Clavius, Christoph, Geometria practica

Table of figures

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[Figure 292]
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        <div xml:id="echoid-div748" type="section" level="1" n="255">
          <pb o="262" file="292" n="292" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s12064" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            quia eſt, vt AB, ad AD, ita CF, ad FD: </s>
            <s xml:id="echoid-s12065" xml:space="preserve">Eſt autem AB, ipſius
              <note symbol="a" position="left" xlink:label="note-292-01" xlink:href="note-292-01a" xml:space="preserve">7. hui{us}.</note>
            dupla; </s>
            <s xml:id="echoid-s12066" xml:space="preserve">erit quo que CF, ipſius FD, dupla. </s>
            <s xml:id="echoid-s12067" xml:space="preserve">Eademqueratione & </s>
            <s xml:id="echoid-s12068" xml:space="preserve">BF, ipſius FE;
              <lb/>
            </s>
            <s xml:id="echoid-s12069" xml:space="preserve">& </s>
            <s xml:id="echoid-s12070" xml:space="preserve">AF, ipſius FH, dupla erit. </s>
            <s xml:id="echoid-s12071" xml:space="preserve">quod eſt ſecundum.</s>
            <s xml:id="echoid-s12072" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12073" xml:space="preserve">
              <emph style="sc">Postremo</emph>
            quia eſt vt AF, ad FH, ita triangulum A F B, ad
              <note symbol="b" position="left" xlink:label="note-292-02" xlink:href="note-292-02a" xml:space="preserve">1. ſexti.</note>
            BFH: </s>
            <s xml:id="echoid-s12074" xml:space="preserve">Eſt autem AF, ipſius F H, oſtenſa dupla; </s>
            <s xml:id="echoid-s12075" xml:space="preserve">erit quoque triangulum A F B,
              <lb/>
            trianguli B F H, duplum. </s>
            <s xml:id="echoid-s12076" xml:space="preserve">Eſt autem & </s>
            <s xml:id="echoid-s12077" xml:space="preserve">triangulum B F C, eiuſdem trianguli B-
              <lb/>
              <note symbol="c" position="left" xlink:label="note-292-03" xlink:href="note-292-03a" xml:space="preserve">38. primi.</note>
            FH, duplum; </s>
            <s xml:id="echoid-s12078" xml:space="preserve"> quod triangula B F H, C F H, æqualia ſint. </s>
            <s xml:id="echoid-s12079" xml:space="preserve">Igitur æqualia erunt triangula AFB, BFC. </s>
            <s xml:id="echoid-s12080" xml:space="preserve">Eodemq; </s>
            <s xml:id="echoid-s12081" xml:space="preserve">modo triangulum AFC, eidem triangulo BFC,
              <lb/>
            æquale erit: </s>
            <s xml:id="echoid-s12082" xml:space="preserve">ac proinde omnia tria AFB, BFC, CFA, æqualia erunt. </s>
            <s xml:id="echoid-s12083" xml:space="preserve">quod eſt
              <lb/>
            tertium.</s>
            <s xml:id="echoid-s12084" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div752" type="section" level="1" n="256">
          <head xml:id="echoid-head281" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s12085" xml:space="preserve">
              <emph style="sc">Itaqve</emph>
            facilè inueniri poteſt punctum intra triangulum, à quo tres rectæ
              <lb/>
            ad tres angulos ductæ ipſum triungulum in tria æqualia triangula partiantur.
              <lb/>
            </s>
            <s xml:id="echoid-s12086" xml:space="preserve">Huiuſmodi enim punctum in propoſito triangulo eſt F, vbi duæ rectæ ex duo-
              <lb/>
            bus quibuſuis angulis ad media puncta oppoſitorum laterum ductæ ſe interſe-
              <lb/>
            cant, vt in tertia parte huius propoſ. </s>
            <s xml:id="echoid-s12087" xml:space="preserve">oſtendimus.</s>
            <s xml:id="echoid-s12088" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div753" type="section" level="1" n="257">
          <head xml:id="echoid-head282" xml:space="preserve">THEOR. 5. PROPOS. 9.</head>
          <p>
            <s xml:id="echoid-s12089" xml:space="preserve">SI in triangulo ducatur recta vtcunque duo latera ſecans: </s>
            <s xml:id="echoid-s12090" xml:space="preserve">Erit totum
              <lb/>
            triangulum ad abſciſſum triangulum, vt rectangulum ſub duobus la-
              <lb/>
            teribus ſectis totius trianguli comprehenſum, ad rectangulum ſub
              <lb/>
            duobus lateribus trianguli abſciſſi, quæ priorum ſegmenta ſunt, com-
              <lb/>
            prehenſum.</s>
            <s xml:id="echoid-s12091" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12092" xml:space="preserve">
              <emph style="sc">In</emph>
            triangulo ABC, recta D E, ſecet latera A B, A C, in D, E. </s>
            <s xml:id="echoid-s12093" xml:space="preserve">Dico eſſe vt re-
              <lb/>
            ctangulum ſub AB, AC, adrectangulum ſub AD, AE, ita tri-
              <lb/>
            angulum ABC, ad triangulum ADE. </s>
            <s xml:id="echoid-s12094" xml:space="preserve">Quoniam enim triangu-
              <lb/>
              <figure xlink:label="fig-292-01" xlink:href="fig-292-01a" number="196">
                <image file="292-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/292-01"/>
              </figure>
            la ABC, ADE, angulum habent communem A; </s>
            <s xml:id="echoid-s12095" xml:space="preserve">habebunt per
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s12096" xml:space="preserve">4. </s>
            <s xml:id="echoid-s12097" xml:space="preserve">ſchol. </s>
            <s xml:id="echoid-s12098" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s12099" xml:space="preserve">23. </s>
            <s xml:id="echoid-s12100" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12101" xml:space="preserve">6. </s>
            <s xml:id="echoid-s12102" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s12103" xml:space="preserve">eandem propor-
              <lb/>
            tionem, quamrectangula ſub lateribus AB, A C, & </s>
            <s xml:id="echoid-s12104" xml:space="preserve">ſub A D,
              <lb/>
            AE, comprehenſa. </s>
            <s xml:id="echoid-s12105" xml:space="preserve">quod oſtendendum erat.</s>
            <s xml:id="echoid-s12106" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div755" type="section" level="1" n="258">
          <head xml:id="echoid-head283" xml:space="preserve">PROBL. 5. PROPOS. 10.</head>
          <p>
            <s xml:id="echoid-s12107" xml:space="preserve">DATVM triangulum ex dato puncto in eius latere in quotlibet par-
              <lb/>
            tes æquales diuidere.</s>
            <s xml:id="echoid-s12108" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12109" xml:space="preserve">
              <emph style="sc">Propositione</emph>
            quartadecima ſcholij propoſ 33. </s>
            <s xml:id="echoid-s12110" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12111" xml:space="preserve">6. </s>
            <s xml:id="echoid-s12112" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s12113" xml:space="preserve">tradidi-
              <lb/>
            mus regulam, qua triangulum in duas partes ſecundum datam proportionem
              <lb/>
            diuidendum ſit: </s>
            <s xml:id="echoid-s12114" xml:space="preserve">Etquo pacto ex triangulo pars imperata ſit auferenda. </s>
            <s xml:id="echoid-s12115" xml:space="preserve">Si igi-
              <lb/>
            tur triangulum ex dato puncto in eius latere quouis ſecandum ſit in </s>
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