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

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              <pb o="152" file="0172" n="172" rhead="GEOMETRIÆ"/>
            & </s>
            <s xml:id="echoid-s3589" xml:space="preserve">rectangulis bis ſub, GN, NP, fient omnia quadrata, GQ, hęc
              <lb/>
            ſi iunxeris omnibus quadratis, FK, cum rectangulis bis ſub, FK, K
              <lb/>
            Q, fient omnia quadrata, FR, quę tandem ſi iunxeris omnibus qua-
              <lb/>
            dratis, DM, cum rectangulis bis ſub, DM, MR, fient omnia qua-
              <lb/>
            drata, DS, quę cum ſint minora omnibus quadratis figurę, Ω, hinc
              <lb/>
            figuræ circumſcriptæ omnia quadrata excedunt omnia quadrata in-
              <lb/>
            ſcriptę minori quantitate, quam ſint omnia quadrata, Ω, & </s>
            <s xml:id="echoid-s3590" xml:space="preserve">ideò ex-
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            cedunt omnia quadrata trianguli, OES, multò minon quantitate:
              <lb/>
            </s>
            <s xml:id="echoid-s3591" xml:space="preserve">Quia ergo omnia quadrata, AS, ad omnia quadrata trianguli, OE
              <lb/>
            S, cum omnibus quadratis, Ω, erant vt omnia quadrata, Τ β, ad om-
              <lb/>
            nia quadrata trianguli, & </s>
            <s xml:id="echoid-s3592" xml:space="preserve">Ζ β, hinc omnia quadrata, AS, ad om-
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            nia quadrata figurę circumſcriptę triangulo, OES, habebunt maio-
              <lb/>
            rem rationem, quam omnia quadrata, Τ β, ad omnia quadrata tri-
              <lb/>
            anguli, & </s>
            <s xml:id="echoid-s3593" xml:space="preserve">Ζ β.</s>
            <s xml:id="echoid-s3594" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3595" xml:space="preserve">Nunc diuidatur ſimiliter, & </s>
            <s xml:id="echoid-s3596" xml:space="preserve">β in punctis, ℟, Δ Σ, ac, OS, in
              <lb/>
            punctis, P, Q, R, & </s>
            <s xml:id="echoid-s3597" xml:space="preserve">per puncta, ℟ Δ Σ, parallelæ ipſi, Ζ β, du-
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            cantur, ℟ V, Δ Χ, Σ Υ, ſecantes, & </s>
            <s xml:id="echoid-s3598" xml:space="preserve">Ζ, in punctis, r, 3, 6, per quę
              <lb/>
            vſque ad proximas parallelas ipſis, & </s>
            <s xml:id="echoid-s3599" xml:space="preserve">β, ΤΖ, æquidiſtantes ducan-
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            tur, Φ Γ, Λ 3, 46, vt triangulo, & </s>
            <s xml:id="echoid-s3600" xml:space="preserve">Ζ β, ſit circumſcripta figura ex
              <lb/>
              <figure xlink:label="fig-0172-01" xlink:href="fig-0172-01a" number="100">
                <image file="0172-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0172-01"/>
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            parallelogrãmis,
              <lb/>
            Φ ℟, Δ Δ, 4 Σ, Υ
              <lb/>
            β, cõpoſita, quia
              <lb/>
            ergo, vt, OS, ad,
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            SR, ita eſt, & </s>
            <s xml:id="echoid-s3601" xml:space="preserve">β,
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            ad, β Σ, vt au-
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            tem, OS, ad, S
              <lb/>
            R, ita ſunt om-
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              <note position="left" xlink:label="note-0172-01" xlink:href="note-0172-01a" xml:space="preserve">10. huius.</note>
            nia quadrata, A
              <lb/>
            S, ad omnia qua-
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            drata, DS, & </s>
            <s xml:id="echoid-s3602" xml:space="preserve">
              <lb/>
            vt, & </s>
            <s xml:id="echoid-s3603" xml:space="preserve">β, ad, β
              <lb/>
            Σ, rta ſunt omnia
              <lb/>
            quadrata, Τ β, ad
              <lb/>
            omnia quadrata,
              <lb/>
            Υ β, ergo omnia
              <lb/>
            quadrata, AS, ad omnia quadrata, DS, ſunt vt omnia quadrata,
              <lb/>
            Τ β, ad omnia quadrata, Υ β, quia verò omnia quadrata, Υ β, ad
              <lb/>
            omnia quadrata, 6 β, .</s>
            <s xml:id="echoid-s3604" xml:space="preserve">@. </s>
            <s xml:id="echoid-s3605" xml:space="preserve">ad omnia quadrata, 4 Σ, ſunt vt quadra-
              <lb/>
              <note position="left" xlink:label="note-0172-02" xlink:href="note-0172-02a" xml:space="preserve">9. huius.</note>
            tum, Ζ β, ad quadratum, 7 β, .</s>
            <s xml:id="echoid-s3606" xml:space="preserve">@. </s>
            <s xml:id="echoid-s3607" xml:space="preserve">ad quadratum, 6 Σ, .</s>
            <s xml:id="echoid-s3608" xml:space="preserve">@. </s>
            <s xml:id="echoid-s3609" xml:space="preserve">vt quadra-
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            tum, β &</s>
            <s xml:id="echoid-s3610" xml:space="preserve">, ad quadratum, & </s>
            <s xml:id="echoid-s3611" xml:space="preserve">Σ, .</s>
            <s xml:id="echoid-s3612" xml:space="preserve">@. </s>
            <s xml:id="echoid-s3613" xml:space="preserve">vt quadrarum, SO, ad quadra-
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            tum, OR, ideſt vt quadratum, ES, ad quadratum, HR, ideſt, vt
              <lb/>
            omnia quadrata, DS, ad omnia quadrata, FR, ergo ex æquali </s>
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