Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div761" type="section" level="1" n="260">
          <p>
            <s xml:id="echoid-s12208" xml:space="preserve">
              <pb o="265" file="295" n="295" rhead="LIBER SEXTVS."/>
            erit ſemiſsi trianguli ABC: </s>
            <s xml:id="echoid-s12209" xml:space="preserve">ac proinde quadrilaterum ABKI, reliquæ ſemiſsitri-
              <lb/>
            anguli ABC, æquale erit. </s>
            <s xml:id="echoid-s12210" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s12211" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12212" xml:space="preserve">
              <emph style="sc">Eadem</emph>
            ratione, ſi pro CG, ſumamus {1/3}. </s>
            <s xml:id="echoid-s12213" xml:space="preserve">vel {1/4}. </s>
            <s xml:id="echoid-s12214" xml:space="preserve">vel quamcumque partem
              <lb/>
            lateris AC, & </s>
            <s xml:id="echoid-s12215" xml:space="preserve">reliqua fiant, vt ſupra, auferemus perrectam ex D, ductam {1/3}. </s>
            <s xml:id="echoid-s12216" xml:space="preserve">vel
              <lb/>
            {1/4}. </s>
            <s xml:id="echoid-s12217" xml:space="preserve">vel deniq; </s>
            <s xml:id="echoid-s12218" xml:space="preserve">talẽ partem ex triangulo ABC, qualis ſumpta eſt C G, ipſius A C,
              <lb/>
            vt perſpicuum eſt.</s>
            <s xml:id="echoid-s12219" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12220" xml:space="preserve">
              <emph style="sc">Leonardvs</emph>
            Piſanus, & </s>
            <s xml:id="echoid-s12221" xml:space="preserve">Nicolaus Tartalea, idem hoc problema ſoluũt,
              <lb/>
            quando datum punctum eſt extra triangulum in tali loco, vt vnum latus trian-
              <lb/>
            guli pro ductum, in illud incidat, cuiuſmodi eſſet punctum F, datum. </s>
            <s xml:id="echoid-s12222" xml:space="preserve">Item
              <lb/>
            quando eſt inter duo latera producta: </s>
            <s xml:id="echoid-s12223" xml:space="preserve">Vt ſi triangulum foret AEC, punctũ au-
              <lb/>
            teminter B, & </s>
            <s xml:id="echoid-s12224" xml:space="preserve">D, exiſteret, ita vt ab eo ſolum per angulum E, duci poſſet linea
              <lb/>
            ſecans latus A C: </s>
            <s xml:id="echoid-s12225" xml:space="preserve">quippe cumrectæ ab eo ad angulos A, C, ductæ nullum latus
              <lb/>
            interſecarent. </s>
            <s xml:id="echoid-s12226" xml:space="preserve">Verum quia hęc curio ſa magis, quam vtilia ſunt, dedita opera à
              <lb/>
            nobis omittuntur. </s>
            <s xml:id="echoid-s12227" xml:space="preserve">Quiautem ea deſiderat, auctores prædictos legere pote-
              <lb/>
            rit. </s>
            <s xml:id="echoid-s12228" xml:space="preserve">Pariratione abſtinemus ab eo problemate, quando punctum datum eſt in-
              <lb/>
            tra triangulum (quod tamen ijdem auctores ſoluere conantur) quia non ſem-
              <lb/>
            per per punctum interius duci poteſt linea, quæ triangulũ bifariam ſecet, vt ex-
              <lb/>
            perientia conſtat.</s>
            <s xml:id="echoid-s12229" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div763" type="section" level="1" n="261">
          <head xml:id="echoid-head286" xml:space="preserve">PROBL. 8. PROPOS. 13.</head>
          <p>
            <s xml:id="echoid-s12230" xml:space="preserve">DATVM parallelogrammum in quotcunq; </s>
            <s xml:id="echoid-s12231" xml:space="preserve">partes æquales perlineas
              <lb/>
            duobus lateribus oppoſitis æquidiſtantes diuidere.</s>
            <s xml:id="echoid-s12232" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12233" xml:space="preserve">
              <emph style="sc">Sit</emph>
            parallelogrammum ABCD, diuidendum verbi gratia in tres partes æ-
              <lb/>
            quales per lineas lateribus AB, DC, æquidiſtantes. </s>
            <s xml:id="echoid-s12234" xml:space="preserve">Diuiſo
              <lb/>
              <figure xlink:label="fig-295-01" xlink:href="fig-295-01a" number="200">
                <image file="295-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/295-01"/>
              </figure>
            alterutro reliquorum duorum laterum, nimirum B C, in
              <lb/>
            tres partes æquales, in quot videlicet parallelogrammum
              <lb/>
            proponitur diuidendum, in E, & </s>
            <s xml:id="echoid-s12235" xml:space="preserve">F, punctis, ducantur EG,
              <lb/>
            FH, ipſis AB, DC, parallelæ: </s>
            <s xml:id="echoid-s12236" xml:space="preserve">factumque erit, quodiube-
              <lb/>
            tur; </s>
            <s xml:id="echoid-s12237" xml:space="preserve"> quod parallelogramma A E, E H, H C, ęqualia
              <note symbol="a" position="right" xlink:label="note-295-01" xlink:href="note-295-01a" xml:space="preserve">1. ſexti vel
                <lb/>
              38. primi.</note>
            propter æquales baſes BE, EF, FC.</s>
            <s xml:id="echoid-s12238" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div765" type="section" level="1" n="262">
          <head xml:id="echoid-head287" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s12239" xml:space="preserve">
              <emph style="sc">Itaqve</emph>
            ſi ex latere auferatur {1/2}. </s>
            <s xml:id="echoid-s12240" xml:space="preserve">vel {1/3}. </s>
            <s xml:id="echoid-s12241" xml:space="preserve">vel {3/4}. </s>
            <s xml:id="echoid-s12242" xml:space="preserve">vel denique qualiſcunque
              <lb/>
            pars, vel partes, & </s>
            <s xml:id="echoid-s12243" xml:space="preserve">per extremum eius punctum parallela lateri AB, ducatur, ab-
              <lb/>
            lata erit ex toto parallelo grammo eadem pars, vel eædem partes. </s>
            <s xml:id="echoid-s12244" xml:space="preserve">Ita vides A E,
              <lb/>
            eſſe partem tertiam parallelogrammi A C, quemadmodum & </s>
            <s xml:id="echoid-s12245" xml:space="preserve">B E, tertia pars eſt
              <lb/>
            lateris B C, &</s>
            <s xml:id="echoid-s12246" xml:space="preserve">c.</s>
            <s xml:id="echoid-s12247" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div766" type="section" level="1" n="263">
          <head xml:id="echoid-head288" xml:space="preserve">PROBL. 9. PROPOS. 14.</head>
          <p>
            <s xml:id="echoid-s12248" xml:space="preserve">DATVM parallelogrammum per rectam ex puncto ſiue extra, ſiue
              <lb/>
            intra ipſum, ſiue in aliquo latere dato ductam, bifariam diuidere.</s>
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