Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div1020" type="section" level="1" n="366">
          <p>
            <s xml:id="echoid-s16598" xml:space="preserve">
              <pb o="355" file="383" n="383" rhead="LIBER OCTAVVS."/>
            debeat linea. </s>
            <s xml:id="echoid-s16599" xml:space="preserve">Ducta enim per datum punctum C, in media, alterutri extrema-
              <lb/>
            rum, vt ipſi HF, parallela CA, ſecante alte-
              <lb/>
              <figure xlink:label="fig-383-01" xlink:href="fig-383-01a" number="273">
                <image file="383-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/383-01"/>
              </figure>
            ram extremam in A; </s>
            <s xml:id="echoid-s16600" xml:space="preserve">& </s>
            <s xml:id="echoid-s16601" xml:space="preserve">ipſi HA, æqualis
              <lb/>
            capiatur AB, ſecabitur ducta BCE, in C,
              <lb/>
            bifariã: </s>
            <s xml:id="echoid-s16602" xml:space="preserve"> quippe cũ ſit BG, ad CE, vt
              <note symbol="a" position="right" xlink:label="note-383-01" xlink:href="note-383-01a" xml:space="preserve">2. ſexti.</note>
            BA, ad rectam AH, &</s>
            <s xml:id="echoid-s16603" xml:space="preserve">c. </s>
            <s xml:id="echoid-s16604" xml:space="preserve">Sic etiam ſi detur
              <lb/>
            punctum I, in media; </s>
            <s xml:id="echoid-s16605" xml:space="preserve">ducta per I, alteru-
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            triextremarum, vtipſi HB, parallela LI,
              <lb/>
            ſumptaque ipſi HL, æquali LF, ſeca-
              <lb/>
            bitur ducta FIK, in I, bifariam; </s>
            <s xml:id="echoid-s16606" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-383-02" xlink:href="note-383-02a" xml:space="preserve">2. ſexti.</note>
            ea quod eſt FI, ad IK, vt FL, ad LH.
              <lb/>
            </s>
            <s xml:id="echoid-s16607" xml:space="preserve">&</s>
            <s xml:id="echoid-s16608" xml:space="preserve">c.</s>
            <s xml:id="echoid-s16609" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16610" xml:space="preserve">
              <emph style="sc">Eadem</emph>
            ratione ducemus lineam, quæ à media ſecetur in duas partes da-
              <lb/>
            tam habentes proportionem. </s>
            <s xml:id="echoid-s16611" xml:space="preserve">Si namque ducta BF, vtcunque ſecetur in datam
              <lb/>
            proportionẽ in G, & </s>
            <s xml:id="echoid-s16612" xml:space="preserve">reliqua fiant, vt ſupra; </s>
            <s xml:id="echoid-s16613" xml:space="preserve"> erit rurſus vt FG, ad GB, ita
              <note symbol="c" position="right" xlink:label="note-383-03" xlink:href="note-383-03a" xml:space="preserve">2. ſexti.</note>
            ad CB; </s>
            <s xml:id="echoid-s16614" xml:space="preserve">Vel vt BG, ad GF, ita BC, ad CE, prout videlicet proportio data eſt FG,
              <lb/>
            ad GB, vel BG, ad GF. </s>
            <s xml:id="echoid-s16615" xml:space="preserve">Sic etiam ſi tres rectæ datæ coeantin H; </s>
            <s xml:id="echoid-s16616" xml:space="preserve">ducta GA, ipſi
              <lb/>
            EF, parallela, fiatque HA, ad AB, vt antecedens datæ proportionis ad conſe-
              <lb/>
            quens: </s>
            <s xml:id="echoid-s16617" xml:space="preserve">ſi ducatur BCE, erit EC, ad CB, vt HA, ad AB. </s>
            <s xml:id="echoid-s16618" xml:space="preserve">Et ſi fiat HA, ad
              <note symbol="d" position="right" xlink:label="note-383-04" xlink:href="note-383-04a" xml:space="preserve">1. ſexti.</note>
            vt conſequens datæ proportionis ad antecedens, erit rurſus BC, ad CE, vt BA,
              <lb/>
            antecedens ad conſequens AH.</s>
            <s xml:id="echoid-s16619" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1026" type="section" level="1" n="367">
          <head xml:id="echoid-head394" xml:space="preserve">PROBL. 14. PROPOS. 23.</head>
          <p>
            <s xml:id="echoid-s16620" xml:space="preserve">CVIVSLIBET lineæ, quamuis minimæ, exhibere multiplicem quam-
              <lb/>
            cunque, etiamſi circino ipſa non accipiatur.
              <lb/>
            </s>
            <s xml:id="echoid-s16621" xml:space="preserve">
              <figure xlink:label="fig-383-02" xlink:href="fig-383-02a" number="274">
                <image file="383-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/383-02"/>
              </figure>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s16622" xml:space="preserve">
              <emph style="sc">Sit</emph>
            ſumenda verbigratia lineolæ AB, tripla. </s>
            <s xml:id="echoid-s16623" xml:space="preserve">Extenſo circino quantumli-
              <lb/>
            bet ex A, ad C, ſumantur ipſi AC, duæ æ-
              <lb/>
              <figure xlink:label="fig-383-03" xlink:href="fig-383-03a" number="275">
                <image file="383-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/383-03"/>
              </figure>
            quales CF, FD, vt tota AD, ipſius AC, ſit
              <lb/>
            tripla. </s>
            <s xml:id="echoid-s16624" xml:space="preserve">Item ipſi CB, ſumantur tres æ qua-
              <lb/>
              <handwritten xlink:label="hd-383-4" xlink:href="hd-383-4a" number="73"/>
            les DG, GH, HE. </s>
            <s xml:id="echoid-s16625" xml:space="preserve">Dico AE, eſſe ipſius AB,
              <lb/>
            triplam. </s>
            <s xml:id="echoid-s16626" xml:space="preserve">Quoniam enim tam multiplex eſt
              <lb/>
            AD, totius AC, quam multiplex eſt ablata
              <lb/>
            DE, ablatæ CB, nimirum tripla: </s>
            <s xml:id="echoid-s16627" xml:space="preserve">erit quoque ita multiplex reliqua EA, reliquæ
              <lb/>
            AB, vt tota totius, videlicet tripla. </s>
            <s xml:id="echoid-s16628" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s16629" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1029" type="section" level="1" n="368">
          <head xml:id="echoid-head395" xml:space="preserve">PROBL. 15. PROPOS. 24.</head>
          <p>
            <s xml:id="echoid-s16630" xml:space="preserve">EX qualibet lineola, quamuis minima, auferre partem, vel partes impe-
              <lb/>
            ratas,</s>
          </p>
          <p>
            <s xml:id="echoid-s16631" xml:space="preserve">
              <emph style="sc">In</emph>
            figura præcedentis@ propoſ. </s>
            <s xml:id="echoid-s16632" xml:space="preserve">ſit ex lineola AB, detrahenda tertia pars. </s>
            <s xml:id="echoid-s16633" xml:space="preserve">Per
              <lb/>
            præcedentem ſumatur ipſius AB, tripla AE, quæ, ſi videbitur nimis exigua, mul-
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            tiplicetur, vt libet. </s>
            <s xml:id="echoid-s16634" xml:space="preserve">In exemplo quadruplicata eſt vſque ad D; </s>
            <s xml:id="echoid-s16635" xml:space="preserve">ita vt AD, ſit
              <lb/>
            ipſius AB, duodecupla: </s>
            <s xml:id="echoid-s16636" xml:space="preserve">(quod ſcietur, ſi numerus partium AE, nimirum 3 </s>
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