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

Table of contents

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[Item 1.]
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[2.] TURNER COLLECTION
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[3.] THE LIBRARY UNIVERSITY OF KEELE
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[4.] GEOMETRIA INDIVISIBILIBVS CONTIN VOR VM Noua quadam ratione promota. _AVTHORE_ P. BONAVENTVRA CAVALERIO MEDIOLANEN _Ordinis S.Hieron. Olim in Almo Bononien. Archigym._ _Prim. Mathematicarum Profeſſ._ In hac poftrema edictione ab erroribus expurgata. _Ad Illuſtriſs. D. D._ MARTIVM VRSINVM PENNÆ MARCHIONEM &c.
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[5.] BONONIÆ, M. DC. LIII.
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[6.] _ILLVSTRISSIME_ MARCHIO
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[7.] PRÆFATIO
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[8.] In huius Libri Autorem.
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[9.] In Librum Geometriæ.
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[10.] Ad Libri Auctorem.
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[11.] Ad Librum Geometriæ.
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[12.] DeLibro Geometriæ.
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[13.] De Libro Geometriæ.
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[14.] Ad Autorem Libri Geometriæ.
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[15.] CAVALERII LIBER PRIMVS. In quo præcipuè de ſectionibus Cylindricorum, & Conicorum, nec non ſimilibus figuris quædam element aria præmittuntur; ac aliquæ Pro-poſitiones lemmaticæ pro ſequen-tibus Libris oſtenduntur. DIFINITIONES. A. I.
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[16.] B.
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[17.] C.
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[18.] A. II.
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[19.] B.
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[20.] C.
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[21.] D.
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[22.] E.
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[23.] SCHOLIVM.
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[24.] III.
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[25.] A. IV.
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[26.] COROLLARIVM.
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[27.] B.
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[28.] V.
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[29.] VI.
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[30.] VII.
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              <pb o="179" file="0199" n="199" rhead="LIBER II."/>
            ſdem Fimiles alteri deſcriptarum .</s>
            <s xml:id="echoid-s4408" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4409" xml:space="preserve">ita omnia plana ſolidi ſimilaris ge-
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            niti ex, ABC, iuxta regulam, BC, (ſimilibus exiſtentibus eiuſdem fi-
              <lb/>
            guris vni deſcriptarum) ad omnia plana ſolidi ſimilaris geniti ex eadem
              <lb/>
            figura iuxta eandem regulam (huius ſimilibus exiſtentibus figuris alteri
              <lb/>
            deſcriptarum) ideſt ita erunt ſolida ſimilaria genita ex eadem figura, A
              <lb/>
            BC, iuxta communem regulam, BC, non tamen ſimilaria ad inuicem.
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            </s>
            <s xml:id="echoid-s4410" xml:space="preserve">ſed, quarum omnia plana ſunt omnes figuræ ſimiles eiuſdem, ABC, ſi-
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            miles inquam, quæ ſunt vnius dictorum ſolidorum vni deſcriptar um à,
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            BC, figurarum, & </s>
            <s xml:id="echoid-s4411" xml:space="preserve">quæ ſunt alterius, ſimiles alteri deſcriptarum fi-
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            gurarum.</s>
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        <div xml:id="echoid-div443" type="section" level="1" n="266">
          <head xml:id="echoid-head281" xml:space="preserve">COROLLARIVM II.</head>
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            <s xml:id="echoid-s4413" xml:space="preserve">_V_Nde ſolida ſimilaria, ſed non ad inuicem, genita ex. </s>
            <s xml:id="echoid-s4414" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s4415" xml:space="preserve">à figuris,
              <lb/>
            ABC, DEF, iuxta regulas, BC, EF, quæ duas figuras planas
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            diſſimiles deſcripſerint, quibus ſint ſimiles figuræ, quæ dicuntur omnia
              <lb/>
            plana dictorum ſimilarium ſolidorum, erunt ad inuicem, vt ipſæ figuræ
              <lb/>
            diſſimiles deſcriptæ ab ipſis, BC, EF, nam ſolidum ſimilare genitum ex,
              <lb/>
            DEF, iuxta regulam, EF, ad ſibi ſimilare genitum ex figura, ABC,
              <lb/>
            iuxta regulam, BC, erit vt figura deſcripta ab, EF, ad ſibi ſimilem fi-
              <lb/>
            guram deſcriptam à, BC, item ſolidum boc ſimilare genitum ex figu-
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            ra, ABC, iuxta regulam, BC, ad ſolidum ſimilare, ſed non fibi,
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            genitum ex eadem figura iuxta eandem regulam, BC, erit vt figura de-
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            ſcripta à, BC, ſimilis deſcriptæ ab, EF, ad figuram ſibi diſſimilem de-
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            ſcriptam ab eadem, BC, (quibus figuris diſſimilibus ſint ſimiles figuræ,
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            quæ dicuntur omnia plana ſolidorum ſimilarium genitorum ex eadem fi-
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            gura, ABC, iuxta communem regulam, BC,) ergo, ex æquali ſolidum
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            ſimilare genitum ex figura, DEF, ad ſolidum ſimilare, ſed non ſibi, ge-
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            nitum ex figura, ABC, (genita intellige iuxta regulas, EF, BC,) erit
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            vt figura deſcripta ab, EF, cui ſunt ſimiles figuræ huius ſolidi, ad figu-
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            ram deſcriptam à, BC, prædictæ diſſimilem, cui ſunt ſimiles figuræ ſoli-
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            di ex, BAC, geniti iuxta regulam, BC.</s>
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        <div xml:id="echoid-div444" type="section" level="1" n="267">
          <head xml:id="echoid-head282" xml:space="preserve">THEOREMA XXXIV. PROPOS. XXXIV.</head>
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            <s xml:id="echoid-s4417" xml:space="preserve">SOlida ſimilaria genita ex parallelogrammis iuxta regu-
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            lam vnum eorundem laterum, ſunt cylindrici; </s>
            <s xml:id="echoid-s4418" xml:space="preserve">& </s>
            <s xml:id="echoid-s4419" xml:space="preserve">ſoli-
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            da ſimilaria genita ex triangulis iuxta regulam vnum eorun-
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            dem laterum, ſunt conici, quorum baſes erunt figuræ à re-
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            gulis deſcriptæ, & </s>
            <s xml:id="echoid-s4420" xml:space="preserve">latera, eorundem parallelogrammorum,
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            vel triangulorum latera regulis inſiſtentia.</s>
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