Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div540" type="section" level="1" n="194">
          <p>
            <s xml:id="echoid-s8859" xml:space="preserve">
              <pb o="200" file="230" n="230" rhead="GEOMETR. PRACT."/>
            circulus æqualis ſitrectangulo ſub AB, BEF, erit quo que ſector A B C D,
              <note symbol="a" position="left" xlink:label="note-230-01" xlink:href="note-230-01a" xml:space="preserve">14. quinti.</note>
            ctangulo ſub AB, BC, æqualis. </s>
            <s xml:id="echoid-s8860" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s8861" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8862" xml:space="preserve">
              <emph style="sc">Eadem</emph>
            ratione procreabitur ſector A B F D A, ex ſemidiametro A B, in ſe-
              <lb/>
            miſſem arcus BFD.</s>
            <s xml:id="echoid-s8863" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8864" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8865" xml:space="preserve">
              <emph style="sc">Sit</emph>
            deinde ſegmentum BCD. </s>
            <s xml:id="echoid-s8866" xml:space="preserve"> Inuento centro A, arcus B C D, & </s>
            <s xml:id="echoid-s8867" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-230-02" xlink:href="note-230-02a" xml:space="preserve">25. tertij.</note>
            gnitis per aliquam menſuram lateribus trianguli A B D, & </s>
            <s xml:id="echoid-s8868" xml:space="preserve">arcu B C D, in eadem
              <lb/>
            menſura, vt Num. </s>
            <s xml:id="echoid-s8869" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8870" xml:space="preserve">diximus, inueſtigetur tam area ſectoris ABCD, quam trian-
              <lb/>
            guli ABD. </s>
            <s xml:id="echoid-s8871" xml:space="preserve">Hæc enim detracta ex illa relinquet aream ſegmenti propoſiti BCD.</s>
            <s xml:id="echoid-s8872" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8873" xml:space="preserve">3. </s>
            <s xml:id="echoid-s8874" xml:space="preserve">
              <emph style="sc">Sit</emph>
            præterea figura lenticularis duobus arcubus G H I, GKI. </s>
            <s xml:id="echoid-s8875" xml:space="preserve">contenta.
              <lb/>
            </s>
            <s xml:id="echoid-s8876" xml:space="preserve">Ducta recta GI, inquiratur, vt Nu. </s>
            <s xml:id="echoid-s8877" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8878" xml:space="preserve">docuimus, vtriuſque ſegmenti GHI, GKI,
              <lb/>
            area. </s>
            <s xml:id="echoid-s8879" xml:space="preserve">Summa enim ex duabus hiſce areis conflata, erit area propoſitæ figuræ
              <lb/>
            GHIK. </s>
            <s xml:id="echoid-s8880" xml:space="preserve">Quod ſi ſegmenta GHI, GKI, ſint æqualia, ſatis erit vnius areaminue-
              <lb/>
            ſtigare. </s>
            <s xml:id="echoid-s8881" xml:space="preserve">Hæc namque duplicata dabit propoſitæ figuræ GHIK, aream.</s>
            <s xml:id="echoid-s8882" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8883" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8884" xml:space="preserve">
              <emph style="sc">Non</emph>
            aliter metiemur figuras ex varijs circulorum ſegmentis coagmen-
              <lb/>
            tatas, ſiue omnes circumferentiæ extrorſus vergant, ſiue introrſum, ſiue partim
              <lb/>
            introrſum, & </s>
            <s xml:id="echoid-s8885" xml:space="preserve">partium extrorſum. </s>
            <s xml:id="echoid-s8886" xml:space="preserve">Vtin tribus his figuris, ſi arcubus ſubten-
              <lb/>
            dantur chordæ, metiemur in prima quadrilaterum ABCD, vt cap. </s>
            <s xml:id="echoid-s8887" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8888" xml:space="preserve">vel 3. </s>
            <s xml:id="echoid-s8889" xml:space="preserve">do cui-
              <lb/>
            mus: </s>
            <s xml:id="echoid-s8890" xml:space="preserve">& </s>
            <s xml:id="echoid-s8891" xml:space="preserve">ſegmenta AEB, BFC, CGD, DHA, vthoccap. </s>
            <s xml:id="echoid-s8892" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s8893" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8894" xml:space="preserve">traditũ eſt. </s>
            <s xml:id="echoid-s8895" xml:space="preserve">Sie-
              <lb/>
            nim hæc ſegmenta quadrilatero adijciantur, quod omnia extrorſum tendant,
              <lb/>
              <figure xlink:label="fig-230-01" xlink:href="fig-230-01a" number="145">
                <image file="230-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/230-01"/>
              </figure>
            conſlabitur area figuræ A E B F C G D H, ex quatuor arcubus compoſitæ.</s>
            <s xml:id="echoid-s8896" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8897" xml:space="preserve">
              <emph style="sc">In</emph>
            ſecunda autem metiemur pentagonum ABCDE, per ea, quæ cap. </s>
            <s xml:id="echoid-s8898" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8899" xml:space="preserve">ſcri-
              <lb/>
            pta ſunt: </s>
            <s xml:id="echoid-s8900" xml:space="preserve">Ex quo ſi dememus quinque ſegmenta introrſum vergentia, quæ qui-
              <lb/>
            dem ex ijs, quæ Num. </s>
            <s xml:id="echoid-s8901" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8902" xml:space="preserve">huius cap. </s>
            <s xml:id="echoid-s8903" xml:space="preserve">ſcripſimus, cognoſcentur, reliqua fiet area ſi-
              <lb/>
            guræ A F B G C H D I E K, ex quinque arcubus conflatæ.</s>
            <s xml:id="echoid-s8904" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8905" xml:space="preserve">
              <emph style="sc">In</emph>
            tertia denique pentagono A B C D E, adij ciemus tria ſegmenta, A F B,
              <lb/>
            A G E, C H D, extrorſum vergentia, & </s>
            <s xml:id="echoid-s8906" xml:space="preserve">ex compoſito numero duo ſegmenta
              <lb/>
            B I C, D K E, introrſum vergentia tollemus, vt area relinquatur figuræ AFBIC-
              <lb/>
            HDKEG, ex quinque arcubus compoſitæ. </s>
            <s xml:id="echoid-s8907" xml:space="preserve">Atque hoc modo agrum quantum-
              <lb/>
            uis irregularem metirilicebit.</s>
            <s xml:id="echoid-s8908" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8909" xml:space="preserve">5. </s>
            <s xml:id="echoid-s8910" xml:space="preserve">
              <emph style="sc">Sit</emph>
            denique in prima figura huius cap. </s>
            <s xml:id="echoid-s8911" xml:space="preserve">ſegmentum circuli LMON, com-
              <lb/>
            prehenſum duabus rectis L M, N O, & </s>
            <s xml:id="echoid-s8912" xml:space="preserve">duobus arcubus LN, MO. </s>
            <s xml:id="echoid-s8913" xml:space="preserve">Exploretur
              <lb/>
            vt Num. </s>
            <s xml:id="echoid-s8914" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8915" xml:space="preserve">declaratum eſt, area vtriuſque ſegmenti P L M, P N O. </s>
            <s xml:id="echoid-s8916" xml:space="preserve">Minor enim
              <lb/>
            area P N O, detracta ex maiori PLM, reliquam ſaciet aream propoſiti ſegmenti
              <lb/>
            L M O N.</s>
            <s xml:id="echoid-s8917" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8918" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8919" xml:space="preserve">
              <emph style="sc">Vt</emph>
            quartus hic liber concludatur, lubet hic appẽdicis loco regulas quaſ-
              <lb/>
            dam alias à noſtro inſtituto non alienas ſubiungere.</s>
            <s xml:id="echoid-s8920" xml:space="preserve"/>
          </p>
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