Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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              <pb o="151" file="0171" n="171" rhead="LIBER II."/>
            drata, Τ β, ad omnia quadrata trianguli, & </s>
            <s xml:id="echoid-s3573" xml:space="preserve">Ζ β, ita non ſunt om-
              <lb/>
            nia quadrata, AS, ad omnia quadrata trianguli, OES, erunt igi-
              <lb/>
            tur ita omnia quadrata, AS, ad maius, vel ad minus omnibus qua-
              <lb/>
            dratis trianguli, OES, ſint exceſſus, vel defectus, omnia quadrata
              <lb/>
            figuræ planæ, Ω, diuidatur autem latus, OS, bifariam, in, Q, &</s>
            <s xml:id="echoid-s3574" xml:space="preserve">,
              <lb/>
            OQ, QS, bifariam in, P, R, & </s>
            <s xml:id="echoid-s3575" xml:space="preserve">ſic deinceps fiat, ita vt ductis per
              <lb/>
            puncta diuiſionum parallelis ipſi, ES, DR, CQ, BP, tandem de-
              <lb/>
            uentum ſit ad parallelogrammum, DS, cuius omnia quadrata, re-
              <lb/>
              <note position="right" xlink:label="note-0171-01" xlink:href="note-0171-01a" xml:space="preserve">Iux. prim.
                <lb/>
              10. Elem.</note>
            gula, ES, ſint minora omnibus quadratis figurę, Ω, per puncta au-
              <lb/>
            tem, in quibus dictæ parallelę ipſam, OE, ſecant, ducantur vſque
              <lb/>
            ad proximas parallelas æquidiſtantes lateribus, AE, OS, ipſę, LN,
              <lb/>
            GK, EM, erit igitur triangulo, OES, circumſcripta figura quæ-
              <lb/>
              <figure xlink:label="fig-0171-01" xlink:href="fig-0171-01a" number="99">
                <image file="0171-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0171-01"/>
              </figure>
            dam cõpoſita ex
              <lb/>
            parallelogrãmo,
              <lb/>
            LP, GQ, FR,
              <lb/>
            DS, & </s>
            <s xml:id="echoid-s3576" xml:space="preserve">alia in-
              <lb/>
            ſcripta compoſi-
              <lb/>
            ta ex parallelo-
              <lb/>
            grammis, 9 Q, I
              <lb/>
            R, HS, ita vt
              <lb/>
            omnia quadrata
              <lb/>
            figuræ circũſcri-
              <lb/>
            ptę, regula, ES,
              <lb/>
            excedant omnia
              <lb/>
            quadrata inſcri-
              <lb/>
            ptæ, regula ea-
              <lb/>
            dẽ, minori quan-
              <lb/>
            titate, quam ſint
              <lb/>
            omnia quadrata figuræ, Ω; </s>
            <s xml:id="echoid-s3577" xml:space="preserve">nam in parallelogrammo, DS, recta,
              <lb/>
            HM, diuidit omnia quadrata, DS, in omnia quadrata, DM, in
              <lb/>
            omnia quadrata, HS, & </s>
            <s xml:id="echoid-s3578" xml:space="preserve">in rectangula bis ſub, DM, MR, veluti
              <lb/>
            punctum, H, diuidit quadratum, DR, in quadrat. </s>
            <s xml:id="echoid-s3579" xml:space="preserve">DH, quad at-
              <lb/>
            HR, & </s>
            <s xml:id="echoid-s3580" xml:space="preserve">rectangulum bis ſub, DHR, ſiue ex 23. </s>
            <s xml:id="echoid-s3581" xml:space="preserve">ſeq. </s>
            <s xml:id="echoid-s3582" xml:space="preserve">ab hac inde-
              <lb/>
            pendente, & </s>
            <s xml:id="echoid-s3583" xml:space="preserve">ideò omnia quadrat. </s>
            <s xml:id="echoid-s3584" xml:space="preserve">DS, excedunt omnia quadrata,
              <lb/>
            HS, omnibus quadratis, DM, & </s>
            <s xml:id="echoid-s3585" xml:space="preserve">rectangulis bis ſub, DM, MR,
              <lb/>
            eodem pacto oſtendemus omnia quadrata, FR, excedere omnia
              <lb/>
            quadrata, IR, omnibus quadratis, FK, & </s>
            <s xml:id="echoid-s3586" xml:space="preserve">rectangulis bis ſub, FK,
              <lb/>
            KQ, & </s>
            <s xml:id="echoid-s3587" xml:space="preserve">ſic omnia quadrata, GQ, excedere omnia quadrata, 9 Q,
              <lb/>
            omnibus quadratis, GN, cum rectangulis bis ſub, GN, NP, & </s>
            <s xml:id="echoid-s3588" xml:space="preserve">in
              <lb/>
            figura circumſcripta ſuperſunt adhuc omnia quadrata, LP, porro ſi
              <lb/>
            hos exceſſus ſimul colligamus fient omnia quadrata, DS, nam ſi
              <lb/>
            omnia quadrata, LP, vel, 9 Q, iunxeris omnibus quadratis, </s>
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