Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div1057" type="section" level="1" n="378">
          <p>
            <s xml:id="echoid-s17211" xml:space="preserve">
              <pb o="365" file="393" n="393" rhead="LIBER OCTAVVS."/>
            pla continuerunt proportionalia, quadratum videlicet FGHI, octogonum A-
              <lb/>
            KBCDA, & </s>
            <s xml:id="echoid-s17212" xml:space="preserve">quadratum ABCD; </s>
            <s xml:id="echoid-s17213" xml:space="preserve">quippe cum prædicta triangula ſint harum fi-
              <lb/>
            gurarum octauæ partes, vtliquet. </s>
            <s xml:id="echoid-s17214" xml:space="preserve">Octogonum igitur medio loco proportiona-
              <lb/>
            le eſt inter quadrata FGHI, ABCD, quod demonſtrandum erat.</s>
            <s xml:id="echoid-s17215" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1059" type="section" level="1" n="379">
          <head xml:id="echoid-head406" xml:space="preserve">THEOR. 14. PROPOS. 32.</head>
          <p>
            <s xml:id="echoid-s17216" xml:space="preserve">SI ex diametro quadrati detrahatur ipſius latus: </s>
            <s xml:id="echoid-s17217" xml:space="preserve">Reliqua linea erit latus
              <lb/>
            alterius quadrati, cuius diameter eſt linea, quæ relinquitur, ſi latus in-
              <lb/>
            uentum bis ex diametro prioris quadrati auferatur; </s>
            <s xml:id="echoid-s17218" xml:space="preserve">vel ſi idem latus
              <lb/>
            inuentum ex prioris quadrati latere tollatur.</s>
            <s xml:id="echoid-s17219" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17220" xml:space="preserve">
              <emph style="sc">Ex</emph>
            diametro BD, quadrati ABCD, abſcindatur recta BE, lateri AB, æqualis,
              <lb/>
            & </s>
            <s xml:id="echoid-s17221" xml:space="preserve">ex eadem diametro dematur reliqua DE, bis vſque ad F, ita vt EF, ſit ipſi DE,
              <lb/>
            æqualis: </s>
            <s xml:id="echoid-s17222" xml:space="preserve">vel (quod idem eſt) reliqua DE, ſiue EF, illi æqualis ex latere AB, hoc
              <lb/>
            eſt, ex BE, auferatur. </s>
            <s xml:id="echoid-s17223" xml:space="preserve">Dico DE, vel EF, latus eſſe quadrati, cuius diameter BF.
              <lb/>
            </s>
            <s xml:id="echoid-s17224" xml:space="preserve">Ductis enim per F, rectis GH, IK, parallelis ipſis AD, AB; </s>
            <s xml:id="echoid-s17225" xml:space="preserve"> erunt G K, H I,
              <note symbol="a" position="right" xlink:label="note-393-01" xlink:href="note-393-01a" xml:space="preserve">coroll. 4.
                <lb/>
              ſecundi.</note>
            diametrum quadrata. </s>
            <s xml:id="echoid-s17226" xml:space="preserve">Dico rectam EF, vel DE, æqualem eſ-
              <lb/>
              <figure xlink:label="fig-393-01" xlink:href="fig-393-01a" number="285">
                <image file="393-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/393-01"/>
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            ſe lateri B G, quadrati G K, cuius diameter B F, reliqua fuit
              <lb/>
            poſt detractionem D E, bis ex diametro B D. </s>
            <s xml:id="echoid-s17227" xml:space="preserve"> Quoniam
              <note symbol="b" position="right" xlink:label="note-393-02" xlink:href="note-393-02a" xml:space="preserve">ſchol. 47.
                <lb/>
              primi.</note>
            nim quadratum ex D F, duplum eſt quadrati ex I F, ſiue ex
              <lb/>
            A G, & </s>
            <s xml:id="echoid-s17228" xml:space="preserve">quadruplum quadrati ex E F; </s>
            <s xml:id="echoid-s17229" xml:space="preserve">ſi quadratum ex D
              <note symbol="c" position="right" xlink:label="note-393-03" xlink:href="note-393-03a" xml:space="preserve">ſchol. 4. ſe-
                <lb/>
              cundi.</note>
            ponatur 4. </s>
            <s xml:id="echoid-s17230" xml:space="preserve">erit quadratum ex A G, 2. </s>
            <s xml:id="echoid-s17231" xml:space="preserve">& </s>
            <s xml:id="echoid-s17232" xml:space="preserve">quadratum ex EF, 1.
              <lb/>
            </s>
            <s xml:id="echoid-s17233" xml:space="preserve">Ac proinde quadratum ex AG, duplum erit quadrati ex EF. </s>
            <s xml:id="echoid-s17234" xml:space="preserve">
              <lb/>
              <note symbol="d" position="right" xlink:label="note-393-04" xlink:href="note-393-04a" xml:space="preserve">ſchol. 47.
                <lb/>
              primi.</note>
            Eſt autem & </s>
            <s xml:id="echoid-s17235" xml:space="preserve">quadratum ex B F, quadrati ex B G, duplum. </s>
            <s xml:id="echoid-s17236" xml:space="preserve"> Igitur erit vt re- cta A G, ad rectam EF, ita recta BF, ad rectam BG; </s>
            <s xml:id="echoid-s17237" xml:space="preserve">quando quidem quadrata ea-
              <lb/>
              <note symbol="e" position="right" xlink:label="note-393-05" xlink:href="note-393-05a" xml:space="preserve">22. ſexti.</note>
            rum proportionalia ſunt, habentia nimirum proportionem duplam. </s>
            <s xml:id="echoid-s17238" xml:space="preserve">Capiatur
              <lb/>
            B L, ipſi BF, æqualis ita vt reliqua LA, reliquæ FE, æqualis ſit. </s>
            <s xml:id="echoid-s17239" xml:space="preserve">Erit igitur quoq;
              <lb/>
            </s>
            <s xml:id="echoid-s17240" xml:space="preserve">AG, ad AL, vt BF, ſiue BL, ad BG; </s>
            <s xml:id="echoid-s17241" xml:space="preserve">Et diuidendo GL, ad LA, vt GL, ad BG. </s>
            <s xml:id="echoid-s17242" xml:space="preserve">
              <note symbol="f" position="right" xlink:label="note-393-06" xlink:href="note-393-06a" xml:space="preserve">9. quinti.</note>
            circa AL, ſiue EF, & </s>
            <s xml:id="echoid-s17243" xml:space="preserve">BG, æquales ſunt. </s>
            <s xml:id="echoid-s17244" xml:space="preserve">quod erat oſtendendum.</s>
            <s xml:id="echoid-s17245" xml:space="preserve"/>
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        <div xml:id="echoid-div1061" type="section" level="1" n="380">
          <head xml:id="echoid-head407" xml:space="preserve">PROBL. 19. PROPOS. 33.</head>
          <p>
            <s xml:id="echoid-s17246" xml:space="preserve">OCTOGONVM æquilaterum, & </s>
            <s xml:id="echoid-s17247" xml:space="preserve">æquiangulum ad datam altitudi-
              <lb/>
            nem, latitudinemue conſtituere.</s>
            <s xml:id="echoid-s17248" xml:space="preserve"/>
          </p>
          <figure number="286">
            <image file="393-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/393-02"/>
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          <p>
            <s xml:id="echoid-s17249" xml:space="preserve">
              <emph style="sc">Sit</emph>
            ad altitudinem datam AB, conſtruendum
              <lb/>
            octogonum æquilaterum, & </s>
            <s xml:id="echoid-s17250" xml:space="preserve">æquiangulum. </s>
            <s xml:id="echoid-s17251" xml:space="preserve">De-
              <lb/>
            ſcripto ex AB, quadrato ABCD, ductiſque diame-
              <lb/>
            tris AC, BD, ſe in E, ſecantibus bifariam, & </s>
            <s xml:id="echoid-s17252" xml:space="preserve">ad an-
              <lb/>
            gulos rectos; </s>
            <s xml:id="echoid-s17253" xml:space="preserve">abſcindantur ad interuallum EA, ex
              <lb/>
            quatuor angulis quadratirectæ æquales A F, A G;
              <lb/>
            </s>
            <s xml:id="echoid-s17254" xml:space="preserve">DH, DI; </s>
            <s xml:id="echoid-s17255" xml:space="preserve">BK, BL; </s>
            <s xml:id="echoid-s17256" xml:space="preserve">CM, CN, iunganturq; </s>
            <s xml:id="echoid-s17257" xml:space="preserve">rectæ HK,
              <lb/>
            G M, L I, N F. </s>
            <s xml:id="echoid-s17258" xml:space="preserve">Dico octogonum FHKGMLIN,
              <lb/>
            eſſe æquilaterum, & </s>
            <s xml:id="echoid-s17259" xml:space="preserve">æquiangulum. </s>
            <s xml:id="echoid-s17260" xml:space="preserve">Quoniam
              <lb/>
            enim rectæ A H, A K; </s>
            <s xml:id="echoid-s17261" xml:space="preserve">B G, B M; </s>
            <s xml:id="echoid-s17262" xml:space="preserve">C L, C I; </s>
            <s xml:id="echoid-s17263" xml:space="preserve">
              <lb/>
            D F, D N, relinquuntur poſt </s>
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