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

Table of contents

< >
[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)
[141.] SCHOLIVM.
Page: 109 (89)
[142.] LEMMA.
Page: 110 (90)
[143.] COROLLARIVM.
Page: 112 (92)
[144.] THEOREMA XLV. PROPOS. XLVIII.
Page: 112 (92)
[145.] COROLLARIVM.
Page: 113 (93)
[146.] THEOREMA XLVI. PROPOS. XLIX.
Page: 114 (94)
[147.] THEOREMA XLVII. PROPOS. L:
Page: 115 (95)
[148.] COROLLARIVM I.
Page: 117 (97)
[149.] COROLLARIVM II.
Page: 117 (97)
[150.] SCHOLIVM.
Page: 118 (98)
< >
page |< < (185) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div459" type="section" level="1" n="278">
          <pb o="185" file="0205" n="205" rhead="LIBER II."/>
        </div>
        <div xml:id="echoid-div461" type="section" level="1" n="279">
          <head xml:id="echoid-head295" xml:space="preserve">I. SECTIO IX.</head>
          <p style="it">
            <s xml:id="echoid-s4542" xml:space="preserve">_I_N Propoſ. </s>
            <s xml:id="echoid-s4543" xml:space="preserve">24. </s>
            <s xml:id="echoid-s4544" xml:space="preserve">habemus quemcumque cylindricum eſſe triplum coni-
              <lb/>
            ci in eadem baſi, & </s>
            <s xml:id="echoid-s4545" xml:space="preserve">altitudine cum ipſo. </s>
            <s xml:id="echoid-s4546" xml:space="preserve">Sit cxpoſitus quicunq; </s>
            <s xml:id="echoid-s4547" xml:space="preserve">cy-
              <lb/>
            lindricus, AE, in baſi, DHEF, in eadem autem baſi, & </s>
            <s xml:id="echoid-s4548" xml:space="preserve">altitudine ſit
              <lb/>
            conicus, DBE, ſic tamen baſi inſiſtens, vt ducto plano per latera conici,
              <lb/>
            idem tranſeat per latera cylindrici, AE, ſit autem ductum tale planum,
              <lb/>
              <figure xlink:label="fig-0205-01" xlink:href="fig-0205-01a" number="122">
                <image file="0205-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0205-01"/>
              </figure>
            quod faciat in conico, DBE, triangulum,
              <lb/>
            DBE, & </s>
            <s xml:id="echoid-s4549" xml:space="preserve">in cylindrico, AE, parallelo-
              <lb/>
              <note position="right" xlink:label="note-0205-01" xlink:href="note-0205-01a" xml:space="preserve">_Cor. 6. &_
                <lb/>
              _16. lib. I._</note>
            grammum, AE, erunt igitur, AE, & </s>
            <s xml:id="echoid-s4550" xml:space="preserve">tri-
              <lb/>
            angulum, DBE, genitrices figuræ eorum-
              <lb/>
              <note position="right" xlink:label="note-0205-02" xlink:href="note-0205-02a" xml:space="preserve">_Corol. 3._
                <lb/>
              _34. huius._</note>
            dem ſolidorum, quæ ſimilaria ad inuicem,
              <lb/>
            vocantur, genita iuxta communem regulam,
              <lb/>
            DE, quod ergo gignitur ex, AE, ad geni-
              <lb/>
            tum ex triangulo, DBE, erit vt omnia qua-
              <lb/>
            drata, AE, ad omnia quadrata trianguli,
              <lb/>
            DBE, regula, DE, ideſt triplum, ſolidum
              <lb/>
            verò ſimilare genitum ex, AE, iuxta re-
              <lb/>
              <note position="right" xlink:label="note-0205-03" xlink:href="note-0205-03a" xml:space="preserve">_24. huius._</note>
            gulam, DE, cuius figuræ ſint ſimiles figuræ, DFEH, eſt cylindricus,
              <lb/>
            AE, & </s>
            <s xml:id="echoid-s4551" xml:space="preserve">ſolidum ſimilare genitum ex triangulo, DBE, iuxta regulam,
              <lb/>
            DE, cuius figuræ ſint ſimiles pariter figuræ, DFEH, eſt conicus, DBE,
              <lb/>
            ergo cylindricus, AE, triplus erit conici, DBE, & </s>
            <s xml:id="echoid-s4552" xml:space="preserve">conſequenter tri-
              <lb/>
            plus erit cuiuſuis alij in eadem baſi, DFEH, & </s>
            <s xml:id="echoid-s4553" xml:space="preserve">altitudine, cum coni-
              <lb/>
              <note position="right" xlink:label="note-0205-04" xlink:href="note-0205-04a" xml:space="preserve">_34. huius._
                <lb/>
              _Per B. Co-_
                <lb/>
              _rollar. 27._
                <lb/>
              _huius._</note>
            co, DBE, exiſtentis, quoniam, vt oſtenſum eſt, conici in eadem alti-
              <lb/>
            tudme ſiantes ſunt, vt baſes, vnde cum baſes ſunt æquales, & </s>
            <s xml:id="echoid-s4554" xml:space="preserve">conici
              <lb/>
            ſunt æquales, verum ergo eſt, quod proponebatur.</s>
            <s xml:id="echoid-s4555" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div463" type="section" level="1" n="280">
          <head xml:id="echoid-head296" xml:space="preserve">K. SECTIO X.</head>
          <p style="it">
            <s xml:id="echoid-s4556" xml:space="preserve">_I_N Prop. </s>
            <s xml:id="echoid-s4557" xml:space="preserve">27. </s>
            <s xml:id="echoid-s4558" xml:space="preserve">habemus ſolida ad inuicem ſimilaria genita ex trape-
              <lb/>
            zijs in eadem baſi (quæ ſit vnum laterum æquidiſtantium) & </s>
            <s xml:id="echoid-s4559" xml:space="preserve">altitu-
              <lb/>
            dine conſtitutis, quorum oppoſitæ baſes ſint æquales, genita, inquam,
              <lb/>
            iuxta communem regulam ipſam baſim, ideſt fruſta conicorum quorum
              <lb/>
            oppoſitæ baſes ſunt figuræ deſcriptæ à lateribus dictorum trapeziorum
              <lb/>
            æquidiſtantibus, eſſe æqualia.</s>
            <s xml:id="echoid-s4560" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum