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

Page concordance

< >
Scan Original
51 31
52 32
53 33
54 34
55 35
56 36
57 37
58 38
59 39
60 40
61 41
62 42
63 43
64 44
65 45
66 46
67 47
68 48
69 49
70 50
71 51
72 52
73 53
74 54
75 55
76 56
77 57
78 58
79 59
80 60
< >
page |< < (32) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div106" type="section" level="1" n="75">
          <p>
            <s xml:id="echoid-s894" xml:space="preserve">
              <pb o="32" file="0052" n="52" rhead="GEOMETRIÆ"/>
            BD, ęquidiſtante, & </s>
            <s xml:id="echoid-s895" xml:space="preserve">quia latus, AB, indefinitè productum oc-
              <lb/>
            currit baſi, etiam dictum baſi ęquidiſtans planum occurret indefini-
              <lb/>
            tè productum ipſi baſi, quod eſt abſurdum, non igitur planum du-
              <lb/>
            ctum per, A, baſi, BD, ęquidiſtans conicum tangit vel ſecat in a-
              <lb/>
            lio, quam in puncto, A, ergo, A, erit illius vnicus vertex reſpectu
              <lb/>
            baſis, BD, quod erat oſtendendum.</s>
            <s xml:id="echoid-s896" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div108" type="section" level="1" n="76">
          <head xml:id="echoid-head87" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s897" xml:space="preserve">_C_Vm autem dicemus verticem alicuius conici, intelligemus ſemper
              <lb/>
            ipſum reſpectu baſis aſſumptum, ideſt punctum, curin reuolutie-
              <lb/>
            ne innititur latus cylindrict, niſi aliud explicetur.</s>
            <s xml:id="echoid-s898" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div109" type="section" level="1" n="77">
          <head xml:id="echoid-head88" xml:space="preserve">THEOREMA XIII. PROPOS. XVI.</head>
          <p>
            <s xml:id="echoid-s899" xml:space="preserve">SI conicus ſecetur vtcumque per verticem ducto plano,
              <lb/>
            concepta in ipſo ſigura, vel figuræ, erit triangulus, vel
              <lb/>
            trianguli.</s>
            <s xml:id="echoid-s900" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s901" xml:space="preserve">Secetur quilibet conicus, ABF, plano vtcumque per verticem
              <lb/>
            ducto, quod in eo producat figuram, ſiue figuras, ABC, AEF.
              <lb/>
            </s>
            <s xml:id="echoid-s902" xml:space="preserve">
              <figure xlink:label="fig-0052-01" xlink:href="fig-0052-01a" number="25">
                <image file="0052-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0052-01"/>
              </figure>
            Dico eas eſſe triangulos, Sit com-
              <lb/>
            munis ſectio illius, & </s>
            <s xml:id="echoid-s903" xml:space="preserve">baſis pro-
              <lb/>
            ducti plani, tota, BF, cuius, CE,
              <lb/>
            portio maneat extra baſim, eſt igi-
              <lb/>
            tur, BF, recta linea, dico etiam
              <lb/>
            eſſe rectas ipſas, AB, AC, AE,
              <lb/>
            AF, ſienim non eſt, AB, recta,
              <lb/>
            ducatur in plano figurę, ABC, re-
              <lb/>
            cta, AOB, igitur, AOB, quę
              <lb/>
            iungit punctum, B, & </s>
            <s xml:id="echoid-s904" xml:space="preserve">verticem coni eſt latus conici, ABF, ergo
              <lb/>
            eſt in ſuperficie coniculari, & </s>
            <s xml:id="echoid-s905" xml:space="preserve">eſt etiam in plano figurę, ABC, ergo
              <lb/>
            eſt in eorum communi ſectione, ideſt cadit ſuper, AB, igitur, AB,
              <lb/>
            erit recta linea, eodem modo oſtendemus ipſas, AC, AE, AF, eſſe
              <lb/>
            rectas, & </s>
            <s xml:id="echoid-s906" xml:space="preserve">ideò erit, ABC, triangulus, vt etiam, AEF, quod erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s907" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div111" type="section" level="1" n="78">
          <head xml:id="echoid-head89" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s908" xml:space="preserve">_E_Odem modo nobis innoteſcit figuras, quæ extra conicum fiunt eſſe
              <lb/>
            triangulos, ideſt, ACE, eſſe triangulum, & </s>
            <s xml:id="echoid-s909" xml:space="preserve">qui ex ipſis inte-
              <lb/>
            gratur, ſcilicet, ABF, pariter eſſe triangulum.</s>
            <s xml:id="echoid-s910" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum