Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div418" type="section" level="1" n="172">
          <pb o="159" file="189" n="189" rhead="LIBER QVARTVS."/>
          <p>
            <s xml:id="echoid-s6208" xml:space="preserve">
              <emph style="sc">Hanc</emph>
            praxim, ſiueregulam, quæ exquiſitiſsima eſt, vt dixi, ita in triangu-
              <lb/>
              <handwritten xlink:label="hd-189-1" xlink:href="hd-189-1a" number="58"/>
            lo A B C, demonſtrabimus. </s>
            <s xml:id="echoid-s6209" xml:space="preserve">Diuiſis angulis A B C, A C B, bifariam per rectas
              <lb/>
            BD, CD, coeuntes in D, ducantur ex D, ad ſingula latera perpendiculares D E,
              <lb/>
            DF, DG, iungatur que recta AD. </s>
            <s xml:id="echoid-s6210" xml:space="preserve">Quoniamigitur duo anguli E, D B E, in trian-
              <lb/>
            gulo DEB, æquales ſunt duobus angulis G, D B G, in triangulo DGB, & </s>
            <s xml:id="echoid-s6211" xml:space="preserve">latus
              <lb/>
            DB; </s>
            <s xml:id="echoid-s6212" xml:space="preserve">commune; </s>
            <s xml:id="echoid-s6213" xml:space="preserve"> erunt tam latera DE, DG, quam BE, BG, æqualia. </s>
            <s xml:id="echoid-s6214" xml:space="preserve">Eodemq;</s>
            <s xml:id="echoid-s6215" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-189-01" xlink:href="note-189-01a" xml:space="preserve">26. primi.</note>
            modo tamlatera DF, DG, æqualia eruntin triangulis DFC, DGC: </s>
            <s xml:id="echoid-s6216" xml:space="preserve">acproinde
              <lb/>
            DE, DF, (cum vtraque ipſi D G, ſit oſtenſa æqualis) inter ſe æquales erunt: </s>
            <s xml:id="echoid-s6217" xml:space="preserve">ideo-
              <lb/>
            que omnes tres perpendiculares DE, DF, DG, æquales inter ſe erunt.</s>
            <s xml:id="echoid-s6218" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6219" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            quia quadrato ex AD, æqualia ſunt tam quadrata ex A E, E
              <note symbol="b" position="right" xlink:label="note-189-02" xlink:href="note-189-02a" xml:space="preserve">47. primi.</note>
            quam quadrata ex A F, F D; </s>
            <s xml:id="echoid-s6220" xml:space="preserve">æqualia erunt quadrata ex A E, E D, quadratis ex
              <lb/>
            AF, FD, Ac proinde ablatis æqualibus quadratis rectarum ED, FD, æqualium,
              <lb/>
            reliqua quadrata rectarum A E, A F, æqualia erunt: </s>
            <s xml:id="echoid-s6221" xml:space="preserve">proptereaque & </s>
            <s xml:id="echoid-s6222" xml:space="preserve">rectæ
              <lb/>
              <figure xlink:label="fig-189-01" xlink:href="fig-189-01a" number="120">
                <image file="189-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/189-01"/>
              </figure>
            ipſæ A E, A F, æquales erunt. </s>
            <s xml:id="echoid-s6223" xml:space="preserve">Igitur cum latera A E,
              <lb/>
            @A D, trianguli A D E, lateribus A F, A D, trianguli
              <lb/>
            A D F, æqualia ſint, & </s>
            <s xml:id="echoid-s6224" xml:space="preserve">baſis E D, baſi F D; </s>
            <s xml:id="echoid-s6225" xml:space="preserve"> erit
              <note symbol="c" position="right" xlink:label="note-189-03" xlink:href="note-189-03a" xml:space="preserve">8. primi.</note>
            gulus D A E, angulo D A F, æqualis.</s>
            <s xml:id="echoid-s6226" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6227" xml:space="preserve">
              <emph style="sc">Qvia</emph>
            verò A E, ipſi A F, & </s>
            <s xml:id="echoid-s6228" xml:space="preserve">E B, ipſi B G, ęqua-
              <lb/>
            lis eſt oſtenſa, erit tota A B, duabus A F, B G, ęqua-
              <lb/>
            lis: </s>
            <s xml:id="echoid-s6229" xml:space="preserve">additiſque æqualibus C G, C F, duę A B, C G,
              <lb/>
            duabus A C, B G, æquales erunt. </s>
            <s xml:id="echoid-s6230" xml:space="preserve">Tam ergo duę A B,
              <lb/>
            C G, quam duæ A C, B G, ſemiſſem trium laterum
              <lb/>
            A B, B C, A C, conſtituent. </s>
            <s xml:id="echoid-s6231" xml:space="preserve">Quocirca C G, vel C F,
              <lb/>
            diifferentia erit inter ſemiſſem laterum, & </s>
            <s xml:id="echoid-s6232" xml:space="preserve">latus A B. </s>
            <s xml:id="echoid-s6233" xml:space="preserve">Item B G, vel BE, differen-
              <lb/>
            tia inter eandem ſemiſſem, & </s>
            <s xml:id="echoid-s6234" xml:space="preserve">latus A C. </s>
            <s xml:id="echoid-s6235" xml:space="preserve">Denique cum A B, C G, ſemiſſem late-
              <lb/>
            rum efficiant, ſitque B G, ipſi B E, æqualis, vt oſtendimus, conſtituent quo que
              <lb/>
            B C, A E, ſemiſſem eorundem laterum: </s>
            <s xml:id="echoid-s6236" xml:space="preserve">ideo que A E, differentia erit inter late-
              <lb/>
            rum ſemiſſem, & </s>
            <s xml:id="echoid-s6237" xml:space="preserve">latus B C. </s>
            <s xml:id="echoid-s6238" xml:space="preserve">Tres ergo rectę A E, E B, C G, & </s>
            <s xml:id="echoid-s6239" xml:space="preserve">ſemiſſem late-
              <lb/>
            rum conſtituunt, & </s>
            <s xml:id="echoid-s6240" xml:space="preserve">tres differentias inter ſemiſſem laterum, & </s>
            <s xml:id="echoid-s6241" xml:space="preserve">tria latera trian-
              <lb/>
            guli.</s>
            <s xml:id="echoid-s6242" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6243" xml:space="preserve">
              <emph style="sc">Prodvctis</emph>
            iam A B, A C, ſit B H, ipſi C G, & </s>
            <s xml:id="echoid-s6244" xml:space="preserve">C I, ipſi B G, æqualis; </s>
            <s xml:id="echoid-s6245" xml:space="preserve">ita vt
              <lb/>
            tam A H, ſemiſsi laterum, rectis videlicet A B, C G, quam A I, eidem ſemiſsi late-
              <lb/>
            rum, rectis nimirum A C, B G, ſit ęqu
              <gap/>
            , conſtet que ex tribus differentiis an-
              <lb/>
            te dictis. </s>
            <s xml:id="echoid-s6246" xml:space="preserve">Ducta quo que H K, ad A H, perpendiculari, quę cum A D, producta
              <lb/>
            conueniat in K; </s>
            <s xml:id="echoid-s6247" xml:space="preserve">connectantur rectę K I, K B, K C. </s>
            <s xml:id="echoid-s6248" xml:space="preserve">Et quia duo latera A H, A K,
              <lb/>
            trianguli AHK, duobus lateribus AI, AK, trianguli AIK, ęqualia ſunt, anguloſ-
              <lb/>
            que ad A, continent ęquales, vt ſupra oſtendimus, æquales quo que erunt &</s>
            <s xml:id="echoid-s6249" xml:space="preserve">
              <note symbol="d" position="right" xlink:label="note-189-04" xlink:href="note-189-04a" xml:space="preserve">4. primi.</note>
            baſes HK, IK, & </s>
            <s xml:id="echoid-s6250" xml:space="preserve">anguli H, I. </s>
            <s xml:id="echoid-s6251" xml:space="preserve">Cum ergo H, per conſtructionem ſit rectus, rectus
              <lb/>
            etiam erit I.</s>
            <s xml:id="echoid-s6252" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6253" xml:space="preserve">
              <emph style="sc">Abscindatvr</emph>
            pręterea BL, ipſi C G, vel B H, æqualis, vt proinde reli-
              <lb/>
            qua C L@ reliquę B G, vel ipſi C I, æqualis ſit, iungaturq; </s>
            <s xml:id="echoid-s6254" xml:space="preserve">recta KL. </s>
            <s xml:id="echoid-s6255" xml:space="preserve">Producta au-
              <lb/>
            tem B H, ſumatur H M, ipſi C I, æqualis, connectatur querecta L M. </s>
            <s xml:id="echoid-s6256" xml:space="preserve">Et quia duo
              <lb/>
            latera KH, HM, trianguli HMK, duobus later bus KI, IC, trianguli CIK, æqua-
              <lb/>
            lia ſunt, angulo ſque H, I, continent ęquales, vt pote rectos: </s>
            <s xml:id="echoid-s6257" xml:space="preserve"> erunt quo que
              <note symbol="e" position="right" xlink:label="note-189-05" xlink:href="note-189-05a" xml:space="preserve">8. primi.</note>
            ſes K M, K C, ęquales: </s>
            <s xml:id="echoid-s6258" xml:space="preserve">at que adeò cum duo latera BM, BK, trianguli BMK, duo-
              <lb/>
            bus lateribus B C, B K, trianguli B C K, ęqualia ſint, (eſt nam que B M, ipſi B C,
              <lb/>
            æqualis, quod partes B H, H M, partibus B L, L C, ſint æquales) ſit que </s>
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