">cuius ſemiſsis 5. </s>
            <s xml:id="echoid-s10255" xml:space="preserve">erit ſegmentum BD, ac
              <lb/>
            proinde alterum CD, erit 16. </s>
            <s xml:id="echoid-s10256" xml:space="preserve">In poſteriori vero triangulo, ſi ex EC, inuenta
              <lb/>
            partium 21. </s>
            <s xml:id="echoid-s10257" xml:space="preserve">dematur latus BC, partium 11. </s>
            <s xml:id="echoid-s10258" xml:space="preserve">relinquetur rurſus BE, 10. </s>
            <s xml:id="echoid-s10259" xml:space="preserve">Qua-
              <lb/>
            re eius dimidium 5. </s>
            <s xml:id="echoid-s10260" xml:space="preserve">dabit rectam BD, extra triangulum inter perpendicula-
              <lb/>
            rem, & </s>
            <s xml:id="echoid-s10261" xml:space="preserve">angulum obtuſum; </s>
            <s xml:id="echoid-s10262" xml:space="preserve">ac proinde tota CD, compoſita ex latere BC, & </s>
            <s xml:id="echoid-s10263" xml:space="preserve">
              <lb/>
            dicto dimidio BD, erit 16.</s>
            <s xml:id="echoid-s10264" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10265" xml:space="preserve">SI igitur fiat, vt latus, in quod perpendicularis ducta eſt, ad ſum-
              <lb/>
              <note position="left" xlink:label="note-334-06" xlink:href="note-334-06a" xml:space="preserve">Praxis.</note>
            mam aliorum duorũ laterum, ita diff@rentia eorundem laterum ad aliud,
              <lb/>
              <note position="left" xlink:label="note-334-07" xlink:href="note-334-07a" xml:space="preserve">Quo pacto
                <lb/>
              ex ipſa ope
                <lb/>
              ratione co
                <lb/>
              gnoſcatur,
                <lb/>
              an perpen-
                <lb/>
              dicularis
                <lb/>
              cadat intra
                <lb/>
              triangulũ,
                <lb/>
              an extra.</note>
            reperietur numerus, qui ſi minor fuerit tertio latere, indicabit perpendi-
              <lb/>
            cularem intra triangulum cecidiſſe, idemq́, extertio latere ablatus relin-
              <lb/>
            quet numerum, cuius dimidium erit minus ſegmentum baſis, hoc autem
              <lb/>
            ex tertio latere demptum reliquum faciet maius ſegmentum. </s>
            <s xml:id="echoid-s10266" xml:space="preserve">Si vero nu-
              <lb/>
            merus per auream regulam inuentus tertium latus ſuperet, argumento
              <lb/>
            eſt, perpenticularem cecidiſſe extra triangulum. </s>
            <s xml:id="echoid-s10267" xml:space="preserve">Quare ſi ex eolatus
              <lb/>
            tertium detrahatur, dabit ſemiſſis reliqui numeri rectam extra triangu-
              <lb/>
            lum inter perpendicularem, & </s>
            <s xml:id="echoid-s10268" xml:space="preserve">angulum obtuſum: </s>
            <s xml:id="echoid-s10269" xml:space="preserve">Eadem vero </s>
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