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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              <pb o="129" file="0149" n="149" rhead="LIBER II."/>
            veluti, BE, ID, iunctæ ſunt in linea, QL, &</s>
            <s xml:id="echoid-s3007" xml:space="preserve">, Σ 2, 3 Λ, in linea,
              <lb/>
            Τ Γ,) ergo quę tangentibus dictis æquidiſtant in ſigur s, KQM, Π
              <lb/>
            Τ Ω, & </s>
            <s xml:id="echoid-s3008" xml:space="preserve">diuidunt incidentes, KM, ΠΩ, ſimiliter ad eandem par-
              <lb/>
            tem, & </s>
            <s xml:id="echoid-s3009" xml:space="preserve">iacent inter ipſas incidentes, & </s>
            <s xml:id="echoid-s3010" xml:space="preserve">circuitum figurarum ad ean-
              <lb/>
            dem partem eodem ordine ſumptæ, ſunt vt ipſæ incidentes, ergo fi-
              <lb/>
            gurę, KQM, ΠΤΩ, ſunt ſimiles, & </s>
            <s xml:id="echoid-s3011" xml:space="preserve">earundem homologarum re-
              <lb/>
              <note position="right" xlink:label="note-0149-01" xlink:href="note-0149-01a" xml:space="preserve">Defin. 10.
                <lb/>
              lib. 1.</note>
            gulæ eædem tangentes, & </s>
            <s xml:id="echoid-s3012" xml:space="preserve">earum incidentes ipſæ, KM, Π Ω.</s>
            <s xml:id="echoid-s3013" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div325" type="section" level="1" n="200">
          <head xml:id="echoid-head215" xml:space="preserve">B. SECTIO SECVNDA.</head>
          <p>
            <s xml:id="echoid-s3014" xml:space="preserve">PRoducantur nunc ipſę, KM, ΠΩ, indefinitè verſus puncta, M,
              <lb/>
            Ω, & </s>
            <s xml:id="echoid-s3015" xml:space="preserve">ab ipſis productis ſumantur partes æquales, MP, ipſi, K
              <lb/>
            M, &</s>
            <s xml:id="echoid-s3016" xml:space="preserve">, ω &</s>
            <s xml:id="echoid-s3017" xml:space="preserve">, ipſi, ΠΩ, & </s>
            <s xml:id="echoid-s3018" xml:space="preserve">per puncta, P, &</s>
            <s xml:id="echoid-s3019" xml:space="preserve">, ducantur dictis tangen-
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            tibus parallelę, ZP, ℟ &</s>
            <s xml:id="echoid-s3020" xml:space="preserve">, quoniam ergo, KM, ΠΩ, ſunt inciden-
              <lb/>
              <note position="right" xlink:label="note-0149-02" xlink:href="note-0149-02a" xml:space="preserve">Corollar.
                <lb/>
              23. lib. 1.</note>
            tes ſimilium figurarum, KQM, ΠΤΩ, ideò habebimus etiam ho-
              <lb/>
            mòlogas earundem regulis ipſis incidentibus, KM, ΠΩ, ductis er-
              <lb/>
            go ex oppoſito tangentibus eaſdem figuras, KQM, ΠΤΩ, paral-
              <lb/>
            lelis ipſis, KP, Π &</s>
            <s xml:id="echoid-s3021" xml:space="preserve">, quæ ſint, XZ, β ℟, poterimus transferre om-
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            nes lineas figura@um, KQM, ΠΤΩ, in figuras ipſis, ZP, ℟ &</s>
            <s xml:id="echoid-s3022" xml:space="preserve">, ad-
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            iacentes, translatione facta regulis, KP, Π &</s>
            <s xml:id="echoid-s3023" xml:space="preserve">, fiant ergo dictę tran-
              <lb/>
              <note position="right" xlink:label="note-0149-03" xlink:href="note-0149-03a" xml:space="preserve">Iux. Sect.
                <lb/>
              A. huius
                <lb/>
              Propoſ.</note>
            ſlationes, vnde reſultent figu@æ, MZP, Ω℟ &</s>
            <s xml:id="echoid-s3024" xml:space="preserve">, quæ erunt æqua-
              <lb/>
            les ipſis, KQM, ΠΤΩ, & </s>
            <s xml:id="echoid-s3025" xml:space="preserve">ſubinde ipſis, ABD, ΦΣΛ, probab-
              <lb/>
            mus autem etiam eaſdem eſſe ſimiles (veluti in figuris, KQM, Π
              <lb/>
              <note position="right" xlink:label="note-0149-04" xlink:href="note-0149-04a" xml:space="preserve">3. huius.</note>
            Τ Ω, factum eſt) &</s>
            <s xml:id="echoid-s3026" xml:space="preserve">, ZP, ℟ &</s>
            <s xml:id="echoid-s3027" xml:space="preserve">, eſſe dictarum figurarum incidentes,
              <lb/>
            & </s>
            <s xml:id="echoid-s3028" xml:space="preserve">homologarum regulas ipſas, MP, Ω &</s>
            <s xml:id="echoid-s3029" xml:space="preserve">, patet autem ex conſtru-
              <lb/>
            ctione integras eſſe in figuris, MZP Π℟ &</s>
            <s xml:id="echoid-s3030" xml:space="preserve">, tum quæ æquidiſtant
              <lb/>
            ipſis, ZP, ℟ &</s>
            <s xml:id="echoid-s3031" xml:space="preserve">, tum ipſis, MP, Π ℟, nam ex prima translatione
              <lb/>
            integras habuimus, quę in figuris, KQM, ΠΤΩ, ipſis, FM, ΔΩ,
              <lb/>
            erant æquidiſtantes, & </s>
            <s xml:id="echoid-s3032" xml:space="preserve">ſubinde etiam integras, quæ in figuris, MZ
              <lb/>
            P, Ω ℟ &</s>
            <s xml:id="echoid-s3033" xml:space="preserve">, ipſis, ZP, ℟ &</s>
            <s xml:id="echoid-s3034" xml:space="preserve">, æquidiſtant, ex ſecunda translatione ve-
              <lb/>
            rò integras habuimus eas, quę ipſis, MP, Ω &</s>
            <s xml:id="echoid-s3035" xml:space="preserve">, æquidiſtant, & </s>
            <s xml:id="echoid-s3036" xml:space="preserve">hęc
              <lb/>
            per conſtructionem, quæ omnia ſeruare opus eſt.</s>
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        <div xml:id="echoid-div327" type="section" level="1" n="201">
          <head xml:id="echoid-head216" xml:space="preserve">C. SECTIO III.</head>
          <p>
            <s xml:id="echoid-s3038" xml:space="preserve">NVncin figuris, MZP, Ω ℟ &</s>
            <s xml:id="echoid-s3039" xml:space="preserve">, à maiori homologarum, MP,
              <lb/>
            Ω &</s>
            <s xml:id="echoid-s3040" xml:space="preserve">, quæ ſit, MP, aicindatur, OP, æqualis ipſi, Ω &</s>
            <s xml:id="echoid-s3041" xml:space="preserve">, & </s>
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              <lb/>
            vt, MP, ad, PO, ita ſit quælibet in figura, MZP, parallela ipſi,
              <lb/>
            MP, adeius portionem, & </s>
            <s xml:id="echoid-s3043" xml:space="preserve">portionum termini ſint ex vna parte in
              <lb/>
            recta, ZP, ex alia verò inlinea, ZO, erit ergo, vt vna ad vnam .</s>
            <s xml:id="echoid-s3044" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s3045" xml:space="preserve">vt, MP, ad, PO, ita omnia ad omnia, .</s>
            <s xml:id="echoid-s3046" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s3047" xml:space="preserve">ita omnes lineæ </s>
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