Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s14975" xml:space="preserve">
              <pb o="319" file="349" n="349" rhead="LIBER SEPTIMVS."/>
            tri AB; </s>
            <s xml:id="echoid-s14976" xml:space="preserve"> eſt que vt quadratum BD, ad quadratum AB, ita circulus ABCD,
              <note symbol="a" position="right" xlink:label="note-349-01" xlink:href="note-349-01a" xml:space="preserve">2. duodec.</note>
            circulum AFBE: </s>
            <s xml:id="echoid-s14977" xml:space="preserve">erit quo que circulus circuli duplus; </s>
            <s xml:id="echoid-s14978" xml:space="preserve">& </s>
            <s xml:id="echoid-s14979" xml:space="preserve">ſemicirculus BAD,
              <lb/>
            ſemicirculi AFB; </s>
            <s xml:id="echoid-s14980" xml:space="preserve">ideo que ſemiſsis ſemicir culi BAD: </s>
            <s xml:id="echoid-s14981" xml:space="preserve">id eſt, quadrãs ABE, (eſt enim ABE, quadrans, ob angulum rectum in centro E,) ſemicirculo AFB, æqua-
              <lb/>
            lis. </s>
            <s xml:id="echoid-s14982" xml:space="preserve">Dempto igitur communi ſegmento AGB, reliquum triangulum AFB, reli-
              <lb/>
            quæ Lunulæ A F B G A, æquale erit: </s>
            <s xml:id="echoid-s14983" xml:space="preserve">ac proinde ſi triangulo fiat quadratum æ-
              <lb/>
            quale erit idem hoc quadratum Lunulæ AFBGA, æquale. </s>
            <s xml:id="echoid-s14984" xml:space="preserve">Atque ita quadrata
              <lb/>
            eſt Lunula AFBGA.</s>
            <s xml:id="echoid-s14985" xml:space="preserve"/>
          </p>
          <figure number="240">
            <image file="349-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/349-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s14986" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            ſitrecta HI, diametri AB, dupla, circa quam ſemicirculo deſcripto,
              <lb/>
            aptentur in eo tresrectæ ſemidiametro huius circuli, hoc eſt, diametro A B, æ-
              <lb/>
            quales HK, KL, LI, continentes ſemiſſem hexagoni: </s>
            <s xml:id="echoid-s14987" xml:space="preserve"> cum latus hexagoni
              <note symbol="b" position="right" xlink:label="note-349-02" xlink:href="note-349-02a" xml:space="preserve">coroll. 15.
                <lb/>
              quarti.</note>
            ſemidiametro æquale. </s>
            <s xml:id="echoid-s14988" xml:space="preserve">Deſcriptis autem circa illas tres rectas ſemicirculis HMK,
              <lb/>
            KOL, LQI, qui ſemicirculo AFB, æquales ſunt, propter diametros æquales;
              <lb/>
            </s>
            <s xml:id="echoid-s14989" xml:space="preserve"> quoniam quadratum rectæ HI, quadrati rectæ HK, quadruplum eſt. </s>
            <s xml:id="echoid-s14990" xml:space="preserve">quod
              <note symbol="c" position="right" xlink:label="note-349-03" xlink:href="note-349-03a" xml:space="preserve">ſchol. 4. ſe-
                <lb/>
              cundi.</note>
            tus lateris ſit duplum: </s>
            <s xml:id="echoid-s14991" xml:space="preserve"> erit quo que circulus diametri H I, circuli diametri HK, quadruplus, & </s>
            <s xml:id="echoid-s14992" xml:space="preserve">ſemicirculus HKLI, ſemicirculis HMK, KOL, LQI, AFB, æ-
              <lb/>
              <note symbol="d" position="right" xlink:label="note-349-04" xlink:href="note-349-04a" xml:space="preserve">2. duodec.</note>
            qualis erit: </s>
            <s xml:id="echoid-s14993" xml:space="preserve">demptiſque ſegmentis communibus HNK, KPL, LRI, reliquum
              <lb/>
            trapezium HKLI, æquale erit tribus Lunulis HNKM, KPLO, LRIQ, vna cum
              <lb/>
            ſemicirculo AFB. </s>
            <s xml:id="echoid-s14994" xml:space="preserve">Si igitur tres illæ Lunulæ quadrentur, vt traditum eſt, & </s>
            <s xml:id="echoid-s14995" xml:space="preserve">tri-
              <lb/>
            bus illis quadratis auferatur ex trapezio rectilineum æquale, hoc eſt,
              <note symbol="e" position="right" xlink:label="note-349-05" xlink:href="note-349-05a" xml:space="preserve">ſchol. 45.
                <lb/>
              primi.</note>
            ratur exceſſus trapezii ſuper tria illa quadrata; </s>
            <s xml:id="echoid-s14996" xml:space="preserve">erit exceſſus hic rectilinea figura
              <lb/>
            ſemicirculo AFB, æqualis. </s>
            <s xml:id="echoid-s14997" xml:space="preserve"> Si igitur huic figuræ quadratum fiat æquale,
              <note symbol="f" position="right" xlink:label="note-349-06" xlink:href="note-349-06a" xml:space="preserve">14. ſecundi.</note>
            idem hoc quadratum ſemicirculo A F B, æquale, & </s>
            <s xml:id="echoid-s14998" xml:space="preserve">quadratum ex illius qua-
              <lb/>
            drati diametro deſcriptum toti circulo AFBE, æquale. </s>
            <s xml:id="echoid-s14999" xml:space="preserve"> quod tam
              <note symbol="g" position="right" xlink:label="note-349-07" xlink:href="note-349-07a" xml:space="preserve">ſchol. 45.
                <lb/>
              primi.</note>
            quadrati duplum ſit, quam circulus ſemicirculi. </s>
            <s xml:id="echoid-s15000" xml:space="preserve">Quadratus ergo circulus eſt.</s>
            <s xml:id="echoid-s15001" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15002" xml:space="preserve">
              <emph style="sc">Hæc</emph>
            eſt quadratura Hyppocratis, acuta quidem, quod Lunulam AGBF,
              <lb/>
              <note position="right" xlink:label="note-349-08" xlink:href="note-349-08a" xml:space="preserve">Fallacia qua-
                <lb/>
              draturæ Hip-
                <lb/>
              pocratis.</note>
            verè quadrauerit, vitio ſa autem, quod tres Lunulas HNKM, KPLO, LRIQ,
              <lb/>
            quadratas à ſe eſſe arbitratur, quod verum non eſt. </s>
            <s xml:id="echoid-s15003" xml:space="preserve">Solum enim ex eius demon-
              <lb/>
            ſtratione Lunula ea quadratur, cuius inferior peripheria eſt quarta pars peri-
              <lb/>
            pheriæ alicuius circuli, ſuperior autem ſemicirculus alterius circuli, qualis fuit
              <lb/>
            Lunula AGBF. </s>
            <s xml:id="echoid-s15004" xml:space="preserve">Nam AGB, quarta pars eſt circumferentiæ ABCD, & </s>
            <s xml:id="echoid-s15005" xml:space="preserve">AFB, ſe-
              <lb/>
            miſsis peripheriæ AFBE. </s>
            <s xml:id="echoid-s15006" xml:space="preserve">At eiuſmodi non ſunttres aliæ Lunulæ, quippe cum
              <lb/>
            earum peripheriæ inferiores HNK, KPL, LRI, ſint ſextæ partes totius circumfe-
              <lb/>
              <note position="right" xlink:label="note-349-09" xlink:href="note-349-09a" xml:space="preserve">Quid deſide-
                <lb/>
              retur in Hip-
                <lb/>
              pocratis qua-
                <lb/>
              dratura.</note>
            rentiæ, quamuis peripheriæ ſuperiores ſint ſemicirculi, vt in illa: </s>
            <s xml:id="echoid-s15007" xml:space="preserve">quæ nondum
              <lb/>
            ſunt quadratæ. </s>
            <s xml:id="echoid-s15008" xml:space="preserve">Quod ſi inuenta eſſet ars quadran di huiuſmodi Lunulas, veriſ-
              <lb/>
            ſimè quo que quadraretur circulus, ſine inuentione lineæ rectæ circuli periphe-
              <lb/>
            riæ æqualis. </s>
            <s xml:id="echoid-s15009" xml:space="preserve">quæ ſanè res foret præclara.</s>
            <s xml:id="echoid-s15010" xml:space="preserve"/>
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