Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s14788" xml:space="preserve">
              <pb o="315" file="345" n="345" rhead="LIBER SEPTIMVS."/>
            cto baſis B C, adinteruallũ GK, arcus circuli deſcribatur, ſecabitis rectam AM,
              <lb/>
            in aliquo puncto, vtin L. </s>
            <s xml:id="echoid-s14789" xml:space="preserve">Sumpta autem LM, ipſi B D, æquali, ducantur rectæ
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              <figure xlink:label="fig-345-01" xlink:href="fig-345-01a" number="237">
                <image file="345-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/345-01"/>
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            DL, BM, quæ parallelæ inter ſe erunt; </s>
            <s xml:id="echoid-s14790" xml:space="preserve">ideo que parallelo grammum erit D M,
              <note symbol="a" position="right" xlink:label="note-345-01" xlink:href="note-345-01a" xml:space="preserve">33. primi.</note>
            triangulo ABC, æquale. </s>
            <s xml:id="echoid-s14791" xml:space="preserve">Dico hoc idem triangulo eſſe Iſoperimetrum, quod
              <lb/>
              <note symbol="b" position="right" xlink:label="note-345-02" xlink:href="note-345-02a" xml:space="preserve">ſchol. 41.
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              primi.</note>
            perſpicuum eſt ex conſtructione: </s>
            <s xml:id="echoid-s14792" xml:space="preserve">quippe cum D L, B M, vtraque æqualis ſit
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            ipſi G K, hoc eſt, ſemiſsi laterum A B, A C, ac proinde ambæ D L, B M, ſimul æ-
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            quales ambobus lateribus AB, AC, ſimul; </s>
            <s xml:id="echoid-s14793" xml:space="preserve">rectæ autem BD, LM, ſimul æquales
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            baſi BC. </s>
            <s xml:id="echoid-s14794" xml:space="preserve">Conſtructum ergo eſt parallelogrammum D M, non rectangulum æ-
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            quale, & </s>
            <s xml:id="echoid-s14795" xml:space="preserve">Iſoperimetrum triangulo ABC.</s>
            <s xml:id="echoid-s14796" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s14797" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi optes rectangulum eidem triangulo ABC, æquale, & </s>
            <s xml:id="echoid-s14798" xml:space="preserve">Iſoperime-
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            trum, ita agendum erit. </s>
            <s xml:id="echoid-s14799" xml:space="preserve">Erectis perpendicularibus B F, D F, erit
              <note symbol="c" position="right" xlink:label="note-345-03" xlink:href="note-345-03a" xml:space="preserve">ſchol. 41.
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              primi.</note>
            BE, triangulo æquale, ſed non Iſoperimetrum; </s>
            <s xml:id="echoid-s14800" xml:space="preserve"> quod BF, DE, minores ſintla- teribus AB, AC, ſed BD, EF, baſi BC, æquales: </s>
            <s xml:id="echoid-s14801" xml:space="preserve">ac proinde ambitus rectanguli
              <lb/>
              <note symbol="d" position="right" xlink:label="note-345-04" xlink:href="note-345-04a" xml:space="preserve">coroll. 19.
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              primi.</note>
            BE, ambitu trianguli ABC, minor; </s>
            <s xml:id="echoid-s14802" xml:space="preserve">ideoque ſi pro ducantur BF, DE, ad æqualita-
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            tem ſemiſsis laterum AB, AC, fiet quidem rectangulum triangulo ABC, Iſope-
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            rimetrum, ſed triangulo maius, cum ſuperet rectangulum BE. </s>
            <s xml:id="echoid-s14803" xml:space="preserve">Inuenta
              <note symbol="e" position="right" xlink:label="note-345-05" xlink:href="note-345-05a" xml:space="preserve">13. ſexti.</note>
            tem inter BF, BD, media proportionali N; </s>
            <s xml:id="echoid-s14804" xml:space="preserve"> erit quadratumrectæ N,
              <note symbol="f" position="right" xlink:label="note-345-06" xlink:href="note-345-06a" xml:space="preserve">17. ſexti.</note>
            lo BE, ideo que & </s>
            <s xml:id="echoid-s14805" xml:space="preserve">triangulo ABC, ęquale. </s>
            <s xml:id="echoid-s14806" xml:space="preserve"> Quia vero BF, BD, ſimul
              <note symbol="g" position="right" xlink:label="note-345-07" xlink:href="note-345-07a" xml:space="preserve">ſchol. 25.
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              quinti.</note>
            res ſunt, quam duplarectæ N; </s>
            <s xml:id="echoid-s14807" xml:space="preserve"> eſt que BM, maior quam BF, erunt BM, BD, ſi- mul multo maiores, quam dupla rectæ N. </s>
            <s xml:id="echoid-s14808" xml:space="preserve">Sumpta ergo QP, ipſi B D, & </s>
            <s xml:id="echoid-s14809" xml:space="preserve">P O,
              <lb/>
              <note symbol="h" position="right" xlink:label="note-345-08" xlink:href="note-345-08a" xml:space="preserve">19. primi.</note>
            ipſi BM, æquali, vt tota QO, duabus BD, BM, ſimul ſit æqualis; </s>
            <s xml:id="echoid-s14810" xml:space="preserve">erit quoque
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            QO, maior quam dupla rectæ N. </s>
            <s xml:id="echoid-s14811" xml:space="preserve">Secetur ergo QO, in R, ita vt N, ſit inter
              <note symbol="i" position="right" xlink:label="note-345-09" xlink:href="note-345-09a" xml:space="preserve">ſchol. 13.
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              ſexti.</note>
            gmenta Q R, RO, media proportionalis, perficiatur que rectangulum QS,
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            ſub ſegmentis QR, RO, comprehenſum. </s>
            <s xml:id="echoid-s14812" xml:space="preserve"> quod quadrato rectæ N, hoc
              <note symbol="k" position="right" xlink:label="note-345-10" xlink:href="note-345-10a" xml:space="preserve">17 ſexti.</note>
            rectangulo BE, vel triangulo ABC, æquale erit. </s>
            <s xml:id="echoid-s14813" xml:space="preserve">Dico idem eſſe triangulo ABC,
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            Iſoperimetrum. </s>
            <s xml:id="echoid-s14814" xml:space="preserve">Quoniam enim QR, RS, ſimul, id eſt, recta QO, æquales ſunt
              <lb/>
            rectis B D, B M, ſimul, ex conſtru ctione; </s>
            <s xml:id="echoid-s14815" xml:space="preserve">eruntreliquæ S T, T Q. </s>
            <s xml:id="echoid-s14816" xml:space="preserve">reliquis LM,
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            L D, æquales: </s>
            <s xml:id="echoid-s14817" xml:space="preserve">ideoque rectangulum QS, parallelogrammo BL, ac proinde & </s>
            <s xml:id="echoid-s14818" xml:space="preserve">
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            triangulo ABC, (cui parallelogrammum BK, Iſoperimetrum eſt oſtenſum) erit
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            Iſoperimetrum. </s>
            <s xml:id="echoid-s14819" xml:space="preserve">Dato igitur triangulo cuicunq; </s>
            <s xml:id="echoid-s14820" xml:space="preserve">parallelogrammum, &</s>
            <s xml:id="echoid-s14821" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14822" xml:space="preserve">con-
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            ſtituimus. </s>
            <s xml:id="echoid-s14823" xml:space="preserve">quod faciendum erat.</s>
            <s xml:id="echoid-s14824" xml:space="preserve"/>
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