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

Table of contents

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[43.] APPENDIX POSTERIOR Pro declaratione Definit. II.
[44.] SCHOLIVM.
[45.] XII.
[46.] XIII.
[47.] XIV.
[48.] XV.
[49.] POSTVLATA I.
[50.] II.
[51.] PROBLEMA I. PROPOS. 1.
[52.] COROLLARIVM.
[53.] PROBLEMA II. PROPOS. II.
[54.] PROBLEMA III. PROPOS. III.
[55.] SCHOLIVM.
[56.] THEOREMA I. PROPOS. IV.
[57.] COROLLARIVM I.
[58.] COROLLARIVM II.
[59.] THEOREMA II. PROPOS. V.
[60.] THEOREMA III. PROPOS. VI.
[61.] COROLLARIVM.
[62.] THEOREMA IV. PROPOS. VII.
[63.] THEOREMA V. PROPOS. VIII.
[64.] COROLLARIV M.
[65.] THEOREMA VI. PROPOS. IX.
[66.] COROLLARIVM.
[67.] THEOREMA VII. PROPOS. X.
[68.] THEOREMA VIII. PROPOS. XI.
[69.] COROLLARIV M.
[70.] LEMMA PRO ANTECED. PROP.
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            <s xml:id="echoid-s456" xml:space="preserve">
              <pb o="11" file="0031" n="31" rhead="LIBER I."/>
            periuntur, ſiue binæ ſimiles, & </s>
            <s xml:id="echoid-s457" xml:space="preserve">vnæ, ac aliæ ſimiliter inter
              <lb/>
              <note position="right" xlink:label="note-0031-01" xlink:href="note-0031-01a" xml:space="preserve">A.E. Def.
                <lb/>
              10.</note>
            ſe diſpoſitæ, vocentur: </s>
            <s xml:id="echoid-s458" xml:space="preserve">Figuræ homologæ dictorum ſimi-
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            lium ſolidorum, ſumptæ regula vna ipſarum, vel oppoſito-
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            rum tangentium, quæ homologarum figurarum plana tan-
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            gentia, ſi libeat, etiam vocentur.</s>
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          <head xml:id="echoid-head53" xml:space="preserve">APPENDIX POSTERIOR
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          Pro declaratione Definit. II.</head>
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            <s xml:id="echoid-s460" xml:space="preserve">_S_Int ſolida, Γ β 3 Φ, AHBM, quorum ſint oppoſita tangen-
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            tia plana, Δ ℟ Ζ &</s>
            <s xml:id="echoid-s461" xml:space="preserve">, ſolidi, Γ β 3 Φ, &</s>
            <s xml:id="echoid-s462" xml:space="preserve">, QP, L Π, ſθ-
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              <note position="right" xlink:label="note-0031-02" xlink:href="note-0031-02a" xml:space="preserve">_B. Def. 2._</note>
            lidi, AHBM, ſint autem alia duo plana, quæ iſtis incidant ad
              <lb/>
            eundem angulum ex eadem parte, Δ Υ QK, illa nempè quo-
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            rum, et dictorum tangentium ſint communes ſictiones, ΔΧ Ζ
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              <figure xlink:label="fig-0031-01" xlink:href="fig-0031-01a" number="7">
                <image file="0031-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0031-01"/>
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            Τ, QF, LK, ſecentur nunc dicta ſolida planis tangentibus pa-
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            rallelis, quæ diuidant eorum altitudinesreſpectu duitorum tan-
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              <note position="right" xlink:label="note-0031-03" xlink:href="note-0031-03a" xml:space="preserve">_D. Def. 2._</note>
            gentium ſump@as ſimiliter ad eandem partem: </s>
            <s xml:id="echoid-s463" xml:space="preserve">Sint autem eo-
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            rum in dictis ſolidis conceptæ ſiguræ planæ ſimiles, ſivna in vno
              <lb/>
              <note position="right" xlink:label="note-0031-04" xlink:href="note-0031-04a" xml:space="preserve">_A. E. Def._
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              _10._</note>
            quoq; </s>
            <s xml:id="echoid-s464" xml:space="preserve">ſolido figura producantur, velſiplures, binæ ſimiles, et fi-
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            militer inter ſe diſpoſitæ, quæ fiunt in vno, ac quæ fiunt in alio ſo-
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            lido, ex. </s>
            <s xml:id="echoid-s465" xml:space="preserve">g. </s>
            <s xml:id="echoid-s466" xml:space="preserve">ipſæ, β Λ, Σ Φ, HE, CM, quæ ſint binæ ſimiles, ideſt,
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            β Λ, ipſi, HE, &</s>
            <s xml:id="echoid-s467" xml:space="preserve">, Σ Φ, ipſi, CM, &</s>
            <s xml:id="echoid-s468" xml:space="preserve">, β λ, Σ Φ, ſimiliter inter
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            ſe diſpoſitæ, ac ipſæ, HE, CM, quarum ſimilium figurarum bo-
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            mologæ duabus quibuſcumque regulis, vt ipſis, ℟ Ω, PR, æqui-
              <lb/>
            dicto
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            nt; </s>
            <s xml:id="echoid-s469" xml:space="preserve">vel ſihæ non ſint cum planis, Δ Υ, QK, </s>
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