Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s14899" xml:space="preserve">
              <pb o="318" file="348" n="348" rhead="GEOMETR. PRACT."/>
            uenta enim diametro per prædictamregulam 1. </s>
            <s xml:id="echoid-s14900" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s14901" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14902" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s14903" xml:space="preserve">8. </s>
            <s xml:id="echoid-s14904" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14905" xml:space="preserve">7. </s>
            <s xml:id="echoid-s14906" xml:space="preserve">circulus il-
              <lb/>
            lius diametri erit is, qui quæritur. </s>
            <s xml:id="echoid-s14907" xml:space="preserve">Viſum eſt autem appendicem hanc libro huic
              <lb/>
            ſeptimo adiungere, quod tractatio de circuli Tetragoniſmo, ſiue quadratura,
              <lb/>
            non parum affinis ſit de iſoperimetris figuris diſputationi.</s>
            <s xml:id="echoid-s14908" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14909" xml:space="preserve">
              <emph style="sc">Qvadratvra</emph>
            autem circuli per numeros, quam Arabes tradiderunt, & </s>
            <s xml:id="echoid-s14910" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-348-01" xlink:href="note-348-01a" xml:space="preserve">Circuli qua-
                <lb/>
              dratura per
                <lb/>
              numeros ſe-
                <lb/>
              cundum Ara-
                <lb/>
              b{es} falſa.</note>
            quam Ioſephus Scaliger in ſuis Cyclometricis elementis veram eſſe credit, o-
              <lb/>
            mnino reiiciẽda eſt, cum ſit extra limites Archimedis, per quos conſtat, propor-
              <lb/>
            tionem circumferentiæ ad diametrum minorem debere eſſe tripla ſeſquiſepti-
              <lb/>
            ma, maiorem verò tripla ſuperdecupartiẽte ſeptuageſimas primas. </s>
            <s xml:id="echoid-s14911" xml:space="preserve">quod in nu-
              <lb/>
            meris Arabum non cernitur. </s>
            <s xml:id="echoid-s14912" xml:space="preserve">Dicunt enim proportionẽ circumferentiæ ad dia-
              <lb/>
            metrum eſſe potentia decuplam: </s>
            <s xml:id="echoid-s14913" xml:space="preserve">adeò vt ſi quadratum circumferentiæ pona-
              <lb/>
            tur 10. </s>
            <s xml:id="echoid-s14914" xml:space="preserve">quadratum diametrum ſit 1. </s>
            <s xml:id="echoid-s14915" xml:space="preserve">quod falſum eſt. </s>
            <s xml:id="echoid-s14916" xml:space="preserve">Nam cum radix quadrata
              <lb/>
            numeri 10. </s>
            <s xml:id="echoid-s14917" xml:space="preserve">ſit maior quam 3 {1/7}. </s>
            <s xml:id="echoid-s14918" xml:space="preserve">quod huius radicis quadratum ſit tantum 9 {43/49}.
              <lb/>
            </s>
            <s xml:id="echoid-s14919" xml:space="preserve">Radix autem vnitatis ſit 1. </s>
            <s xml:id="echoid-s14920" xml:space="preserve">eſſet maior proportio circumferentiæ ad diametrum,
              <lb/>
            quam tripla ſeſquiſeptima: </s>
            <s xml:id="echoid-s14921" xml:space="preserve">cum tamen ſecundum Archimedem ſit minor. </s>
            <s xml:id="echoid-s14922" xml:space="preserve">
              <lb/>
            Item quia poſita diametro 7. </s>
            <s xml:id="echoid-s14923" xml:space="preserve">circumferentia minor eſt, quam 22. </s>
            <s xml:id="echoid-s14924" xml:space="preserve">ex Archimede; </s>
            <s xml:id="echoid-s14925" xml:space="preserve">
              <lb/>
            erit quadratum circumferentiæ minus, quam 484. </s>
            <s xml:id="echoid-s14926" xml:space="preserve">quod ad 49. </s>
            <s xml:id="echoid-s14927" xml:space="preserve">quadratum dia
              <lb/>
            metri minorem proportionem habet, quam decuplam; </s>
            <s xml:id="echoid-s14928" xml:space="preserve">quippe cum 490. </s>
            <s xml:id="echoid-s14929" xml:space="preserve">ad
              <lb/>
            49. </s>
            <s xml:id="echoid-s14930" xml:space="preserve">proportionem habeant decuplam. </s>
            <s xml:id="echoid-s14931" xml:space="preserve">Minor igitur eſt proportio quadrati cir-
              <lb/>
            cumferentiæ ad qua dratum diametri, quam decupla.</s>
            <s xml:id="echoid-s14932" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14933" xml:space="preserve">
              <emph style="sc">Simili</emph>
            modo reiicienda eſt ratio quadrandi circuli per numeros Alberti
              <lb/>
              <note position="left" xlink:label="note-348-02" xlink:href="note-348-02a" xml:space="preserve">Quadr atura
                <lb/>
              circuli per nu
                <lb/>
              meros ex Al-
                <lb/>
              berto Durero
                <lb/>
              falſa.</note>
            Dureri, qui exiſtimat, di
              <unsure/>
            uiſa diametro circuliin octo partes æquales, diametrum
              <lb/>
            quadrati circulo æqualis eſſe 10. </s>
            <s xml:id="echoid-s14934" xml:space="preserve">adeò vt diameter quadrari circulo æqualis ad
              <lb/>
            diametrum circuli proportionem habeat, quam 10. </s>
            <s xml:id="echoid-s14935" xml:space="preserve">ad 8. </s>
            <s xml:id="echoid-s14936" xml:space="preserve">quod etiam falſum eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s14937" xml:space="preserve">Nam cum quadratum diametri 10. </s>
            <s xml:id="echoid-s14938" xml:space="preserve">ſit 100. </s>
            <s xml:id="echoid-s14939" xml:space="preserve">duplumque quadrati, cuius diame- ter eſt 10. </s>
            <s xml:id="echoid-s14940" xml:space="preserve">& </s>
            <s xml:id="echoid-s14941" xml:space="preserve">quod circulo diametri 8. </s>
            <s xml:id="echoid-s14942" xml:space="preserve">dicitur æquale: </s>
            <s xml:id="echoid-s14943" xml:space="preserve">erit quadratum circulo æ-
              <lb/>
              <note symbol="a" position="left" xlink:label="note-348-03" xlink:href="note-348-03a" xml:space="preserve">ſchol. 47,
                <lb/>
              primi.</note>
            quale 50. </s>
            <s xml:id="echoid-s14944" xml:space="preserve">Sed ex diametro 8. </s>
            <s xml:id="echoid-s14945" xml:space="preserve">reperitur area circuli maior, quam vera, 50 {2/7}. </s>
            <s xml:id="echoid-s14946" xml:space="preserve">vt
              <lb/>
            cap. </s>
            <s xml:id="echoid-s14947" xml:space="preserve">7. </s>
            <s xml:id="echoid-s14948" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14949" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14950" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s14951" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14952" xml:space="preserve">tradidimus. </s>
            <s xml:id="echoid-s14953" xml:space="preserve">Vera ergo circuli area maior erit, quam 50 {2/7}.
              <lb/>
            </s>
            <s xml:id="echoid-s14954" xml:space="preserve">atque adeò multò maior, quam 50. </s>
            <s xml:id="echoid-s14955" xml:space="preserve">Eſt igitur quadratum Alberti minus area
              <lb/>
            circuli, non autem æquale.</s>
            <s xml:id="echoid-s14956" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14957" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14958" xml:space="preserve">
              <emph style="sc">Iam</emph>
            verò, vt ad quadraturam circuli per lineas aggrediamur, pudet me
              <lb/>
              <note position="left" xlink:label="note-348-04" xlink:href="note-348-04a" xml:space="preserve">Falſa qua-
                <lb/>
              dratura cir-
                <lb/>
              culi per line{as}
                <lb/>
              Campano a-
                <lb/>
              ſcripta.</note>
            refellere illam, quæ imperitis vera eſſe videtur, & </s>
            <s xml:id="echoid-s14959" xml:space="preserve">quam ſciolus, neſcio quis,
              <lb/>
            Campano Mathematico non indo cto affinxit, typiſque mandauit. </s>
            <s xml:id="echoid-s14960" xml:space="preserve">Eſt autem
              <lb/>
            talis. </s>
            <s xml:id="echoid-s14961" xml:space="preserve">Linea recta circumferentiæ circuli æqualis (quo pacto autem eiuſmo di
              <lb/>
            linea inueniatur, non docet) ſecetur in 4. </s>
            <s xml:id="echoid-s14962" xml:space="preserve">partes æquales, ex quibus quadratum
              <lb/>
            conſtituatur. </s>
            <s xml:id="echoid-s14963" xml:space="preserve">quod ſciolus ille circulo dicit eſſe æquale. </s>
            <s xml:id="echoid-s14964" xml:space="preserve">quæ res omnin ò Geo-
              <lb/>
            metraindigna eſt, & </s>
            <s xml:id="echoid-s14965" xml:space="preserve">planè ridicula. </s>
            <s xml:id="echoid-s14966" xml:space="preserve">Si enim quadratum illud circulo eſt Iſope-
              <lb/>
            rimetrum; </s>
            <s xml:id="echoid-s14967" xml:space="preserve"> circulus autem omnium figurarum rectilinearum ſibi iſo perime-
              <note symbol="b" position="left" xlink:label="note-348-05" xlink:href="note-348-05a" xml:space="preserve">13. hui{us}.
                <lb/>
              Quadratura
                <lb/>
              Hyppocratis
                <lb/>
              Chii.</note>
            trarum capaciſsimus eſt, quis non videt, quadratum illud circulo minus eſſe?</s>
            <s xml:id="echoid-s14968" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14969" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14970" xml:space="preserve">
              <emph style="sc">De</emph>
            Tetragoniſmo etiam Hippo cratis Chij nihil dicerem, niſi in eius de-
              <lb/>
            monſtrationè acumen ingenij lateret, quamuis metam propoſitam non attin-
              <lb/>
            gat. </s>
            <s xml:id="echoid-s14971" xml:space="preserve">Ita enim progreditur. </s>
            <s xml:id="echoid-s14972" xml:space="preserve">Sit quadrandus circulus AFBE, cuius diameter AB,
              <lb/>
              <note symbol="c" position="left" xlink:label="note-348-06" xlink:href="note-348-06a" xml:space="preserve">9. quinti.</note>
            ex qua deſcribatur quadratum ABCD, circa quod circulus deſcribatur
              <note symbol="d" position="left" xlink:label="note-348-07" xlink:href="note-348-07a" xml:space="preserve">31. tertii.</note>
            CD, cuius diameter BD, datum circulum AFBE, ſecet in E. </s>
            <s xml:id="echoid-s14973" xml:space="preserve">Ducta ergo recta AE,
              <lb/>
              <note symbol="e" position="left" xlink:label="note-348-08" xlink:href="note-348-08a" xml:space="preserve">ſchol. 26.
                <lb/>
              primi.</note>
            erit angulus AEB, in ſemicirculo rectus, ideoque perpendicularis AE, diui- det baſem B D, trianguli Iſoſcelis ABD, bifariam: </s>
            <s xml:id="echoid-s14974" xml:space="preserve">ac proinde E, centrum erit
              <lb/>
              <note symbol="f" position="left" xlink:label="note-348-09" xlink:href="note-348-09a" xml:space="preserve">ſchol. 27.
                <lb/>
              primi.</note>
            circuli ABCD. </s>
            <s xml:id="echoid-s14975" xml:space="preserve"> Et quia quadratum diametri BD, duplum eſt quadrati </s>
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