Clavius, Christoph, Geometria practica

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          <pb o="328" file="358" n="358" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s15342" xml:space="preserve">
              <emph style="sc">Vt</emph>
            quoque ſine vllo labore dato cuicunq; </s>
            <s xml:id="echoid-s15343" xml:space="preserve">circulo quadratum æquale ex-
              <lb/>
            hibeamus, vtendum erit hoc artificio. </s>
            <s xml:id="echoid-s15344" xml:space="preserve">Inuento ſemellatere quadrati alicui cir-
              <lb/>
              <note position="left" xlink:label="note-358-01" xlink:href="note-358-01a" xml:space="preserve">Facilis inuen-
                <lb/>
              tio quadrati
                <lb/>
              circulo æqua-
                <lb/>
              lis.</note>
            culo æqualis, vt paulò ante docuimus, conſtruemus figuram ad quadrandos
              <lb/>
            alios circulos quo ſcunque accommodatiſsimam, hoc modo. </s>
            <s xml:id="echoid-s15345" xml:space="preserve">Detur circulus
              <lb/>
            A B C, diametri A C, ſitque A B, media proportionalis inter ſemidiametrum,
              <lb/>
            & </s>
            <s xml:id="echoid-s15346" xml:space="preserve">rectam ſemicircumferentiæ æqualem inuentam ex præcedenti figura, ita vt
              <lb/>
            quadratum rectæ AB, circulo diametri A C, ſit æquale: </s>
            <s xml:id="echoid-s15347" xml:space="preserve"> accommodetur AB,
              <note symbol="a" position="left" xlink:label="note-358-02" xlink:href="note-358-02a" xml:space="preserve">1. quinti.</note>
            circulo, quæ certius applicabitur, ſi fortè circinus ex A, ad interuallũ datæ AB,
              <lb/>
            deſcriptus nimis oblique peripheriam A B C, ſecet in B, hoc modo. </s>
            <s xml:id="echoid-s15348" xml:space="preserve">Duabus
              <lb/>
            rectis, nimirum diametro AC, & </s>
            <s xml:id="echoid-s15349" xml:space="preserve">lateri AB, quadrati inuento reperiatur tertia ꝓ-
              <lb/>
            portionalis AD. </s>
            <s xml:id="echoid-s15350" xml:space="preserve">Perpendicularis namque DB, cadet in punctum B, in quod la-
              <lb/>
              <note symbol="b" position="left" xlink:label="note-358-03" xlink:href="note-358-03a" xml:space="preserve">coroll. 8.
                <lb/>
              ſexti.</note>
            tus inuentum duci debet: </s>
            <s xml:id="echoid-s15351" xml:space="preserve"> propterea quod tres rectæ AC, AB, AD, ſunt conti- nuè proportionales, quemadmodum recta A C, latus quadrati inuentum, & </s>
            <s xml:id="echoid-s15352" xml:space="preserve">
              <lb/>
            AD, continuam ſeruant proportionem, ex conſtructione. </s>
            <s xml:id="echoid-s15353" xml:space="preserve">Liquet autem inter
              <lb/>
            AC, AD, vnam tantum poſſe eſſe mediam proportionalem. </s>
            <s xml:id="echoid-s15354" xml:space="preserve">Hac figura extru-
              <lb/>
            cta, dicto citius quemcunque circulum quadrabimus. </s>
            <s xml:id="echoid-s15355" xml:space="preserve">Sinamque diametro da-
              <lb/>
            ti circulirectam æqualem abſcindemus A F, circa quam ſemicirculus deſcriba-
              <lb/>
            tur, reſecabit is ex recta AB, latus AE, cuius quadratum circulo dato eſt æqua-
              <lb/>
              <figure xlink:label="fig-358-01" xlink:href="fig-358-01a" number="248">
                <image file="358-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/358-01"/>
              </figure>
            le. </s>
            <s xml:id="echoid-s15356" xml:space="preserve">Quia enim angulus externus AEF, inter-
              <lb/>
            no ABC, æqualis eſt: </s>
            <s xml:id="echoid-s15357" xml:space="preserve"> quod vterque in
              <note symbol="c" position="left" xlink:label="note-358-04" xlink:href="note-358-04a" xml:space="preserve">31. tertii.</note>
            circulo rectus ſit; </s>
            <s xml:id="echoid-s15358" xml:space="preserve"> erunt E F, B C, parallelæ;</s>
            <s xml:id="echoid-s15359" xml:space="preserve">
              <note symbol="d" position="left" xlink:label="note-358-05" xlink:href="note-358-05a" xml:space="preserve">28. primi.</note>
            ideoque triangula AEF, ABC, æquiangula. </s>
            <s xml:id="echoid-s15360" xml:space="preserve">
              <note symbol="e" position="left" xlink:label="note-358-06" xlink:href="note-358-06a" xml:space="preserve">4. ſexti.</note>
            Igitur erit CA, ad AB, vt FA, ad AE; </s>
            <s xml:id="echoid-s15361" xml:space="preserve">Et permu-
              <lb/>
            tando CA, ad FA, vt AB, ad AE. </s>
            <s xml:id="echoid-s15362" xml:space="preserve"> Ideoque
              <note symbol="f" position="left" xlink:label="note-358-07" xlink:href="note-358-07a" xml:space="preserve">22. ſexti.</note>
            rit quoque quadratum ex AC, ad quadratum
              <lb/>
            ex A F: </s>
            <s xml:id="echoid-s15363" xml:space="preserve"> hoc eſt, vt circulus diametri A C,
              <note symbol="g" position="left" xlink:label="note-358-08" xlink:href="note-358-08a" xml:space="preserve">2. duodec.</note>
            circulum diametri A F, vt quadratum ex A B,
              <lb/>
            ad quadratum ex AE. </s>
            <s xml:id="echoid-s15364" xml:space="preserve">Eſt autem circulus dia-
              <lb/>
            metri A C, quadrato ex A B, per conſtru ctio-
              <lb/>
            nem, ęquale. </s>
            <s xml:id="echoid-s15365" xml:space="preserve"> Igitur & </s>
            <s xml:id="echoid-s15366" xml:space="preserve">circulus diametri
              <note symbol="h" position="left" xlink:label="note-358-09" xlink:href="note-358-09a" xml:space="preserve">14. quinti.</note>
            quadrato ex AE, æquale erit. </s>
            <s xml:id="echoid-s15367" xml:space="preserve">Ita quo que qua-
              <lb/>
            dratum rectæ A G, circulo diametri A H, erit
              <lb/>
            ęquale. </s>
            <s xml:id="echoid-s15368" xml:space="preserve">Et ſic de cęteris.</s>
            <s xml:id="echoid-s15369" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15370" xml:space="preserve">
              <emph style="sc">Iam</emph>
            verò quoniam lib. </s>
            <s xml:id="echoid-s15371" xml:space="preserve">4. </s>
            <s xml:id="echoid-s15372" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s15373" xml:space="preserve">6. </s>
            <s xml:id="echoid-s15374" xml:space="preserve">propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s15375" xml:space="preserve">
              <note position="left" xlink:label="note-358-10" xlink:href="note-358-10a" xml:space="preserve">Facilis inuen-
                <lb/>
              tio quadrati-
                <lb/>
              circulo æqua-
                <lb/>
              lis ex Archi-
                <lb/>
              mede.</note>
            3. </s>
            <s xml:id="echoid-s15376" xml:space="preserve">ex Archimede demonſtrauimus, quadratũ
              <lb/>
            diametri ad circulum habere ferme propor-
              <lb/>
            tionem, quam 14. </s>
            <s xml:id="echoid-s15377" xml:space="preserve">ad 11. </s>
            <s xml:id="echoid-s15378" xml:space="preserve">ſi quis volet ſecundũ
              <lb/>
            hanc proportionem reperire quadratum cir-
              <lb/>
            culo æquale; </s>
            <s xml:id="echoid-s15379" xml:space="preserve">diuidenda erit recta A C, in 14.
              <lb/>
            </s>
            <s xml:id="echoid-s15380" xml:space="preserve">partes æquales, & </s>
            <s xml:id="echoid-s15381" xml:space="preserve">ex vndecima parte D, (ita vt AD, contineat partes 11. </s>
            <s xml:id="echoid-s15382" xml:space="preserve">& </s>
            <s xml:id="echoid-s15383" xml:space="preserve">DC,
              <lb/>
            3.) </s>
            <s xml:id="echoid-s15384" xml:space="preserve">ex citanda perpendicularis DB, vſque ad circumferentiam circa A C, deſcri-
              <lb/>
            ptam. </s>
            <s xml:id="echoid-s15385" xml:space="preserve">Recta enim enim ducta A B, latus erit quadrati circulo diametri A C, æ-
              <lb/>
              <note symbol="i" position="left" xlink:label="note-358-11" xlink:href="note-358-11a" xml:space="preserve">coroll. 2.
                <lb/>
              ſexti.</note>
            qualis. </s>
            <s xml:id="echoid-s15386" xml:space="preserve"> Cum enim tres rectæ AC, AB, AD, ſint continue proportionales; </s>
            <s xml:id="echoid-s15387" xml:space="preserve"> erit quadratum ex A C, ad quadratum ex A B, vt A C, ad A D, videlicet vt 14. </s>
            <s xml:id="echoid-s15388" xml:space="preserve">ad 11.
              <lb/>
            </s>
            <s xml:id="echoid-s15389" xml:space="preserve">
              <note symbol="k" position="left" xlink:label="note-358-12" xlink:href="note-358-12a" xml:space="preserve">coroll. 20.
                <lb/>
              ſexti.</note>
            Cum ergo etiam ſit, vt diximus, quadratum diametriad circulum, vt 14. </s>
            <s xml:id="echoid-s15390" xml:space="preserve">ad 11.
              <lb/>
            </s>
            <s xml:id="echoid-s15391" xml:space="preserve">ferme: </s>
            <s xml:id="echoid-s15392" xml:space="preserve"> erit quadratum ex AC, ad quadratum ex AB, vt ad circulum
              <note symbol="l" position="left" xlink:label="note-358-13" xlink:href="note-358-13a" xml:space="preserve">11. quinti.</note>
            AC. </s>
            <s xml:id="echoid-s15393" xml:space="preserve"> Igitur quadratum ex AB, circulo diametri A C, æquale erit. </s>
            <s xml:id="echoid-s15394" xml:space="preserve">Quod ſi
              <note symbol="m" position="left" xlink:label="note-358-14" xlink:href="note-358-14a" xml:space="preserve">9. quinti.</note>
            </s>
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