Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div1009" type="section" level="1" n="362">
          <pb o="352" file="380" n="380" rhead="GEOMETR. PRACT."/>
        </div>
        <div xml:id="echoid-div1011" type="section" level="1" n="363">
          <head xml:id="echoid-head390" xml:space="preserve">PROBL. 11. PROPOS. 19.</head>
          <p>
            <s xml:id="echoid-s16417" xml:space="preserve">DATIS duabus rectis inæqualibus, quarum maior diametrum qua-
              <lb/>
            drati ex minore deſcripti non ſuperet: </s>
            <s xml:id="echoid-s16418" xml:space="preserve">maiorem ita ſecare in duas
              <lb/>
            partes inæquales, vt earum quadrata ſimul ſumpta quadrato minoris
              <lb/>
            lineæ ſint æqualia,</s>
          </p>
          <p>
            <s xml:id="echoid-s16419" xml:space="preserve">
              <emph style="sc">Sint</emph>
            datæ duæ rectæ AB, maior, & </s>
            <s xml:id="echoid-s16420" xml:space="preserve">AC, minor, ita vt AB, non ſit maior dia-
              <lb/>
            metro quadrati ex AC, deſcripti. </s>
            <s xml:id="echoid-s16421" xml:space="preserve">Erigatur perpendicularis AD, maiori AB, æ-
              <lb/>
            qualis: </s>
            <s xml:id="echoid-s16422" xml:space="preserve">Et ducta recta B D, ſecetur bifariam in E, iungatur que recta AE,
              <note symbol="a" position="left" xlink:label="note-380-01" xlink:href="note-380-01a" xml:space="preserve">ſchol. 26.
                <lb/>
              primi.</note>
            ad B D, perpendicularis erit: </s>
            <s xml:id="echoid-s16423" xml:space="preserve">diuidetque angulum rectum A, bifariam in duos
              <lb/>
            ſemirectos: </s>
            <s xml:id="echoid-s16424" xml:space="preserve"> Suntautem & </s>
            <s xml:id="echoid-s16425" xml:space="preserve">B, D, ſemirecti. </s>
            <s xml:id="echoid-s16426" xml:space="preserve"> Igitur latera E A, E B,
              <note symbol="b" position="left" xlink:label="note-380-02" xlink:href="note-380-02a" xml:space="preserve">2. coroll.
                <lb/>
              32. primi.</note>
            ſunt; </s>
            <s xml:id="echoid-s16427" xml:space="preserve">ac proinde AB, diameter erit quadrati rectæ AE. </s>
            <s xml:id="echoid-s16428" xml:space="preserve">Et quoniam A B, poni-
              <lb/>
              <note symbol="c" position="left" xlink:label="note-380-03" xlink:href="note-380-03a" xml:space="preserve">6. primi.</note>
            tur non maior diametro quadrati minoris A C, non erit A C, minor quam A E,
              <lb/>
            ſed vel maior, vel æqualis. </s>
            <s xml:id="echoid-s16429" xml:space="preserve">Si namque minor eſſet A C, quam A E, ſumpta ipſi
              <lb/>
            æquali AL, ductaque LM, ipſi EB, parallela, eſſet AM, diameter quadratimino-
              <lb/>
            ris A L, ideoque maior AB, ſuperaret diametrum quadrati ex minore deſcripti.
              <lb/>
            </s>
            <s xml:id="echoid-s16430" xml:space="preserve">quod non ponitur. </s>
            <s xml:id="echoid-s16431" xml:space="preserve">Sit ergo primum A C, maior quam A E, productaque AE,
              <lb/>
            vt A F, ipſi A C, ſit æqualis, deſcribatur ex A, per
              <lb/>
              <figure xlink:label="fig-380-01" xlink:href="fig-380-01a" number="269">
                <image file="380-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/380-01"/>
              </figure>
            C, F, circulus ſecans BD, in H, N, demittaturque
              <lb/>
            HI, ad AB, perpendicularis. </s>
            <s xml:id="echoid-s16432" xml:space="preserve">Dico maiorem AB, ita
              <lb/>
            eſſe ſectam in I, vt quadrata rectarum AI, IB, æqua-
              <lb/>
            lia ſint quadrato minoris A O. </s>
            <s xml:id="echoid-s16433" xml:space="preserve">Quoniam enim an-
              <lb/>
            gulus I, rectus eſt, & </s>
            <s xml:id="echoid-s16434" xml:space="preserve">B, ſemirectus: </s>
            <s xml:id="echoid-s16435" xml:space="preserve">erit quoque H,
              <lb/>
            in triangulo B H I, ſemirectus; </s>
            <s xml:id="echoid-s16436" xml:space="preserve"> ideoque
              <note symbol="d" position="left" xlink:label="note-380-04" xlink:href="note-380-04a" xml:space="preserve">6. primi.</note>
            ra B I, H I, æqualia erunt. </s>
            <s xml:id="echoid-s16437" xml:space="preserve"> Cum ergo, ducta
              <note symbol="e" position="left" xlink:label="note-380-05" xlink:href="note-380-05a" xml:space="preserve">47. primi.</note>
            cta A H, quadrata rectarum A I, I H, quadrato re-
              <lb/>
            ctæ A H, æqualia ſint; </s>
            <s xml:id="echoid-s16438" xml:space="preserve">erunt quoque quadrata ſe-
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            gmentorum A I, I B, æqualia quadrato rectæ A H,
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            hoc eſt, quadrato rectæ AC. </s>
            <s xml:id="echoid-s16439" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s16440" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16441" xml:space="preserve">
              <emph style="sc">Sit</emph>
            deinde minor linea data A K, æqualis ipſi
              <lb/>
            AE, ita vt maior AB, diametro quadrati ex minore
              <lb/>
            A E, deſcripti æqualis ſit. </s>
            <s xml:id="echoid-s16442" xml:space="preserve">Demittatur perpendicu-
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            laris EG, quæ & </s>
            <s xml:id="echoid-s16443" xml:space="preserve">baſem AB, & </s>
            <s xml:id="echoid-s16444" xml:space="preserve">angulum rectum E, diuidet bifariam in
              <note symbol="f" position="left" xlink:label="note-380-06" xlink:href="note-380-06a" xml:space="preserve">ſchol. 26.
                <lb/>
              primi.</note>
            ctos. </s>
            <s xml:id="echoid-s16445" xml:space="preserve">Dico AB, ita eſſe ſectam in G, vt quadrata ſegmentorum æqualium A G,
              <lb/>
            GB, æqualia ſint quadrato minoris AK, vel AE. </s>
            <s xml:id="echoid-s16446" xml:space="preserve"> Erunt enim rurſus latera
              <note symbol="g" position="left" xlink:label="note-380-07" xlink:href="note-380-07a" xml:space="preserve">6. primi.</note>
            GB, æqualia, ob ſemirectos angulos æquales B, & </s>
            <s xml:id="echoid-s16447" xml:space="preserve">E, in triangulo BEG. </s>
            <s xml:id="echoid-s16448" xml:space="preserve">
              <note symbol="h" position="left" xlink:label="note-380-08" xlink:href="note-380-08a" xml:space="preserve">47. primi.</note>
            ergo quadrata rectarum AG, GE, æqualia ſint quadrato rectæ AE, erunt quo-
              <lb/>
            que quadrata ſegmentorum AG, GB, æqualia quadrato AE, vel minoris lineæ
              <lb/>
            A K. </s>
            <s xml:id="echoid-s16449" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s16450" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16451" xml:space="preserve">
              <emph style="sc">Si</emph>
            ex altera ſectione N, demittatur perpendicularis NO, erit AB, ſecta in O,
              <lb/>
            vt in I, ita vt etiam quadrata ſegmentorum BO, OA, æqualia ſint quadrato mi-
              <lb/>
            noris AC, vel AH. </s>
            <s xml:id="echoid-s16452" xml:space="preserve"> Cum enim rectæ BD, BA, ſectæ ſint proportionaliter in
              <note symbol="i" position="left" xlink:label="note-380-09" xlink:href="note-380-09a" xml:space="preserve">2. ſexti.</note>
            I, & </s>
            <s xml:id="echoid-s16453" xml:space="preserve">N, O, ſintque æquales B H, N D; </s>
            <s xml:id="echoid-s16454" xml:space="preserve"> (propterea quod perpendicularis
              <note symbol="k" position="left" xlink:label="note-380-10" xlink:href="note-380-10a" xml:space="preserve">3. tertii.</note>
            ſecat H N, bifariam. </s>
            <s xml:id="echoid-s16455" xml:space="preserve">Ablatis ergo æqualibus E H, E N, ex æqualibus E B, E </s>
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