Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s16555" xml:space="preserve">
              <pb o="354" file="382" n="382" rhead="GEOMETR. PRACT."/>
            maiora ſuntlatere AC; </s>
            <s xml:id="echoid-s16556" xml:space="preserve">erit reliqua CD, minor latere BC; </s>
            <s xml:id="echoid-s16557" xml:space="preserve">ac proinde duo qua-
              <lb/>
            drata AD, DC, minora duobus quadratis AB, BC. </s>
            <s xml:id="echoid-s16558" xml:space="preserve">Eſt autem quadratum AC,
              <lb/>
            minus duplo quadratorum AD, DC: </s>
            <s xml:id="echoid-s16559" xml:space="preserve"> propterea quod æquale eſt
              <note symbol="a" position="left" xlink:label="note-382-01" xlink:href="note-382-01a" xml:space="preserve">4. ſecundi.</note>
            quadratis AD, DC, vna cum rectangulo bis ſub AD, DC; </s>
            <s xml:id="echoid-s16560" xml:space="preserve">quod quidem rectan-
              <lb/>
            gulum bis, minus eſt duobus quadratis AD, DC, ex Lemmate propoſ. </s>
            <s xml:id="echoid-s16561" xml:space="preserve">39. </s>
            <s xml:id="echoid-s16562" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s16563" xml:space="preserve">10. </s>
            <s xml:id="echoid-s16564" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s16565" xml:space="preserve">Multo ergo minus erit quadratum AC, duplo quadratorum AB, BC. </s>
            <s xml:id="echoid-s16566" xml:space="preserve">
              <lb/>
            quod erat demonſtrandum.</s>
            <s xml:id="echoid-s16567" xml:space="preserve"/>
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        <div xml:id="echoid-div1020" type="section" level="1" n="366">
          <head xml:id="echoid-head393" xml:space="preserve">PROBL. 13. PROPOS. 22.</head>
          <p>
            <s xml:id="echoid-s16568" xml:space="preserve">DATIS tribus rectis vtcunque in plano non parallelis, niſi quando ex-
              <lb/>
            tremæ à media æqualiter diſtant, rectam lineam ducere, & </s>
            <s xml:id="echoid-s16569" xml:space="preserve">quidem
              <lb/>
            per datum punctum in media, ſi omnes tres in vno puncto conue-
              <lb/>
            niant; </s>
            <s xml:id="echoid-s16570" xml:space="preserve">ita vt eius ſegmenta inter mediam, & </s>
            <s xml:id="echoid-s16571" xml:space="preserve">extremas ſint inter ſe æ-
              <lb/>
            qualia, vel datam habeant proportionem.</s>
            <s xml:id="echoid-s16572" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s16573" xml:space="preserve">
              <emph style="sc">Sint</emph>
            tres rectæ AB, CD, EF. </s>
            <s xml:id="echoid-s16574" xml:space="preserve">Ducatur vt cunque recta BF, ſecans omnes
              <lb/>
            tres. </s>
            <s xml:id="echoid-s16575" xml:space="preserve">qua ſecta bifariamin G, ſi quidem punctum G, cadet in mediam, factum
              <lb/>
            erit, quodiubetur. </s>
            <s xml:id="echoid-s16576" xml:space="preserve">Si verò G, cadet extra lineam mediam CD, agatur per G,
              <lb/>
            alteri extremarum, nimirum ipſi EF, (dummodo einon æquidiſtet media CD)
              <lb/>
            parallela AG, ſecans mediam in C. </s>
            <s xml:id="echoid-s16577" xml:space="preserve">Cum
              <lb/>
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                <image file="382-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/382-01"/>
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            enim CD, ponatur non æquidiſtareipſi
              <lb/>
            EF, ſecabit vtique productam EF, & </s>
            <s xml:id="echoid-s16578" xml:space="preserve">pro-
              <lb/>
            inde eius quoque parallelam AG. </s>
            <s xml:id="echoid-s16579" xml:space="preserve">Quod
              <lb/>
            ſi CD, ipſi EF, æquidiſtaret, ducenda eſſet
              <lb/>
            per G, ipſi AB, parallela. </s>
            <s xml:id="echoid-s16580" xml:space="preserve">Poſtremò ex B,
              <lb/>
            puncto ductæ rectæ BF, ſumpto in extre-
              <lb/>
            ma AB, cui non æquidiſtat AG, ducatur
              <lb/>
            per C, vbi parallela AG, mediam CD, ſe-
              <lb/>
            cat, recta BC, ſecans EF, in E. </s>
            <s xml:id="echoid-s16581" xml:space="preserve">Dico re-
              <lb/>
            ctas BC, CE, æquales eſſe. </s>
            <s xml:id="echoid-s16582" xml:space="preserve">Cum enim in
              <lb/>
            triangulo BEF, recta CG, ſit baſi EF, parallela: </s>
            <s xml:id="echoid-s16583" xml:space="preserve"> erit vt BG, ad GF, ita BC,
              <note symbol="b" position="left" xlink:label="note-382-02" xlink:href="note-382-02a" xml:space="preserve">2. ſexti.</note>
            ad CE; </s>
            <s xml:id="echoid-s16584" xml:space="preserve">Sed BG, ipſi GF, per conſtructionem, æqualis eſt. </s>
            <s xml:id="echoid-s16585" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s16586" xml:space="preserve">BC, ipſi CE,
              <lb/>
            æqualis erit.</s>
            <s xml:id="echoid-s16587" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s16588" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi per G, agatur ipſi AB, parallela GI, ſecans mediam CD, in I; </s>
            <s xml:id="echoid-s16589" xml:space="preserve">erit
              <lb/>
            ducta FIK, ſecta quoque bifariam in I: </s>
            <s xml:id="echoid-s16590" xml:space="preserve">propterea quod in triangulo FBK, recta
              <lb/>
            GI, baſi BK, æquidiſtat; </s>
            <s xml:id="echoid-s16591" xml:space="preserve"> ideoque ſicut BF, in G, diuiſa eſt bifariam, ita
              <note symbol="c" position="left" xlink:label="note-382-03" xlink:href="note-382-03a" xml:space="preserve">2. ſexti.</note>
            que FK, in I, bifariam ſecabitur.</s>
            <s xml:id="echoid-s16592" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s16593" xml:space="preserve">
              <emph style="sc">Ex</emph>
            his patet, cur media linea non debeat vtrique extremæ æquidiſtare, ſed
              <lb/>
            vel neutri, vel alteri tantum. </s>
            <s xml:id="echoid-s16594" xml:space="preserve">Nam ſi vtrique æquidiſtaret, recta per G,
              <note symbol="d" position="left" xlink:label="note-382-04" xlink:href="note-382-04a" xml:space="preserve">30. primi.</note>
            parallela alterutra extremarum, æquidiſtaret quoque mediæ, ac proinde eam
              <lb/>
            non ſecaret. </s>
            <s xml:id="echoid-s16595" xml:space="preserve">Quod ſi neutri æquidiſtet, duci poterit per G, parallela vtrilibet
              <lb/>
            extremarum. </s>
            <s xml:id="echoid-s16596" xml:space="preserve">Si verò vni extremarum æquidiſtet, ducenda erit per G, alteripa-
              <lb/>
            rallela.</s>
            <s xml:id="echoid-s16597" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16598" xml:space="preserve">
              <emph style="sc">Iam</emph>
            verò ſi tres datæ rectæ coeant in eodem puncto productæ, vt in H,
              <lb/>
            facilius erit problema, etiamſi in media linea detur punctum C, per quod </s>
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