Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s11747" xml:space="preserve">
              <pb o="255" file="285" n="285" rhead="LIBER SEXTVS."/>
            uiſo enim quo cunque latere, nimirum B C, in I, ſecundum datam proportio-
              <lb/>
            nem D, ad E, iunctaque recta AI, erit triangulum ABI, ad triangulum AIC,
              <note symbol="a" position="right" xlink:label="note-285-01" xlink:href="note-285-01a" xml:space="preserve">1. ſexti.</note>
            BI, ad IC, id eſt, vt D, ad E. </s>
            <s xml:id="echoid-s11748" xml:space="preserve"> Siigitur ſuper B C, inter rectas BA, CA,
              <note symbol="b" position="right" xlink:label="note-285-02" xlink:href="note-285-02a" xml:space="preserve">2. hui{us}.</note>
            tur trapezium BL, per parallelam LM, æquale triangulo ABI, quod eſt antece-
              <lb/>
            dens: </s>
            <s xml:id="echoid-s11749" xml:space="preserve">erit reliquum triangulum ALM, reliquo triangulo AIC, æquale. </s>
            <s xml:id="echoid-s11750" xml:space="preserve">
              <note symbol="c" position="right" xlink:label="note-285-03" xlink:href="note-285-03a" xml:space="preserve">7. quinti.</note>
            re erit trapezium BL, ad triangulum A L M, vt triangulum ABI, ad triangulum
              <lb/>
            AIC, hoc eſt, vt BI, ad IC, vel vt D, ad E.</s>
            <s xml:id="echoid-s11751" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11752" xml:space="preserve">
              <emph style="sc">Sed</emph>
            diuidendum iam ſit triangulum ABC, in datam proportionem D, ad E,
              <lb/>
            per lineam parallelam cuicunque lineæ F: </s>
            <s xml:id="echoid-s11753" xml:space="preserve">quæ ſi æquidiſtet vni laterum, par-
              <lb/>
            tiemur triangulum in datam proportionem, per rectam illi lateri parallelam,
              <lb/>
              <figure xlink:label="fig-285-01" xlink:href="fig-285-01a" number="189">
                <image file="285-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/285-01"/>
              </figure>
            vt iam tradidimus, ſiue antecedens vergere debeat ad angulum lateri illi oppo-
              <lb/>
              <note symbol="d" position="right" xlink:label="note-285-04" xlink:href="note-285-04a" xml:space="preserve">30. primi.</note>
            ſitum, ſiue ad ipſummet latus: </s>
            <s xml:id="echoid-s11754" xml:space="preserve">factumque erit, quod iubetur; </s>
            <s xml:id="echoid-s11755" xml:space="preserve"> cum parallela illa æquidiſtet etiam datæ rectæ lineæ.</s>
            <s xml:id="echoid-s11756" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11757" xml:space="preserve">
              <emph style="sc">Si</emph>
            verò data recta F, nulli laterum æquidiſtet, ducatur illi ex aliquo angulo
              <lb/>
            parallela intra triangulum cadens, qualis eſt B G. </s>
            <s xml:id="echoid-s11758" xml:space="preserve">Si igitur antecedens propor-
              <lb/>
            tionis ſtatuendum ſit ad partes A, ſecabimus latus A C, in H, in datam propor-
              <lb/>
            tionem D, ad E. </s>
            <s xml:id="echoid-s11759" xml:space="preserve">Cadat autem primo punctum H, inter G, & </s>
            <s xml:id="echoid-s11760" xml:space="preserve">C; </s>
            <s xml:id="echoid-s11761" xml:space="preserve">inueniatur-
              <lb/>
            que inter GC, & </s>
            <s xml:id="echoid-s11762" xml:space="preserve">eius partem CH, terminatam in angulo C, parallelæ BG, oppo-
              <lb/>
            ſito media proportionalis C I; </s>
            <s xml:id="echoid-s11763" xml:space="preserve">& </s>
            <s xml:id="echoid-s11764" xml:space="preserve">per I, ipſi B G, vel ipſi F, parallela agatur I K;
              <lb/>
            </s>
            <s xml:id="echoid-s11765" xml:space="preserve">quam dico, problema efficere: </s>
            <s xml:id="echoid-s11766" xml:space="preserve">hoc eſt, eſſe trapezium A B K I, ad triangulum
              <lb/>
            IKC, vt D, ad E. </s>
            <s xml:id="echoid-s11767" xml:space="preserve"> Quoniam enim eſt (ducta recta B H,) vt triangulum GBC,
              <note symbol="e" position="right" xlink:label="note-285-05" xlink:href="note-285-05a" xml:space="preserve">coroll. 19.
                <lb/>
              ſexti.</note>
            triangulum IKC, ita GC, ad CH; </s>
            <s xml:id="echoid-s11768" xml:space="preserve">quod tres GC, CI, CH, ſint continuè pro-
              <lb/>
            portionales, & </s>
            <s xml:id="echoid-s11769" xml:space="preserve">triangula ſimilia ſimiliter que poſita: </s>
            <s xml:id="echoid-s11770" xml:space="preserve"> Vt autem GC, ad CH,
              <note symbol="f" position="right" xlink:label="note-285-06" xlink:href="note-285-06a" xml:space="preserve">1. ſexti.</note>
            eſt quo que triangulum G B C, ad triangulum H B C; </s>
            <s xml:id="echoid-s11771" xml:space="preserve"> erunt triangula I K
              <note symbol="g" position="right" xlink:label="note-285-07" xlink:href="note-285-07a" xml:space="preserve">9. quinti.</note>
            HBC, æqualia: </s>
            <s xml:id="echoid-s11772" xml:space="preserve">Ac proinde & </s>
            <s xml:id="echoid-s11773" xml:space="preserve">reliquum trapezium A B K I, reliquo triangulo
              <lb/>
            ABH, æquale erit. </s>
            <s xml:id="echoid-s11774" xml:space="preserve"> Igitur erit vt trapezium ABKI, ad triangulum ICK, ita
              <note symbol="h" position="right" xlink:label="note-285-08" xlink:href="note-285-08a" xml:space="preserve">7. quinti.</note>
            gulum ABH, ad triangulum HBC: </s>
            <s xml:id="echoid-s11775" xml:space="preserve">hoc eſt, ita AH, ad HC, velita D, ad E. </s>
            <s xml:id="echoid-s11776" xml:space="preserve">quod
              <lb/>
            eſt propoſitum.</s>
            <s xml:id="echoid-s11777" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11778" xml:space="preserve">
              <emph style="sc">Cadat</emph>
            deinde punctum L, (Ponimus iam datam proportionem E, ad D,
              <lb/>
            diuiſamque eſſe A C, in L, ſecundum datam proportionem) inter A, & </s>
            <s xml:id="echoid-s11779" xml:space="preserve">G. </s>
            <s xml:id="echoid-s11780" xml:space="preserve">In-
              <lb/>
            uenta ergo inter G A, & </s>
            <s xml:id="echoid-s11781" xml:space="preserve">eius partem AL, terminatã in angulo A, parallelæ B G,
              <lb/>
            oppoſito, media proportionali AM, agatur per M, ipſi GB, ideo que & </s>
            <s xml:id="echoid-s11782" xml:space="preserve">ipſi F, pa-
              <lb/>
            rallela MN: </s>
            <s xml:id="echoid-s11783" xml:space="preserve">quam dico problema efficere, hoc eſt, eſſe triangulum A M N, ad
              <lb/>
            trapezium M N B C, vt E, ad D. </s>
            <s xml:id="echoid-s11784" xml:space="preserve">Iuncta namque recta B L, quoniam eſt,
              <note symbol="i" position="right" xlink:label="note-285-09" xlink:href="note-285-09a" xml:space="preserve">coroll. 19.
                <lb/>
              ſexti.</note>
            triangulum A B G, ad triangulum A M N, ita AG, ad AL: </s>
            <s xml:id="echoid-s11785" xml:space="preserve">quod tres AG, AM,
              <lb/>
            AL, continuè proportionales ſint, & </s>
            <s xml:id="echoid-s11786" xml:space="preserve">triangula ſimilia ſimiliter que poſita: </s>
            <s xml:id="echoid-s11787" xml:space="preserve">
              <note symbol="k" position="right" xlink:label="note-285-10" xlink:href="note-285-10a" xml:space="preserve">1. ſexti.</note>
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