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

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          <p style="it">
            <s xml:id="echoid-s10269" xml:space="preserve">
              <pb o="323" file="335" n="335" rhead=""/>
            tertio lateri adiuncta offeret alteram rectam inter perpendicularem, & </s>
            <s xml:id="echoid-s10270" xml:space="preserve">
              <lb/>
            angulum acutum.</s>
            <s xml:id="echoid-s10271" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10272" xml:space="preserve">SI ergo ab vno angulo trianguli cuiuſuis notorum laterum, &</s>
            <s xml:id="echoid-s10273" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10274" xml:space="preserve">Quod fa-
              <lb/>
            ciendum erat.</s>
            <s xml:id="echoid-s10275" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div858" type="section" level="1" n="466">
          <head xml:id="echoid-head498" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s10276" xml:space="preserve">_
              <emph style="sc">VIDe</emph>
            S_ igitur, in vtraque praxi calculum ipſum monſtrare, num perpendicula
              <lb/>
            ris intra triangulum cadat, an vero extra.</s>
            <s xml:id="echoid-s10277" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10278" xml:space="preserve">_
              <emph style="sc">IDEm</emph>
            _ hoc problema abſolui poteſt per propoſ. </s>
            <s xml:id="echoid-s10279" xml:space="preserve">_13._ </s>
            <s xml:id="echoid-s10280" xml:space="preserve">aut _12._ </s>
            <s xml:id="echoid-s10281" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10282" xml:space="preserve">_2._ </s>
            <s xml:id="echoid-s10283" xml:space="preserve">
              <emph style="sc">E</emph>
            ucl. </s>
            <s xml:id="echoid-s10284" xml:space="preserve">prout per@
              <lb/>
            pendicularis intra triangulum cadit, vel extra. </s>
            <s xml:id="echoid-s10285" xml:space="preserve">Cadat enim primũ perpendicularis
              <lb/>
            _AD,_ intra, ſintq́; </s>
            <s xml:id="echoid-s10286" xml:space="preserve">latera, vt prius; </s>
            <s xml:id="echoid-s10287" xml:space="preserve">_
              <emph style="sc">Ab</emph>
            , 13. </s>
            <s xml:id="echoid-s10288" xml:space="preserve">AC, 20 BC._ </s>
            <s xml:id="echoid-s10289" xml:space="preserve">_21._ </s>
            <s xml:id="echoid-s10290" xml:space="preserve">_
              <emph style="sc">E</emph>
            _ritq; </s>
            <s xml:id="echoid-s10291" xml:space="preserve">vterq; </s>
            <s xml:id="echoid-s10292" xml:space="preserve">angulus _B, C,_
              <lb/>
            acutus, propter rectos angulos ad _D._ </s>
            <s xml:id="echoid-s10293" xml:space="preserve">cũ tam duo anguli _B,_ & </s>
            <s xml:id="echoid-s10294" xml:space="preserve">ADB, quàm duo _C,_ & </s>
            <s xml:id="echoid-s10295" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-335-01" xlink:href="note-335-01a" xml:space="preserve">17. primi.</note>
            _
              <emph style="sc">A</emph>
            DC,_ ſint duobus rectis minores. </s>
            <s xml:id="echoid-s10296" xml:space="preserve">Quoniam igitur quadratũ ex _AC,_ minus eſt, quàm
              <lb/>
            duo quadrata ex _AB,
              <emph style="sc">B</emph>
            C,_ rectangulo bis cõprehenſo ſub _
              <emph style="sc">Cb, b</emph>
            D;_ </s>
            <s xml:id="echoid-s10297" xml:space="preserve">ſi quadratũ lateris
              <lb/>
              <note position="right" xlink:label="note-335-02" xlink:href="note-335-02a" xml:space="preserve">13. ſecundi.</note>
            _AC,_ nempe 400. </s>
            <s xml:id="echoid-s10298" xml:space="preserve">auferatur ex ſumma quadratorum laterum _AB,
              <emph style="sc">B</emph>
            C,_ nimirum ex
              <lb/>
            _610._ </s>
            <s xml:id="echoid-s10299" xml:space="preserve">reliquum erit rectangulũ ſub _
              <emph style="sc">Cb</emph>
            , BD,_ bis com-
              <lb/>
              <figure xlink:label="fig-335-01" xlink:href="fig-335-01a" number="180">
                <image file="335-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/335-01"/>
              </figure>
            prehẽſum _210._ </s>
            <s xml:id="echoid-s10300" xml:space="preserve">Semiſsis ergo huius, vtpote _105._ </s>
            <s xml:id="echoid-s10301" xml:space="preserve">erit re-
              <lb/>
            ctangulum ſub _
              <emph style="sc">Cb, b</emph>
            D,_ comprehenſum: </s>
            <s xml:id="echoid-s10302" xml:space="preserve">quo diuiſ@
              <lb/>
            per latus _BC,_ hoc eſt, per _21._ </s>
            <s xml:id="echoid-s10303" xml:space="preserve">exibit ſegmentum _
              <emph style="sc">B</emph>
            D,_
              <lb/>
            _5._ </s>
            <s xml:id="echoid-s10304" xml:space="preserve">Reliquum ergo _CD,_ erit _16._ </s>
            <s xml:id="echoid-s10305" xml:space="preserve">Quod tamen eodem mo
              <lb/>
            do reperirs poteſt, ſi quadratum lateris _AB,_ ex qua-
              <lb/>
            dratis laterum _AC,
              <emph style="sc">C</emph>
            B,_ ſubducatur, &</s>
            <s xml:id="echoid-s10306" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10307" xml:space="preserve">_
              <emph style="sc">E</emph>
            _ſt enim
              <lb/>
              <note position="right" xlink:label="note-335-03" xlink:href="note-335-03a" xml:space="preserve">13. ſecundi.</note>
            & </s>
            <s xml:id="echoid-s10308" xml:space="preserve">illud minus, quàm hæc duo, rectangulo ſub _
              <emph style="sc">Bc</emph>
            ,_
              <lb/>
            _
              <emph style="sc">C</emph>
            D,_ bis comprehenſo.</s>
            <s xml:id="echoid-s10309" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10310" xml:space="preserve">_
              <emph style="sc">CA</emph>
            DAT_ deinde perpendicularis _AD,_ extra, ſintq́;
              <lb/>
            </s>
            <s xml:id="echoid-s10311" xml:space="preserve">latera, vt prius; </s>
            <s xml:id="echoid-s10312" xml:space="preserve">_AB, 13. </s>
            <s xml:id="echoid-s10313" xml:space="preserve">
              <emph style="sc">Ac</emph>
            , 20. </s>
            <s xml:id="echoid-s10314" xml:space="preserve">
              <emph style="sc">Bc</emph>
            , 11._ </s>
            <s xml:id="echoid-s10315" xml:space="preserve">_E_ritq́; </s>
            <s xml:id="echoid-s10316" xml:space="preserve">
              <lb/>
            angulus _
              <emph style="sc">A</emph>
              <emph style="sc">Bc</emph>
            ,_ obtuſus: </s>
            <s xml:id="echoid-s10317" xml:space="preserve">propterea quod duo _D,_ & </s>
            <s xml:id="echoid-s10318" xml:space="preserve">
              <lb/>
            _ABD,_ ſunt duobus rectis minores; </s>
            <s xml:id="echoid-s10319" xml:space="preserve">ac proinde _
              <emph style="sc">AB</emph>
            D,_
              <lb/>
              <note position="right" xlink:label="note-335-04" xlink:href="note-335-04a" xml:space="preserve">17. primi</note>
            acutus, cum _D,_ rectus ſit. </s>
            <s xml:id="echoid-s10320" xml:space="preserve">Quia ergo quadratum ex
              <lb/>
            _
              <emph style="sc">AC</emph>
            ,_ maius eſt, quàm duo quadrataex _
              <emph style="sc">A</emph>
            B,
              <emph style="sc">BC</emph>
            ,_ re-
              <lb/>
              <note position="right" xlink:label="note-335-05" xlink:href="note-335-05a" xml:space="preserve">12. ſecundi.</note>
            ctangulo bis comprehenſo ſub _
              <emph style="sc">C</emph>
            B, BD;_ </s>
            <s xml:id="echoid-s10321" xml:space="preserve">ſi ſumma quadratorum laterum _
              <emph style="sc">Ab, bc</emph>
            ,_
              <lb/>
            id eſt, _290._ </s>
            <s xml:id="echoid-s10322" xml:space="preserve">auferatur ex _400._ </s>
            <s xml:id="echoid-s10323" xml:space="preserve">quadrato lateris _
              <emph style="sc">Ac</emph>
            ,_ relinquetur rectangulum bis
              <lb/>
            comprehenſum ſub _
              <emph style="sc">CB, B</emph>
            D, 110._ </s>
            <s xml:id="echoid-s10324" xml:space="preserve">Semiſsis ergo huius, nimirum _55._ </s>
            <s xml:id="echoid-s10325" xml:space="preserve">erit rectangulum
              <lb/>
            ſub _
              <emph style="sc">CB, B</emph>
            D,_ contentum: </s>
            <s xml:id="echoid-s10326" xml:space="preserve">quo diuiſo per 11. </s>
            <s xml:id="echoid-s10327" xml:space="preserve">latus _
              <emph style="sc">BC</emph>
            ,_ prodibit recta _
              <emph style="sc">B</emph>
            D,_ extra
              <lb/>
            triangulum, _5._ </s>
            <s xml:id="echoid-s10328" xml:space="preserve">quæcum _11._ </s>
            <s xml:id="echoid-s10329" xml:space="preserve">latere _
              <emph style="sc">BC</emph>
            ,_ componet rectam _
              <emph style="sc">C</emph>
            D, 16._</s>
            <s xml:id="echoid-s10330" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10331" xml:space="preserve">ITAQVE, cadente perpendiculari intra triangulum; </s>
            <s xml:id="echoid-s10332" xml:space="preserve">Siſemiſſis
              <lb/>
              <note position="right" xlink:label="note-335-06" xlink:href="note-335-06a" xml:space="preserve">Praxis.</note>
            differentiæinter quadratum vtriusuis laterum ambientium angulum, à
              <lb/>
            quo perpendicularis demiſſa eſt, & </s>
            <s xml:id="echoid-s10333" xml:space="preserve">ſummam quadratorum ex reliquis
              <lb/>
            duobus lateribus deſcriptorum, diuidatur per latus, in quod perpendicu-
              <lb/>
            laris cadit, producetur ſegmentum baſis prope angulum, quem continent
              <lb/>
            latera, quorum ſumma quadratorum accepta fuit: </s>
            <s xml:id="echoid-s10334" xml:space="preserve">Hoc autem ſegmentum
              <lb/>
            ex eadem-baſe det ractum relinquet alterum ſegmentum.</s>
            <s xml:id="echoid-s10335" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10336" xml:space="preserve">CADENTE ver o perpendiculari extra triangulum; </s>
            <s xml:id="echoid-s10337" xml:space="preserve">Si ſe miſſis
              <lb/>
            diffcrentiæinter quadratum lateris angulo obtuſo oppoſiti, & </s>
            <s xml:id="echoid-s10338" xml:space="preserve"/>
          </p>
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