Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s15300" xml:space="preserve">
              <pb o="327" file="357" n="357" rhead="LIBER SEPTIMVS."/>
            ergo AD, æqualis ſit oſtenſa Quadranti ſemidiametri AE; </s>
            <s xml:id="echoid-s15301" xml:space="preserve"> erit quoqe N,
              <note symbol="a" position="right" xlink:label="note-357-01" xlink:href="note-357-01a" xml:space="preserve">14. quinti.</note>
            lis Quadranti ſemidiametri O. </s>
            <s xml:id="echoid-s15302" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s15303" xml:space="preserve"/>
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        <div xml:id="echoid-div935" type="section" level="1" n="327">
          <head xml:id="echoid-head354" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s15304" xml:space="preserve">DATO circulo quadratum æquale conſtituere.</s>
            <s xml:id="echoid-s15305" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15306" xml:space="preserve">
              <emph style="sc">Sit</emph>
            quadrandus circulus ad interuallum ſemidiametri B C, deſcriptus. </s>
            <s xml:id="echoid-s15307" xml:space="preserve">Tri-
              <lb/>
              <note position="right" xlink:label="note-357-02" xlink:href="note-357-02a" xml:space="preserve">Quadratum
                <lb/>
              circulo æqua-
                <lb/>
              le exhibere.</note>
            bus rectis A E, baſi Quadratricis; </s>
            <s xml:id="echoid-s15308" xml:space="preserve">A D, lateri eiuſdem pręcedentis figuræ, & </s>
            <s xml:id="echoid-s15309" xml:space="preserve">rectę
              <lb/>
              <figure xlink:label="fig-357-01" xlink:href="fig-357-01a" number="246">
                <image file="357-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/357-01"/>
              </figure>
            BC, inuenta quarta proportionali F; </s>
            <s xml:id="echoid-s15310" xml:space="preserve">erit ex coroll. </s>
            <s xml:id="echoid-s15311" xml:space="preserve">3.
              <lb/>
            </s>
            <s xml:id="echoid-s15312" xml:space="preserve">antecedenti recta F, quadranti circuli dati æqualis,
              <lb/>
            atq; </s>
            <s xml:id="echoid-s15313" xml:space="preserve">eius dupla ſemicircumferentiæ æqualis erit. </s>
            <s xml:id="echoid-s15314" xml:space="preserve">In-
              <lb/>
            uenta autem inter ſemidiametrum B C, & </s>
            <s xml:id="echoid-s15315" xml:space="preserve">duplami-
              <lb/>
            pſius F, media proportionali GH: </s>
            <s xml:id="echoid-s15316" xml:space="preserve">Dico quadratum
              <lb/>
            ex G H, deſcriptum æquale eſſe circulo ad interual-
              <lb/>
              <note symbol="b" position="right" xlink:label="note-357-03" xlink:href="note-357-03a" xml:space="preserve">4. Iſoperi-
                <lb/>
              metrorum.</note>
            lum B C, deſcripto. </s>
            <s xml:id="echoid-s15317" xml:space="preserve"> Quoniam enim rectangulum ſub B C, ſemidiametro, & </s>
            <s xml:id="echoid-s15318" xml:space="preserve">ſub ſemicircumferẽtia cir-
              <lb/>
            culi, id eſt, ſub dupla rectæ F, inuentæ, æquale eſt cir-
              <lb/>
              <note symbol="c" position="right" xlink:label="note-357-04" xlink:href="note-357-04a" xml:space="preserve">17. ſexti.</note>
            culo: </s>
            <s xml:id="echoid-s15319" xml:space="preserve"> Prędicto autem rectangulo æquale eſt qua- dratum lateris G H; </s>
            <s xml:id="echoid-s15320" xml:space="preserve">erit quoque quadratum lateris
              <lb/>
            G H, circulo ſemidiametri B C, æquale.</s>
            <s xml:id="echoid-s15321" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15322" xml:space="preserve">
              <emph style="sc">Vervm</emph>
            vt expedite linea recta inueniatur æqualis quartæ parti circumfe-
              <lb/>
              <note position="right" xlink:label="note-357-05" xlink:href="note-357-05a" xml:space="preserve">Facilis inuen-
                <lb/>
              tio rectæ æqu@
                <lb/>
              lis circumfe-
                <lb/>
              rentiæ.</note>
            rentiæ dati circuli, atque id circo & </s>
            <s xml:id="echoid-s15323" xml:space="preserve">ſemicircumferentiæ, vel toti circumferentiæ,
              <lb/>
            conſtruenda erit figura eiuſmodi. </s>
            <s xml:id="echoid-s15324" xml:space="preserve">Fiat angulus rectus D A E, recta que AD, ęqua-
              <lb/>
            lis ſit ſemidiametro Quadrantis, ex quo Quadratrix deſcripta eſt; </s>
            <s xml:id="echoid-s15325" xml:space="preserve">& </s>
            <s xml:id="echoid-s15326" xml:space="preserve">AE, baſi
              <lb/>
            eiuſdem Quadratricis æqualis. </s>
            <s xml:id="echoid-s15327" xml:space="preserve">Vel certe ex centro
              <lb/>
              <figure xlink:label="fig-357-02" xlink:href="fig-357-02a" number="247">
                <image file="357-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/357-02"/>
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            A, noua Quadratrix deſcribatur DE, cuius latus AD,
              <lb/>
            & </s>
            <s xml:id="echoid-s15328" xml:space="preserve">baſis A E. </s>
            <s xml:id="echoid-s15329" xml:space="preserve">Ducta namquerecta D E, conſtru-
              <lb/>
            cta erit figura aptiſsima ad rectam circumferen-
              <lb/>
            tię dati circuli æqualem inueniendam. </s>
            <s xml:id="echoid-s15330" xml:space="preserve">Si
              <lb/>
            enim circuli quadrandi ſemidiametro abſcindatur æ-
              <lb/>
            qualis AF, ducanturque F G, ipſi D E, parallela; </s>
            <s xml:id="echoid-s15331" xml:space="preserve">erit
              <lb/>
            ex coroll. </s>
            <s xml:id="echoid-s15332" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15333" xml:space="preserve">antecedenti A G, æqualis quartæ parti
              <lb/>
            circumferentiæ dati circuli, cuius ſemidiameter nimi-
              <lb/>
            rum eſt AF, (quemadmodum A D, quartæ parti cir-
              <lb/>
            cumferentiæ circuli ſemidiametri AE, æqualis eſt, vt
              <lb/>
            ex coroll. </s>
            <s xml:id="echoid-s15334" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15335" xml:space="preserve">præcedenti conſtat) propterea
              <note symbol="d" position="right" xlink:label="note-357-06" xlink:href="note-357-06a" xml:space="preserve">4. ſexti.</note>
            A F, A G, eandem habent proportionem, quam A E,
              <lb/>
            AD. </s>
            <s xml:id="echoid-s15336" xml:space="preserve">Eadem ratione, ductis HI, KL, MN, eidem DE,
              <lb/>
            parallelis, erunt AI, AL, AN, æquales quartis parti-
              <lb/>
            bus circumferentiarum circulorum ex ſemidiame-
              <lb/>
            tris AH, AK, AM, deſcriptorum. </s>
            <s xml:id="echoid-s15337" xml:space="preserve">Hæautem rectæ
              <lb/>
            duplicatę ſemicir cumferentijs æquales erunt, & </s>
            <s xml:id="echoid-s15338" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s15339" xml:space="preserve">Atque hac arte inuenietur recta ęqualis quartæ parti
              <lb/>
            circumferentię cuiuſuis circuli, ſi eius ſemidiametro ex recta A E, æqualem
              <lb/>
            lineam abſcindemus, ab eiuſque extremo rectæ DE, parallelã ducemus, &</s>
            <s xml:id="echoid-s15340" xml:space="preserve">c.</s>
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