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

Table of contents

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[71.] THEOREMA IX. PROPOS. XII.
Page: 47 (27)
[72.] COROLLARIV M.
Page: 48 (28)
[73.] THEOREMA X. PROPOS. XIII.
Page: 48 (28)
[74.] THEOREMA XI. PROPOS. XIV.
Page: 50 (30)
[75.] THEOREMA XII. PROPOS. XV.
Page: 51 (31)
[76.] SCHOLIVM.
Page: 52 (32)
[77.] THEOREMA XIII. PROPOS. XVI.
Page: 52 (32)
[78.] COROLLARIVM.
Page: 52 (32)
[79.] THEOREMA XIV. PROPOS. XVII.
Page: 53 (33)
[80.] COROLLARIVM.
Page: 53 (33)
[81.] THEOREMA XV. PROPOS. XVIII.
Page: 54 (34)
[82.] COROLLARIVM.
Page: 55 (35)
[83.] THEOREMA XVI. PROPOS. XIX.
Page: 55 (35)
[84.] COROLLARIVMI.
Page: 57 (37)
[85.] COROLLARIVM II.
Page: 57 (37)
[86.] THEOREMA XVII. PROPOS. XX.
Page: 58 (38)
[87.] THE OREMA XVIII. PROPOS. XXI.
Page: 58 (38)
[88.] COROLLARIVM.
Page: 59 (39)
[89.] THEOREMA XIX. PROPOS. XXII.
Page: 60 (40)
[90.] COROLLARIVM I.
Page: 62 (42)
[91.] COROLLARIVM II.
Page: 62 (42)
[92.] LEMMA PRO ANTECED. PROP.
Page: 62 (42)
[93.] THEOREMA XX. PROPOS. XXIII.
Page: 63 (43)
[94.] COROLLARIVM.
Page: 63 (43)
[95.] THEOREMA XXI. PROPOS. XXIV.
Page: 63 (43)
[96.] COROLLARIVM.
Page: 65 (45)
[97.] THEOREMA XXII. PROPOS. XXV.
Page: 65 (45)
[98.] COROLLARIVM.
Page: 66 (46)
[99.] THEOREMA XXIII. PROPOS. XXVI.
Page: 67 (47)
[100.] THEOREMA XXIV. PROPOS XXVII.
Page: 69 (49)
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            nia quadrata, AS, ad omnia quadrata, FR, erunt vt omnia qua-
              <lb/>
              <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-
              <lb/>
            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-
              <lb/>
            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
              <lb/>
            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
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            ergo omnia quadrata, AS, ad maius, quam ſint omnia quadrata
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            trianguli, OES, habenteandem rationem, quam omnia quadrata,
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            Τ β, ad omnia quadrata trianguli, & </s>
            <s xml:id="echoid-s3622" xml:space="preserve">Ζ β.</s>
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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,
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            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-
              <lb/>
            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-
              <lb/>
            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>
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            β, in punctis, ℟, Δ, Σ, ſimiliter ac, OS, diuiditur in, P, Q, R, & </s>
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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,
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            & </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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