Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div860" type="section" level="1" n="299">
          <p>
            <s xml:id="echoid-s14076" xml:space="preserve">
              <pb o="298" file="328" n="328" rhead="GEOMETR. PRACT."/>
            angulum ADC, maius eſſe triangulo ABC. </s>
            <s xml:id="echoid-s14077" xml:space="preserve">Producatur enim AD, ad partes D,
              <lb/>
              <figure xlink:label="fig-328-01" xlink:href="fig-328-01a" number="220">
                <image file="328-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/328-01"/>
              </figure>
            ſitque D E, æqualis ipſi A D, ſiue ipſi D C. </s>
            <s xml:id="echoid-s14078" xml:space="preserve">Ducantur
              <lb/>
              <note symbol="a" position="left" xlink:label="note-328-01" xlink:href="note-328-01a" xml:space="preserve">20. primi.</note>
            quoque rectæ DB, BE. </s>
            <s xml:id="echoid-s14079" xml:space="preserve"> Quoniam igitur AB, BE, ma- iores ſunt, quam A E, hoc eſt, quam A D, D C, ſimul,
              <lb/>
            hoc eſt, quam A B, B C, ſimul; </s>
            <s xml:id="echoid-s14080" xml:space="preserve">ablata communi A B,
              <lb/>
            erit B E, maior quam B C. </s>
            <s xml:id="echoid-s14081" xml:space="preserve">Et quia latera E D, D B, tri-
              <lb/>
            anguli EDB, æqualia ſunt lateribus CD, DB, trianguli
              <lb/>
            CDB. </s>
            <s xml:id="echoid-s14082" xml:space="preserve">At verò baſis BE, baſe BC, maior, erit
              <note symbol="b" position="left" xlink:label="note-328-02" xlink:href="note-328-02a" xml:space="preserve">25. primi.</note>
            EDB, maior angulo C D B. </s>
            <s xml:id="echoid-s14083" xml:space="preserve">Quare angulus EDB,
              <lb/>
            maior eſt, quam dimidium anguli EDC: </s>
            <s xml:id="echoid-s14084" xml:space="preserve">Eſt autem an-
              <lb/>
            gulus DAC, dimidium anguli EDC; </s>
            <s xml:id="echoid-s14085" xml:space="preserve"> propterea
              <note symbol="c" position="left" xlink:label="note-328-03" xlink:href="note-328-03a" xml:space="preserve">5. primi.</note>
            anguli DAC, DCA, æquales ſunt, & </s>
            <s xml:id="echoid-s14086" xml:space="preserve">his ſimul
              <note symbol="d" position="left" xlink:label="note-328-04" xlink:href="note-328-04a" xml:space="preserve">32. primi.</note>
            ptis ęqualis quo que externus angulus E D C. </s>
            <s xml:id="echoid-s14087" xml:space="preserve">Maior
              <lb/>
            igitur erit angulus EDB, angulo DAC. </s>
            <s xml:id="echoid-s14088" xml:space="preserve"> Fiat angulus EDF, ęqualis angulo
              <note symbol="e" position="left" xlink:label="note-328-05" xlink:href="note-328-05a" xml:space="preserve">23. primi.</note>
            terno DAC; </s>
            <s xml:id="echoid-s14089" xml:space="preserve">cadetque DF, recta ſupra rectam DB, æquidiſtabit que rectæ A C.</s>
            <s xml:id="echoid-s14090" xml:space="preserve">
              <note symbol="f" position="left" xlink:label="note-328-06" xlink:href="note-328-06a" xml:space="preserve">28. primi.</note>
            Producatur DF, donec cum AB, protracta conueniat in F, ducaturq; </s>
            <s xml:id="echoid-s14091" xml:space="preserve">recta F C.
              <lb/>
            </s>
            <s xml:id="echoid-s14092" xml:space="preserve"> Quoniam igitur triangula ADC, AFC, æqualia ſunt, triangulum autem
              <note symbol="g" position="left" xlink:label="note-328-07" xlink:href="note-328-07a" xml:space="preserve">37. primi.</note>
            maius eſt triangulo ABC; </s>
            <s xml:id="echoid-s14093" xml:space="preserve">maius quoque erit triangulum ADC, triangulo ABC.
              <lb/>
            </s>
            <s xml:id="echoid-s14094" xml:space="preserve">Quam ob rem duorum triangulorum Iſoperimetrorum eandem habentium
              <lb/>
            baſim, &</s>
            <s xml:id="echoid-s14095" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14096" xml:space="preserve">quod demonſtrandum erat.</s>
            <s xml:id="echoid-s14097" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div862" type="section" level="1" n="300">
          <head xml:id="echoid-head327" xml:space="preserve">THEOR. 8. PROPOS. 9.</head>
          <note position="left" xml:space="preserve">Proprietas
            <lb/>
          duorum tri-
            <lb/>
          angulorum
            <lb/>
          rectangulorũ
            <lb/>
          ſimilium.</note>
          <p>
            <s xml:id="echoid-s14098" xml:space="preserve">IN ſimilibus triangulis rectangulis quadratum à lateribus, quæ angulis
              <lb/>
            rectis ſubtenduntur, tanquam ab vna linea, deſcriptum, æquale eſt
              <lb/>
            quadratis duobus ſimul, quæ à reliquis homologis lateribus tanquam
              <lb/>
            ex duabus lineis, ita vt quælibet duo latera homologa conficiant vnã
              <lb/>
            lineam rectam, deſcribuntur.</s>
            <s xml:id="echoid-s14099" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14100" xml:space="preserve">
              <emph style="sc">Sint</emph>
            triangula rectangula ſimilia ABC, DEF, ita vt anguli B, & </s>
            <s xml:id="echoid-s14101" xml:space="preserve">E, ſint
              <lb/>
              <figure xlink:label="fig-328-02" xlink:href="fig-328-02a" number="221">
                <image file="328-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/328-02"/>
              </figure>
            recti, anguli verò C, & </s>
            <s xml:id="echoid-s14102" xml:space="preserve">F, inter ſe æquales; </s>
            <s xml:id="echoid-s14103" xml:space="preserve">itemque
              <lb/>
            anguli A, & </s>
            <s xml:id="echoid-s14104" xml:space="preserve">D, inter ſe æquales; </s>
            <s xml:id="echoid-s14105" xml:space="preserve">homologaque late-
              <lb/>
            ra AB, DE; </s>
            <s xml:id="echoid-s14106" xml:space="preserve">Item BC, EF, & </s>
            <s xml:id="echoid-s14107" xml:space="preserve">AC, DF. </s>
            <s xml:id="echoid-s14108" xml:space="preserve">Dico quadratũ
              <lb/>
            ex AC, DF, tanquam ex linea vna, deſcriptum, æqua-
              <lb/>
            le eſſe duobus quadratis, quorumvnum ex AB, DE,
              <lb/>
            tanquam exvna linea, alterum verò ex BC, EF, tan-
              <lb/>
            quam exvna quoque linea, deſcribitur. </s>
            <s xml:id="echoid-s14109" xml:space="preserve">Producta
              <lb/>
            namque DE, ad partes E, ſumatur E G, æqualis rectæ
              <lb/>
            A B, & </s>
            <s xml:id="echoid-s14110" xml:space="preserve">ducatur G H, recta æquidiſtans rectæ E F, do-
              <lb/>
            nec cum DF, producta conueniat in puncto H; </s>
            <s xml:id="echoid-s14111" xml:space="preserve">Dein-
              <lb/>
            de per F, ducatur recta F I, æquidiſtans rectæ EG. </s>
            <s xml:id="echoid-s14112" xml:space="preserve">Erit
              <lb/>
            igitur triangulum FIH, æquiangulum triangulo DEF,
              <lb/>
            hoc eſt, triangulo ABC. </s>
            <s xml:id="echoid-s14113" xml:space="preserve"> Nam angulus FIH,
              <note symbol="h" position="left" xlink:label="note-328-09" xlink:href="note-328-09a" xml:space="preserve">29. primi.</note>
            lis eſt angulo G, & </s>
            <s xml:id="echoid-s14114" xml:space="preserve">hic æqualis angulo D E F,
              <note symbol="i" position="left" xlink:label="note-328-10" xlink:href="note-328-10a" xml:space="preserve">29. primi.</note>
            eſt, angulo B; </s>
            <s xml:id="echoid-s14115" xml:space="preserve">angulus verò H, æqualis eſt </s>
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