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

Table of contents

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[Item 1.]
[2.] TURNER COLLECTION
[3.] THE LIBRARY UNIVERSITY OF KEELE
[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.
[5.] BONONIÆ, M. DC. LIII.
[6.] _ILLVSTRISSIME_ MARCHIO
[7.] PRÆFATIO
[8.] In huius Libri Autorem.
[9.] In Librum Geometriæ.
[10.] Ad Libri Auctorem.
[11.] Ad Librum Geometriæ.
[12.] DeLibro Geometriæ.
[13.] De Libro Geometriæ.
[14.] Ad Autorem Libri Geometriæ.
[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.
[16.] B.
[17.] C.
[18.] A. II.
[19.] B.
[20.] C.
[21.] D.
[22.] E.
[23.] SCHOLIVM.
[24.] III.
[25.] A. IV.
[26.] COROLLARIVM.
[27.] B.
[28.] V.
[29.] VI.
[30.] VII.
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          <pb o="16" file="0036" n="36" rhead="GEOMETRIÆ"/>
          <p>
            <s xml:id="echoid-s558" xml:space="preserve">Sit propoſita quæcumque figura plana, AOVE, & </s>
            <s xml:id="echoid-s559" xml:space="preserve">in ipſiu@
              <lb/>
            plano duæ rectæ lineæ, BD, IT, vtcumq; </s>
            <s xml:id="echoid-s560" xml:space="preserve">ſe inuicem fecante@
              <lb/>
              <note position="left" xlink:label="note-0036-01" xlink:href="note-0036-01a" xml:space="preserve">Def. 14.</note>
              <figure xlink:label="fig-0036-01" xlink:href="fig-0036-01a" number="10">
                <image file="0036-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0036-01"/>
              </figure>
            in puncto; </s>
            <s xml:id="echoid-s561" xml:space="preserve">C, oportet illi parallelogrammum
              <lb/>
            circumſcribere, cuius latera rectis, SD, IT,
              <lb/>
            ſint parallela. </s>
            <s xml:id="echoid-s562" xml:space="preserve">Ducantur ergo oppoſitæ tan-
              <lb/>
            gentes figuræ, AOVE, reſpectu ipſius, IT,
              <lb/>
            quæ ſint, KM, HL, & </s>
            <s xml:id="echoid-s563" xml:space="preserve">aliæ duæ reſpectu ip-
              <lb/>
              <note position="left" xlink:label="note-0036-02" xlink:href="note-0036-02a" xml:space="preserve">Cor. ant.</note>
            ſius, BD, quæ ſint, KH, ML, quæ cum
              <lb/>
            prædictis concurrent, nam ſunt parallelæ ip-
              <lb/>
            ſis, BD, IT, quæ inuicem concurrunr, ſit
              <lb/>
            ergo concurſus in punctis, K, M, L, H, igi-
              <lb/>
            tur, KL, erit parallelogrammum, cuius ſin-
              <lb/>
            gula latera tangent ambitum ſiguræ, vt in
              <lb/>
            punctis, A, O, V, E, & </s>
            <s xml:id="echoid-s564" xml:space="preserve">ideò erit figuræ, AOVE, circumfcri-
              <lb/>
              <note position="left" xlink:label="note-0036-03" xlink:href="note-0036-03a" xml:space="preserve">Def. 14.</note>
            ptum, habens latera duabus datis rectis lineis, BD, IT, in figu-
              <lb/>
            ræ, AOVE, plano ſe inuicem ſecantibus, parallela; </s>
            <s xml:id="echoid-s565" xml:space="preserve">quod effi-
              <lb/>
            cere, &</s>
            <s xml:id="echoid-s566" xml:space="preserve">c.</s>
            <s xml:id="echoid-s567" xml:space="preserve"/>
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        <div xml:id="echoid-div68" type="section" level="1" n="54">
          <head xml:id="echoid-head65" xml:space="preserve">PROBLEMA III. PROPOS. III.</head>
          <p>
            <s xml:id="echoid-s568" xml:space="preserve">CVilibet ſolido parallelepipedum circumſcribere, cu-
              <lb/>
            ius plana oppoſita tribus datis planis, ſe inuicem ſe-
              <lb/>
            cantibus, ſint parallela.</s>
            <s xml:id="echoid-s569" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s570" xml:space="preserve">Sit ſolidum,
              <lb/>
              <figure xlink:label="fig-0036-02" xlink:href="fig-0036-02a" number="11">
                <image file="0036-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0036-02"/>
              </figure>
            ACBD, quod-
              <lb/>
            cumq; </s>
            <s xml:id="echoid-s571" xml:space="preserve">in quo
              <lb/>
            tria plana, A
              <lb/>
            CBD, AB, C
              <lb/>
            D, ſe inuicem
              <lb/>
            fecent, quæli-
              <lb/>
            bet duo, opor-
              <lb/>
            tetſolido, AC
              <lb/>
              <note position="left" xlink:label="note-0036-04" xlink:href="note-0036-04a" xml:space="preserve">Def. 1@.</note>
            BD, paralle-
              <lb/>
            lepipedum cir-
              <lb/>
            cūſcribere, cu-
              <lb/>
            ius oppoſita
              <lb/>
            plana prædi-
              <lb/>
            ctis planis ſint
              <lb/>
            parallela. </s>
            <s xml:id="echoid-s572" xml:space="preserve">Du-
              <lb/>
            cātur duo pla-
              <lb/>
            na oppoſita
              <lb/>
              <note position="left" xlink:label="note-0036-05" xlink:href="note-0036-05a" xml:space="preserve">Coroll. 1.
                <lb/>
              huius.</note>
            tangentia dictum ſolidum reſpectu cuiuſuis planorum ſe </s>
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