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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            <s xml:id="echoid-s315" xml:space="preserve">
              <pb o="5" file="0025" n="25" rhead="LIBERI."/>
            nomina fectionum conicorum latera recta, ſeu tranſuerſa,
              <lb/>
            ſumantur, prout ab Apollonio definiuntur, hoctantum ani-
              <lb/>
            maduerſo, me in ſequentibus aliquando abuti eiſdem no-
              <lb/>
            minibus ſectionum coni, Parabolæ .</s>
            <s xml:id="echoid-s316" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s317" xml:space="preserve">Hyperbolæ, Ellipſis,
              <lb/>
            & </s>
            <s xml:id="echoid-s318" xml:space="preserve">oppoſitarum ſectionum, ſpatia videlicet intelligens ſub
              <lb/>
            illis, & </s>
            <s xml:id="echoid-s319" xml:space="preserve">earum baſibus, compręhenſa, quod ex modo lo-
              <lb/>
            quendi tunc euidenter cognoſcitur. </s>
            <s xml:id="echoid-s320" xml:space="preserve">Cætera deniq Apol-
              <lb/>
            lonij, & </s>
            <s xml:id="echoid-s321" xml:space="preserve">quæ ab Archimede circa Sphęroides, & </s>
            <s xml:id="echoid-s322" xml:space="preserve">Conoides,
              <lb/>
            definiuntur, niſi alia afferatur à me definitio, ſumantur,
              <lb/>
            prout ab ipſis vſurpantur.</s>
            <s xml:id="echoid-s323" xml:space="preserve"/>
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        <div xml:id="echoid-div32" type="section" level="1" n="29">
          <head xml:id="echoid-head39" xml:space="preserve">VI.</head>
          <p>
            <s xml:id="echoid-s324" xml:space="preserve">FIguram planam circa diametrum, vocat Apollonius,
              <lb/>
            Conicorum, cum in ea ductis quotuis lineis cuidam
              <lb/>
            æquidiſtantibus, omnes bifariam à quadam recta linea di-
              <lb/>
            uiduntur, quam vocat diametrum, ſieas oblique ſecet, & </s>
            <s xml:id="echoid-s325" xml:space="preserve">
              <lb/>
            axem, ſi eas rectè diuidat, & </s>
            <s xml:id="echoid-s326" xml:space="preserve">ipſam figuram circa diame-
              <lb/>
            trum, vel axem.</s>
            <s xml:id="echoid-s327" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s328" xml:space="preserve">Siergo figura circa axem, reuoluatur circa eundem do-
              <lb/>
            nec redeat, vnde diſceſſit, deſcripta in tali reuolutione ab
              <lb/>
            eadem ſolida figura dicatur: </s>
            <s xml:id="echoid-s329" xml:space="preserve">ſolidum rotundum, eiuſdem
              <lb/>
            verò axis, circa quem fit reuolutio.</s>
            <s xml:id="echoid-s330" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div33" type="section" level="1" n="30">
          <head xml:id="echoid-head40" xml:space="preserve">VII.</head>
          <p>
            <s xml:id="echoid-s331" xml:space="preserve">SImiles Cylindrici, & </s>
            <s xml:id="echoid-s332" xml:space="preserve">Conicidicantur, quorum baſes
              <lb/>
            ſunt ſimiles (iuxta definitionem 10. </s>
            <s xml:id="echoid-s333" xml:space="preserve">ſimilium figura-
              <lb/>
            rum infra poſitam, ſubint ellige, veliuxta aliorum defini-
              <lb/>
            tiones, quas cum prędictam concordare infra oſtendemus)
              <lb/>
            in quibus ſumptis duabus homologis lineis, vel lateribus
              <lb/>
            vtcumque, & </s>
            <s xml:id="echoid-s334" xml:space="preserve">per ipſas, & </s>
            <s xml:id="echoid-s335" xml:space="preserve">latera extenſis planis ipſa ad ean-
              <lb/>
            dem partem ęquè ad baſes inclinantur, horumq. </s>
            <s xml:id="echoid-s336" xml:space="preserve">conceptę
              <lb/>
            in eiſdem figurę ſunt ſimiles, nempè ſimilia parallelogram-
              <lb/>
            ma in cylindricis, & </s>
            <s xml:id="echoid-s337" xml:space="preserve">ſimilia triangula in conicis, quorum ho-
              <lb/>
            mologa latera ſint ſumptę in baſibus homologę.</s>
            <s xml:id="echoid-s338" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div34" type="section" level="1" n="31">
          <head xml:id="echoid-head41" xml:space="preserve">VIII.</head>
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            <s xml:id="echoid-s339" xml:space="preserve">SImiles ſphęroides dieentur, quę ex ſimilium ellipſium
              <lb/>
            reuolutione oriuntur.</s>
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