Clavius, Christoph, Geometria practica

Table of figures

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          <p>
            <s xml:id="echoid-s7756" xml:space="preserve">
              <pb o="183" file="213" n="213" rhead="LIBER QVARTVS."/>
            Octogoniæqualis, cadet punctumk, citra F, & </s>
            <s xml:id="echoid-s7757" xml:space="preserve">i, citra H, quod E T, minor ſit
              <lb/>
            ſemidiametro circuli, & </s>
            <s xml:id="echoid-s7758" xml:space="preserve">ambitus Octogoni minor peripheria eiuſdem circuli. </s>
            <s xml:id="echoid-s7759" xml:space="preserve">I-
              <lb/>
            gitur ducta recta ki, erit triangulum G k i, minus triangulo F G H, pars toto. </s>
            <s xml:id="echoid-s7760" xml:space="preserve">Eſt
              <lb/>
            autem triangulum k Gi, Octogono æquale: </s>
            <s xml:id="echoid-s7761" xml:space="preserve">quippe cum ex ſcholio propoſ. </s>
            <s xml:id="echoid-s7762" xml:space="preserve">41.
              <lb/>
            </s>
            <s xml:id="echoid-s7763" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s7764" xml:space="preserve">1, Euclid. </s>
            <s xml:id="echoid-s7765" xml:space="preserve">æquale ſit rectangulo ſub G k, & </s>
            <s xml:id="echoid-s7766" xml:space="preserve">ſemiſſe ipſius Gi, comprehenſo,
              <lb/>
            quod per propoſitionem 2. </s>
            <s xml:id="echoid-s7767" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s7768" xml:space="preserve">7. </s>
            <s xml:id="echoid-s7769" xml:space="preserve">de Iſoperimetris Octogono æquale eſt. </s>
            <s xml:id="echoid-s7770" xml:space="preserve">O-
              <lb/>
            ctogonum ergo minus eſt triangulo F G H. </s>
            <s xml:id="echoid-s7771" xml:space="preserve">Non ergo maius eſt: </s>
            <s xml:id="echoid-s7772" xml:space="preserve">ac proinde cir-
              <lb/>
            culus triangulo maius eſſe nequit.</s>
            <s xml:id="echoid-s7773" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7774" xml:space="preserve">
              <emph style="sc">Sit</emph>
            deinde, ſi fieri poteſt, circulus ABCD, minor quam triangulum FGH,
              <lb/>
            magnitudinez. </s>
            <s xml:id="echoid-s7775" xml:space="preserve">Circumſcribatur circulo quadratum IKL M, cuius latera cir-
              <lb/>
            culum tangantin punctis A, B, C, D. </s>
            <s xml:id="echoid-s7776" xml:space="preserve">quod maius erit triangulo FGH. </s>
            <s xml:id="echoid-s7777" xml:space="preserve">Cum
              <lb/>
            enim eius ambitus (vt lib. </s>
            <s xml:id="echoid-s7778" xml:space="preserve">8. </s>
            <s xml:id="echoid-s7779" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s7780" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7781" xml:space="preserve">probabimus) maior ſit peripheria circuli,
              <lb/>
            hoc eſt, recta G H, & </s>
            <s xml:id="echoid-s7782" xml:space="preserve">perpendicularis E A, ipſi F G, æqualis, erit triangulum re-
              <lb/>
            ctangulum latus vnum habens æqualeipſi F G, & </s>
            <s xml:id="echoid-s7783" xml:space="preserve">alterum maius latere GH, (æ-
              <lb/>
            quale nimirum ambitui quadrati I K L M.) </s>
            <s xml:id="echoid-s7784" xml:space="preserve">maius triangulo FGH. </s>
            <s xml:id="echoid-s7785" xml:space="preserve">Cum ergo
              <lb/>
            triangulum illud, per ſcholium propoſ. </s>
            <s xml:id="echoid-s7786" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7787" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s7788" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7789" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s7790" xml:space="preserve">ſit æquale rectangulo
              <lb/>
            ſub FG, & </s>
            <s xml:id="echoid-s7791" xml:space="preserve">ſemiſſe ambitus quadrati IKLM, comprehenſo: </s>
            <s xml:id="echoid-s7792" xml:space="preserve">hoc autem rectan-
              <lb/>
            gulum per propoſ. </s>
            <s xml:id="echoid-s7793" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7794" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s7795" xml:space="preserve">7. </s>
            <s xml:id="echoid-s7796" xml:space="preserve">de Iſoperimetris, qua drato IKLM, æquale; </s>
            <s xml:id="echoid-s7797" xml:space="preserve">erit quo-
              <lb/>
            que quadratum IKLM, maius triangulo F G H. </s>
            <s xml:id="echoid-s7798" xml:space="preserve">Et quia triangulum F G H, po-
              <lb/>
            nitur æquale circulo, & </s>
            <s xml:id="echoid-s7799" xml:space="preserve">magnitudini z. </s>
            <s xml:id="echoid-s7800" xml:space="preserve">ſimul, ac proinde maius quã z, erit quo-
              <lb/>
            que quadratum IKLM, (quod maius eſſe oſtendimus triangulo FGH,) maius,
              <lb/>
            quam z. </s>
            <s xml:id="echoid-s7801" xml:space="preserve">Siigitur ex quadrato IKLM, auferatur plus, quam dimidium, & </s>
            <s xml:id="echoid-s7802" xml:space="preserve">à reſi-
              <lb/>
            dio plus etiam quam dimidium, at queita deinceps, relin quetur tandem
              <note symbol="a" position="right" xlink:label="note-213-01" xlink:href="note-213-01a" xml:space="preserve">1. decimi.</note>
            gnitudo minor, quam z.</s>
            <s xml:id="echoid-s7803" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7804" xml:space="preserve">Hæc autem detractio continua fiet, ſi primo loco auferatur circul{us} A B C D: </s>
            <s xml:id="echoid-s7805" xml:space="preserve">Hic
              <lb/>
              <figure xlink:label="fig-213-01" xlink:href="fig-213-01a" number="135">
                <image file="213-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/213-01"/>
              </figure>
            enim maior eſt ſemiſſe quadrati I K L M, propterea quod
              <lb/>
            quadratum inſcriptum (quod min{us} eſt circulo, pars toto)
              <lb/>
            ſemiſſis eſt quadrati circumſcripti, exſcholio propoſ. </s>
            <s xml:id="echoid-s7806" xml:space="preserve">9. </s>
            <s xml:id="echoid-s7807" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s7808" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7809" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s7810" xml:space="preserve">Quod ſi ducta recta E K, ſecante circulum in
              <lb/>
            O, ducatur per O, ad E K, perpendicularis V X, quæ
              <note symbol="b" position="right" xlink:label="note-213-02" xlink:href="note-213-02a" xml:space="preserve">16. tertij.</note>
            culum tanget in O: </s>
            <s xml:id="echoid-s7811" xml:space="preserve">idemque fiat, ductis rectis EL, EM,
              <lb/>
            EI, &</s>
            <s xml:id="echoid-s7812" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7813" xml:space="preserve">deſcriptum erit Octogonum a quilaterum, & </s>
            <s xml:id="echoid-s7814" xml:space="preserve">æ-
              <lb/>
              <figure xlink:label="fig-213-02" xlink:href="fig-213-02a" number="136">
                <image file="213-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/213-02"/>
              </figure>
            quiangulũ VXY a b c d e V, vt conſtat ex conſtructione, demonſtratione propoſ. </s>
            <s xml:id="echoid-s7815" xml:space="preserve">12. </s>
            <s xml:id="echoid-s7816" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s7817" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7818" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s7819" xml:space="preserve">quippe cum ad E A, E O, & </s>
            <s xml:id="echoid-s7820" xml:space="preserve">adreliqu{as} ſemidiametros Octogoni inſcripti ductæ
              <lb/>
            ſint perpendiculares ve, V X, &</s>
            <s xml:id="echoid-s7821" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7822" xml:space="preserve">Quoniã vero v A, v O, per 2. </s>
            <s xml:id="echoid-s7823" xml:space="preserve">coroll propoſ. </s>
            <s xml:id="echoid-s7824" xml:space="preserve">36. </s>
            <s xml:id="echoid-s7825" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s7826" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7827" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s7828" xml:space="preserve">
              <lb/>
            æqual{es} ſunt; </s>
            <s xml:id="echoid-s7829" xml:space="preserve"> & </s>
            <s xml:id="echoid-s7830" xml:space="preserve">eſt K V, maior quam v O: </s>
            <s xml:id="echoid-s7831" xml:space="preserve">erit quoque K V, maior quam v A, ideoque
              <note symbol="c" position="right" xlink:label="note-213-03" xlink:href="note-213-03a" xml:space="preserve">19. primi.</note>
            & </s>
            <s xml:id="echoid-s7832" xml:space="preserve">triangulum K v O, triangulo v A O, mai{us} erit; </s>
            <s xml:id="echoid-s7833" xml:space="preserve"> cum ſit triangulum ad
              <note symbol="d" position="right" xlink:label="note-213-04" xlink:href="note-213-04a" xml:space="preserve">1. ſexti.</note>
            vt baſis ad baſem. </s>
            <s xml:id="echoid-s7834" xml:space="preserve">Igitur triangulum K V O, mai{us} erit, quam dimidium </s>
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