Clavius, Christoph, Geometria practica

Table of figures

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          <p>
            <s xml:id="echoid-s8339" xml:space="preserve">
              <pb o="192" file="222" n="222" rhead="GEOMETR. PRACT."/>
            rectę B G, BF. </s>
            <s xml:id="echoid-s8340" xml:space="preserve">Quoniamigitur E F. </s>
            <s xml:id="echoid-s8341" xml:space="preserve">ad diametrum E G, proportionem habet
              <lb/>
            triplam ſeſquiſeptimam, ex conſtructione; </s>
            <s xml:id="echoid-s8342" xml:space="preserve">erit per pręcedentem E F, circum-
              <lb/>
            ferentiæ circuli fermè æqualis. </s>
            <s xml:id="echoid-s8343" xml:space="preserve">Cum ergo BE, ęqualis ſit ſemidiametro: </s>
            <s xml:id="echoid-s8344" xml:space="preserve">erit per 1.
              <lb/>
            </s>
            <s xml:id="echoid-s8345" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s8346" xml:space="preserve">triangulum BEF, circulo æquale proximè: </s>
            <s xml:id="echoid-s8347" xml:space="preserve">Triangulum autem B E G,
              <lb/>
            quarta pars erit quadrati E H. </s>
            <s xml:id="echoid-s8348" xml:space="preserve">Quia verò poſito latere E G, 7. </s>
            <s xml:id="echoid-s8349" xml:space="preserve">recta E F, eſt 22. </s>
            <s xml:id="echoid-s8350" xml:space="preserve">
              <lb/>
            erit triangulum BEF, hoc eſt, circulus ABCD, ad triangulum BEG, vt 22. </s>
            <s xml:id="echoid-s8351" xml:space="preserve">ad 7.</s>
            <s xml:id="echoid-s8352" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-222-01" xlink:href="note-222-01a" xml:space="preserve">1. ſexti.</note>
            Sed poſito triangulo B E G, 7. </s>
            <s xml:id="echoid-s8353" xml:space="preserve">quadratum EGHI, ipſius quadruplum, eſt 28.
              <lb/>
            </s>
            <s xml:id="echoid-s8354" xml:space="preserve">Igitur circulus ad quadratum, eſt fermè, vt 22. </s>
            <s xml:id="echoid-s8355" xml:space="preserve">ad 28. </s>
            <s xml:id="echoid-s8356" xml:space="preserve">hoc eſt, vt 11. </s>
            <s xml:id="echoid-s8357" xml:space="preserve">ad 14. </s>
            <s xml:id="echoid-s8358" xml:space="preserve">quod
              <lb/>
            erat demonſtrandum.</s>
            <s xml:id="echoid-s8359" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div507" type="section" level="1" n="182">
          <head xml:id="echoid-head189" xml:space="preserve">DE AREA CIRCVLI, INVENTIONE-
            <lb/>
          que circumferentiæ ex diametro, & diametri
            <lb/>
          ex circumfetentia.</head>
          <head xml:id="echoid-head190" xml:space="preserve">
            <emph style="sc">Capvt</emph>
          VII.</head>
          <p>
            <s xml:id="echoid-s8360" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8361" xml:space="preserve">
              <emph style="sc">QVoniam</emph>
            triangulum rectangulum, cuius vnum latus circa angu-
              <lb/>
            lumrectum ſemidiametro circuli, & </s>
            <s xml:id="echoid-s8362" xml:space="preserve">alterum peripheriæ eiuſdem æ-
              <lb/>
            quale eſt, areæ circuli adæquatur: </s>
            <s xml:id="echoid-s8363" xml:space="preserve">huius autem trianguli area
              <note symbol="b" position="left" xlink:label="note-222-02" xlink:href="note-222-02a" xml:space="preserve">1. de Dimẽſ.
                <lb/>
              circuli.</note>
            ductu perpendicularis in ſemiſlem baſis producitur, vt cap. </s>
            <s xml:id="echoid-s8364" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8365" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s8366" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8367" xml:space="preserve">huius li-
              <lb/>
            bri ſcripſimus: </s>
            <s xml:id="echoid-s8368" xml:space="preserve">Fit vt area circuli producatur ex multiplicatione ſemidiam{et}ri in
              <lb/>
              <note position="left" xlink:label="note-222-03" xlink:href="note-222-03a" xml:space="preserve">Area circuli
                <lb/>
              trib. viis, ex
                <lb/>
              cognita dia-
                <lb/>
              metro, & cir-
                <lb/>
              cumferentia.</note>
              <figure xlink:label="fig-222-01" xlink:href="fig-222-01a" number="142">
                <image file="222-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/222-01"/>
              </figure>
            ſemiſſem peripheriæ: </s>
            <s xml:id="echoid-s8369" xml:space="preserve">(ſi nimirum bæſis illi{us} trianguli
              <lb/>
            ſtatuatur lat{us}, quod peripheriæ æquale eſt) Vel ex du-
              <lb/>
            ctutoti{us} peripheriæ in ſemiſſem ſemidiam{et}ri, hoc est,
              <lb/>
            in quartam partem diam{et}ri: </s>
            <s xml:id="echoid-s8370" xml:space="preserve">ſumendo videlicet in eo-
              <lb/>
            dem triangulo pro baſe lat{us}, quod ſemidiam{et}ro est æ.
              <lb/>
            </s>
            <s xml:id="echoid-s8371" xml:space="preserve">quale.) </s>
            <s xml:id="echoid-s8372" xml:space="preserve">Vel denique ex ductu toti{us} diam{et}ri in quartam peripheriæ partem, quod ita
              <lb/>
            perſpicuum faciemus.</s>
            <s xml:id="echoid-s8373" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8374" xml:space="preserve">
              <emph style="sc">Repetatvr</emph>
            figura pręcedentis propoſitionis, diuidaturque EF, quę pe-
              <lb/>
            ripheriæ circuli eſt æqualis, bifariam in L, ita vt EL, ſemiperipherię ſit æqualis:
              <lb/>
            </s>
            <s xml:id="echoid-s8375" xml:space="preserve">Item EL, bifariam ſecetur in M, vt EM, æqualis ſit quartę parti peripherię. </s>
            <s xml:id="echoid-s8376" xml:space="preserve">Et
              <lb/>
            tandem BE, bifariam quo que ſecetur in N, vt EN, ſemiſsis ſit ſemidiametri BE,
              <lb/>
            hoc eſt, quarta pars totius diametri. </s>
            <s xml:id="echoid-s8377" xml:space="preserve"> Et quia triangulum BEF, æquale eſt
              <note symbol="c" position="left" xlink:label="note-222-04" xlink:href="note-222-04a" xml:space="preserve">1. de Dimẽſ.
                <lb/>
              circuli.</note>
            culo ABCD; </s>
            <s xml:id="echoid-s8378" xml:space="preserve">erit quo que rectangulũ ſub ſemidiametro BE, & </s>
            <s xml:id="echoid-s8379" xml:space="preserve">ſemiperip heria
              <lb/>
            EL, comprehenſum (quod per propoſitionem 1. </s>
            <s xml:id="echoid-s8380" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8381" xml:space="preserve">7. </s>
            <s xml:id="echoid-s8382" xml:space="preserve">huius, triangulo ęquale
              <lb/>
            eſt.) </s>
            <s xml:id="echoid-s8383" xml:space="preserve">eidem circulo ęquale; </s>
            <s xml:id="echoid-s8384" xml:space="preserve">quod eſt primum.</s>
            <s xml:id="echoid-s8385" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8386" xml:space="preserve">
              <emph style="sc">Non</emph>
            aliter rectangulum comprehenſum ſub tota peripheria EF, & </s>
            <s xml:id="echoid-s8387" xml:space="preserve">EN,
              <lb/>
            quarta parte d@ametri (quod per propoſ. </s>
            <s xml:id="echoid-s8388" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s8389" xml:space="preserve">7. </s>
            <s xml:id="echoid-s8390" xml:space="preserve">huius, eidem triangulo æquale
              <lb/>
            eſt) eidem circulo erit æquale, quod eſt ſecundum.</s>
            <s xml:id="echoid-s8391" xml:space="preserve"/>
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