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

Table of handwritten notes

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              <pb o="153" file="0173" n="173" rhead="LIBER II."/>
            nia quadrata, AS, ad omnia quadrata, FR, erunt vt omnia qua-
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              <note position="right" xlink:label="note-0173-01" xlink:href="note-0173-01a" xml:space="preserve">9. huius.</note>
            drata, Τ β, ad omnia quadrata, 4 Σ: </s>
            <s xml:id="echoid-s3614" xml:space="preserve">Eodem pacto oſtendemus om-
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            nia quadrata, AS, ad omnia quadrata, GQ, elle vt omnia quadra-
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            ta, Τ β, ad omnia quadrata, Λ Δ, & </s>
            <s xml:id="echoid-s3615" xml:space="preserve">tandem omnia quadrata, AS,
              <lb/>
            ad omnia quadrata, LP, eſſe vt omnia quadrata, Τ β, ad omnia
              <lb/>
            quadrata, Φ ℟, vnde, colligendo, omnia quadrata, AS, ad omnia
              <lb/>
            quadrata parallelogrammorum, DS, FR, GQ, LP, ideſt figurę
              <lb/>
            circumſcriptæ, erunt vt omnia quadrata, Τ β, ad omnia quadrata
              <lb/>
              <note position="right" xlink:label="note-0173-02" xlink:href="note-0173-02a" xml:space="preserve">Defin. @@
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              lib. 10</note>
            parallelogrammorum, Φ ℟, Λ Δ, 4 Σ, Υ β, ideſt ad omnia quadrata
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            figuræ circumicriptæ triangulo, & </s>
            <s xml:id="echoid-s3616" xml:space="preserve">Ζ β, ſed omnia quadrata, AS,
              <lb/>
            ad omnia quadrata figuræ circumſcriptæ triangulo, OES, oſtenſa
              <lb/>
            ſunt habere maiorem rationem, quam omnia quadrata, Τ β, ad om-
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            nia quadrata trianguli, & </s>
            <s xml:id="echoid-s3617" xml:space="preserve">Ζ β, ergo omnia quadrata, Τ β, ad om-
              <lb/>
            nia quadrata figuræ circumſcriptæ triangulo, & </s>
            <s xml:id="echoid-s3618" xml:space="preserve">Ζ β, habebunt ma-
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            iorem rationem, quam ad omnia quadrata trianguli, & </s>
            <s xml:id="echoid-s3619" xml:space="preserve">Ζ β, ergo
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            omnia quadrata figuræ circumſcriptæ triangulo, & </s>
            <s xml:id="echoid-s3620" xml:space="preserve">Ζ β, minora c-
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            runt omnibus quadratis trianguli, & </s>
            <s xml:id="echoid-s3621" xml:space="preserve">Ζ β, quod eſt abſurdum, non
              <lb/>
            ergo omnia quadrata, AS, ad maius, quam ſint omnia quadrata
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            trianguli, OES, habenteandem rationem, quam omnia quadrata,
              <lb/>
            Τ β, ad omnia quadrata trianguli, & </s>
            <s xml:id="echoid-s3622" xml:space="preserve">Ζ β.</s>
            <s xml:id="echoid-s3623" xml:space="preserve"/>
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            <s xml:id="echoid-s3624" xml:space="preserve">Dico autem neque ad minus eiuſdem habere eandem rationem,
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            ſint enim defectus adhuc omnia quadra a figurę, Ω, & </s>
            <s xml:id="echoid-s3625" xml:space="preserve">ſit circumſcri-
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            pta triangulo, OES, figura ex parallelogrammis, LP, GQ, FR,
              <lb/>
            DS, & </s>
            <s xml:id="echoid-s3626" xml:space="preserve">al@a inſcripta ex parallelogrammis, MQ, IR, HS, com-
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            poſita, ita vt omnia quadrata circumſcriptæ ſuperent omnia qua-
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            drata inſcriptę minori quantitate, quam ſint omnia quadrata, Ω, er-
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            go omnia quadrata trianguli, OES, ſuperabunt omnia quadrata in-
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            icriptæ figuræ multo minoriquan@tate, ſunt autem omnia quadra-
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            ta, AS, ad omnia quadrata trianguli, OES, detractis omnibus qua-
              <lb/>
            drat@s, Ω, vt omnia quadrata, Τ β, ad omnia quadrata trianguli, & </s>
            <s xml:id="echoid-s3627" xml:space="preserve">
              <lb/>
            Ζ β, ergo omnia quadrata, AS, ad omnia quadrata inſcriptæ figu-
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            ræ habebunt minorem rationem, quam omnia quadrata, Τ β, ad
              <lb/>
            omnia quadrata trianguli, & </s>
            <s xml:id="echoid-s3628" xml:space="preserve">Ζ β. </s>
            <s xml:id="echoid-s3629" xml:space="preserve">Diuidatur nunc pariter latus, & </s>
            <s xml:id="echoid-s3630" xml:space="preserve">
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            β, in punctis, ℟, Δ, Σ, ſimiliter ac, OS, diuiditur in, P, Q, R, & </s>
            <s xml:id="echoid-s3631" xml:space="preserve">
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            cæ@era, vt ſupra, fiant, vt habeamus figuram inſcriptam ex paralle-
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            logrammis, Τ Δ, 3 Σ, 6 β, compoſitam, oſtendemus igitur, vt ſu-
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            pra, omnia quadrata, AS, ad omnia quadrata figurę inſcriptę trian-
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            gulo, OES, eſſe vt omnia quadrata, Τ β, ad omnia quadrata figu-
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            ræ inſcriptæ triangulo, & </s>
            <s xml:id="echoid-s3632" xml:space="preserve">Ζ β, ſunt autem omnia quadrata, AS, ad
              <lb/>
            omnia quadrata figuræ inſcriptæ triangulo, OES, in minori ratio-
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            ne, quam ſint omnia quadrata, Τ β, ad omnia quadrata trianguli,
              <lb/>
            & </s>
            <s xml:id="echoid-s3633" xml:space="preserve">Ζ β, ergo omnia quadrata, Τ β, ad omnia quadrata figurę </s>
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