Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div1005" type="section" level="1" n="359">
          <p>
            <s xml:id="echoid-s16374" xml:space="preserve">
              <pb o="351" file="379" n="379" rhead="LIBER OCTAVVS."/>
            æquale; </s>
            <s xml:id="echoid-s16375" xml:space="preserve"> ideoque L M, media proportionalis eritinter maiorem exceſſum,
              <note symbol="a" position="right" xlink:label="note-379-01" xlink:href="note-379-01a" xml:space="preserve">17. ſexti.</note>
            duplum minoris exceſſus. </s>
            <s xml:id="echoid-s16376" xml:space="preserve">Quo circaſi inter maiorem exceſſum, & </s>
            <s xml:id="echoid-s16377" xml:space="preserve">duplum mi-
              <lb/>
            noris exceſſus, ſumatur media proportionalis LM, habebitur rurſus differentia
              <lb/>
            inter minus latus, & </s>
            <s xml:id="echoid-s16378" xml:space="preserve">minorem exceſſum, &</s>
            <s xml:id="echoid-s16379" xml:space="preserve">c,</s>
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        <div xml:id="echoid-div1007" type="section" level="1" n="360">
          <head xml:id="echoid-head387" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s16380" xml:space="preserve">
              <emph style="sc">Hoc</emph>
            problema, vna cum antecedente Theoremate in Gallia, vnde mihi
              <lb/>
            tranſmiſſum eſt, abingenioſo quodam Geometra demonſtratum fuit, cuius no-
              <lb/>
            men, ſi mihi eſſet cognitum, hic libenter aſſcriberem. </s>
            <s xml:id="echoid-s16381" xml:space="preserve">Idem tamen problemaad
              <lb/>
            finem lib. </s>
            <s xml:id="echoid-s16382" xml:space="preserve">2. </s>
            <s xml:id="echoid-s16383" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s16384" xml:space="preserve">ex Marino Gheraldo Patritio Raguſino aliter quo que de-
              <lb/>
            monſtrauimus non infeliciter.</s>
            <s xml:id="echoid-s16385" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1008" type="section" level="1" n="361">
          <head xml:id="echoid-head388" xml:space="preserve">PROBL. 9. PROPOS. 17.</head>
          <p>
            <s xml:id="echoid-s16386" xml:space="preserve">DATO exceſſu diametri rectanguli ſupra maius latus, & </s>
            <s xml:id="echoid-s16387" xml:space="preserve">exceſſu ma-
              <lb/>
            ioris lateris ſupra minus: </s>
            <s xml:id="echoid-s16388" xml:space="preserve">vtrumque latus, ac diametrum inuenire.</s>
            <s xml:id="echoid-s16389" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16390" xml:space="preserve">
              <emph style="sc">Qvoniam</emph>
            , vt in præcedenti problem. </s>
            <s xml:id="echoid-s16391" xml:space="preserve">dictum eſt, exceſſus maioris lateris
              <lb/>
            ſupra minus, æqualis eſt differentiæ inter exceſſus diametri ſupra vtrumque la-
              <lb/>
            tus: </s>
            <s xml:id="echoid-s16392" xml:space="preserve">fit vt exceſſus diametri ſupra maius latus, additus ad exceſſum maioris la-
              <lb/>
            teris ſupra minus, conficiat exceſſum diametri ſupra minus latus. </s>
            <s xml:id="echoid-s16393" xml:space="preserve">Quare cum
              <lb/>
            cogniti ſint exceſſus diametri ſupra vtrumque latus, reliqua cognoſcentur, vt in
              <lb/>
            præmiſſo problemate traditum eſt.</s>
            <s xml:id="echoid-s16394" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1009" type="section" level="1" n="362">
          <head xml:id="echoid-head389" xml:space="preserve">PROBL. 10. PROPOS. 18.</head>
          <p>
            <s xml:id="echoid-s16395" xml:space="preserve">SECTA linea recta vtcunque, adiungere ei verſus vtramuis partem li-
              <lb/>
            neam rectam, ita vt quadratum totius rectæ compoſitæ æquale ſit qua-
              <lb/>
            drato rectæ adiunctæ; </s>
            <s xml:id="echoid-s16396" xml:space="preserve">vna cum quadrato rectæ, quæ ex adiuncta, & </s>
            <s xml:id="echoid-s16397" xml:space="preserve">
              <lb/>
            proximo ſegmento prioris lineæ conflatur.</s>
            <s xml:id="echoid-s16398" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16399" xml:space="preserve">
              <emph style="sc">In</emph>
            figura propoſ. </s>
            <s xml:id="echoid-s16400" xml:space="preserve">15. </s>
            <s xml:id="echoid-s16401" xml:space="preserve">ſit recta EF, ſecta in C, vtcunque, oporteatque ei verſus
              <lb/>
            F, adiungere rectam, ita vt quadratum totius comp oſitæ ſit æquale, quadrato
              <lb/>
            adiunctæ, vna cum quadrato rectæ ex ſegmento F C, & </s>
            <s xml:id="echoid-s16402" xml:space="preserve">adiuncta compoſitæ.
              <lb/>
            </s>
            <s xml:id="echoid-s16403" xml:space="preserve">
              <figure xlink:label="fig-379-01" xlink:href="fig-379-01a" number="268">
                <image file="379-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/379-01"/>
              </figure>
            Statuantur EF, EC, exceſſus, quibus diameter alicuius re-
              <lb/>
            ctanguli vtrumque latus ſuperat. </s>
            <s xml:id="echoid-s16404" xml:space="preserve">Atque ex propoſ. </s>
            <s xml:id="echoid-s16405" xml:space="preserve">16. </s>
            <s xml:id="echoid-s16406" xml:space="preserve">in-
              <lb/>
            ueniatur minus latus BF. </s>
            <s xml:id="echoid-s16407" xml:space="preserve">Dico rectam BF, ipſi EF, adiun-
              <lb/>
            ctam efficere, quod proponitur. </s>
            <s xml:id="echoid-s16408" xml:space="preserve">Fiat enim rectangulum
              <lb/>
            AC, ſub BC, & </s>
            <s xml:id="echoid-s16409" xml:space="preserve">CD, ipſi BF, æquali comprehẽſum. </s>
            <s xml:id="echoid-s16410" xml:space="preserve">Et quia
              <lb/>
            FC, differentia exceſſuum addita minori lateri inuẽto BF,
              <lb/>
            facit maius latus, vt propoſ. </s>
            <s xml:id="echoid-s16411" xml:space="preserve">16. </s>
            <s xml:id="echoid-s16412" xml:space="preserve">dictũ eſt, erit BE, diametro
              <lb/>
            BD æqualis, quando quidem excedit minus latus BF, vel CD, recta EF, & </s>
            <s xml:id="echoid-s16413" xml:space="preserve">maius
              <lb/>
            recta EC. </s>
            <s xml:id="echoid-s16414" xml:space="preserve"> Quoniam verò quadratum rectæ BE, hoc eſt, diametri BD,
              <note symbol="b" position="right" xlink:label="note-379-02" xlink:href="note-379-02a" xml:space="preserve">47. primi.</note>
            eſt quadrato rectæ CD, id eſt, adiunctæ BF, vna cum quadrato rectæ B C, com-
              <lb/>
            poſitæ ex adiuncta BF, & </s>
            <s xml:id="echoid-s16415" xml:space="preserve">proximo ſegmento F C, liquidò conſtatid, quod pro-
              <lb/>
            ponitur.</s>
            <s xml:id="echoid-s16416" xml:space="preserve"/>
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