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

Table of contents

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[111.] COROLLARIV M.
Page: 81 (61)
[112.] LEMMA VI.
Page: 81 (61)
[113.] COROLLARIVM.
Page: 83 (63)
[114.] THEOREMA XXVI. PROPOS. XXIX.
Page: 83 (63)
[115.] THEOREMA XXVII. PROPOS. XXX.
Page: 87 (67)
[116.] LEMMA.
Page: 89 (69)
[117.] THEOREMA XXVIII. PROPOS. XXXI.
Page: 90 (70)
[118.] DEFINITIO.
Page: 91 (71)
[119.] DEFINITIO.
Page: 91 (71)
[120.] THEOREMA XXIX. PROPOS. XXXII.
Page: 92 (72)
[121.] THEOREMA XXX. PROPOS. XXXIII.
Page: 95 (75)
[122.] THEOREMA XXXI. PROPOS. XXXIV.
Page: 96 (76)
[123.] COROLLARIVM.
Page: 97 (77)
[124.] THEOREMA XXXII. PROPOS. XXXV.
Page: 97 (77)
[125.] COROLLARIVM.
Page: 98 (78)
[126.] THEOREMA XXXIII. PROPOS. XXXVI.
Page: 98 (78)
[127.] THEOREMA XXXIV. PROPOS. XXXVII.
Page: 99 (79)
[128.] COROLLARIVM.
Page: 101 (81)
[129.] THEOREMA XXXV. PROPOS. XXXVIII.
Page: 101 (81)
[130.] THEOREMA XXXVI. PROPOS. XXXIX.
Page: 103 (83)
[131.] THEOREMA XXXVII. PROPOS. XL.
Page: 103 (83)
[132.] SCHOLIVM.
Page: 104 (84)
[133.] THEOREMA XXXVIII. PROPOS. XLI.
Page: 105 (85)
[134.] THEOREMA XXXIX PROPOS. XLII.
Page: 105 (85)
[135.] THEOREMA XL. PROPOS. XLIII.
Page: 105 (85)
[136.] THEOREMA XLI. PROPOS. XLIV.
Page: 106 (86)
[137.] THEOREMA XLII. PROPOS. XLV.
Page: 107 (87)
[138.] THEOREMA XLIII. PROPOS. XLVI.
Page: 107 (87)
[139.] THEOREMA XLIV. PROPOS. XLVII.
Page: 108 (88)
[140.] COROLLARIVM.
Page: 109 (89)
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        <div xml:id="echoid-div194" type="section" level="1" n="126">
          <p>
            <s xml:id="echoid-s1985" xml:space="preserve">
              <pb o="79" file="0099" n="99" rhead="LIBERI."/>
            ZX. </s>
            <s xml:id="echoid-s1986" xml:space="preserve">Dico hanc tangere dicta ſolida, ſi enim non tangit ſecet, ve-
              <lb/>
            luti, D2N, in puncto, N, igitur punctus. </s>
            <s xml:id="echoid-s1987" xml:space="preserve">n. </s>
            <s xml:id="echoid-s1988" xml:space="preserve">erit extra planum figu-
              <lb/>
            ræper axem, nam ipſa, D2N, eſt parallela ipſi, ZX, quæ eſt ad
              <lb/>
            rectos angulos figuræ per axem tranſeunti, & </s>
            <s xml:id="echoid-s1989" xml:space="preserve">ideò etiam, D2N,
              <lb/>
              <note position="right" xlink:label="note-0099-01" xlink:href="note-0099-01a" xml:space="preserve">8. Vndec.
                <lb/>
              Elem.</note>
            eſt illi ad rectos angulos, occurrit autem illi in puncto, 2, ergo non
              <lb/>
            occurret illi in alio puncto, ergo, N, eſt extra planum figuræ per a-
              <lb/>
            xem, ducatur per, N, planum æquidiſtans plano, PXRZ, circuli,
              <lb/>
              <note position="right" xlink:label="note-0099-02" xlink:href="note-0099-02a" xml:space="preserve">34. huius.</note>
            quod producat circulum, BNFC, & </s>
            <s xml:id="echoid-s1990" xml:space="preserve">ſit, BF, communisſectio ip-
              <lb/>
            ſius circuli, & </s>
            <s xml:id="echoid-s1991" xml:space="preserve">figuræ per axem, quæ erit ipſius circuli diameter, &</s>
            <s xml:id="echoid-s1992" xml:space="preserve">,
              <lb/>
              <note position="right" xlink:label="note-0099-03" xlink:href="note-0099-03a" xml:space="preserve">Corol. 34
                <lb/>
              huius.</note>
            N, non erit aliquis punctorum, BF, ergo ſi ab, N, duxerimus ipſi,
              <lb/>
            ZX, parallelam, vt, NC, cum etiam, BF, ſit parallela ipſi, PR,
              <lb/>
            continebunt angulos æquales, ſed, ZX, ſecat perpendiculariter, P
              <lb/>
              <note position="right" xlink:label="note-0099-04" xlink:href="note-0099-04a" xml:space="preserve">10. Vnd.
                <lb/>
              Elem.</note>
            R, ergo, NC, ſecabit perpendiculariter, BF, ducta non ab extre-
              <lb/>
            mitate diametri, ergo intra circulum, BCFN, erit, & </s>
            <s xml:id="echoid-s1993" xml:space="preserve">bifariam ſe-
              <lb/>
            cabitur ab ipſa, BF, ergo non tranſibit per circuitum figuræ per a-
              <lb/>
            xem ductæ, & </s>
            <s xml:id="echoid-s1994" xml:space="preserve">per ipſum tranſit, D2N, ergo, NC, N2D, ſunt
              <lb/>
            duæ rectæ lineæ eidem, ZX, parallelę, ergo etiam inter ſe erunt pa-
              <lb/>
            rallelæ, quod eſt abſurdum, cum tranſeant per idem punctum, N,
              <lb/>
            ergo ducta per punctum ambitus figuræ per axem parallela ipſi, ZX,
              <lb/>
            tanget dicta ſolida: </s>
            <s xml:id="echoid-s1995" xml:space="preserve">Sit nobis nunc punctus, N, pro puncto vtcung;
              <lb/>
            </s>
            <s xml:id="echoid-s1996" xml:space="preserve">in ſuperficie ambiente ſumpto extra circuitum figuræ per axem, à
              <lb/>
            quo ducta ipſi, ZX, parallela, occurrat producta ſuperficiei ambienti
              <lb/>
            in puncto, C, oſtendemus ergo eodem modo ſupra adhibito (poſt-
              <lb/>
            quam duxerimus per, N, planum circulo, PXRZ, æquidiſtans,
              <lb/>
            quod in ſolido producat circulum, BNFC,) ipſam, NC, intra cir-
              <lb/>
            culum, BNFC, cadere, & </s>
            <s xml:id="echoid-s1997" xml:space="preserve">bifariam diuidi à recta, BF, ſiue à figu@a
              <lb/>
            per axem ducta (nam eſt, NC, perpendicularis ipſi, BF,) quod o-
              <lb/>
            ſtendere opus erat.</s>
            <s xml:id="echoid-s1998" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div196" type="section" level="1" n="127">
          <head xml:id="echoid-head138" xml:space="preserve">THEOREMA XXXIV. PROPOS. XXXVII.</head>
          <p>
            <s xml:id="echoid-s1999" xml:space="preserve">SI ſolidum rotundum, vel conus ſcalenus, ſecentur plano
              <lb/>
            per axem, & </s>
            <s xml:id="echoid-s2000" xml:space="preserve">deinde alio plano ſecentur, cuius, & </s>
            <s xml:id="echoid-s2001" xml:space="preserve">vnius
              <lb/>
            planorum rectè axem ſecantium communis ſectio ſit recta li-
              <lb/>
            nea perpendicularis communi ſectioni eiuſdem, & </s>
            <s xml:id="echoid-s2002" xml:space="preserve">plani per
              <lb/>
            axem; </s>
            <s xml:id="echoid-s2003" xml:space="preserve">figura à ſecundo ſecante plano in ſolido producta erit
              <lb/>
            circa axem, in cono ſcaleno autem erit circa axem, vel dia-
              <lb/>
            metrum, & </s>
            <s xml:id="echoid-s2004" xml:space="preserve">axis, vel diameter erit communis ſectio per dicta
              <lb/>
            ſecantia plana productarum figurarum.</s>
            <s xml:id="echoid-s2005" xml:space="preserve"/>
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