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

Page concordance

< >
Scan Original
31 11
32 12
33 13
34 14
35 15
36 16
37 17
38 18
39 19
40 20
41 21
42 22
43 23
44 24
45 25
46 26
47 27
48 28
49 29
50 30
51 31
52 32
53 33
54 34
55 35
56 36
57 37
58 38
59 39
60 40
< >
page |< < (42) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div128" type="section" level="1" n="89">
          <pb o="42" file="0062" n="62" rhead="GEOMETRIÆ"/>
        </div>
        <div xml:id="echoid-div130" type="section" level="1" n="90">
          <head xml:id="echoid-head101" xml:space="preserve">COROLLARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s1114" xml:space="preserve">QVoniam oſtendimus, tum, DC, BR, tum etiam, EF, IO, eſſe vt
              <lb/>
            ipſas incidentes, PH, NK, habetur ſimilium figurar um homo-
              <lb/>
            logas pariter eſſe, vt incidentes earundem, & </s>
            <s xml:id="echoid-s1115" xml:space="preserve">oppoſitarum tangentium,
              <lb/>
            quæ ſunt earundem regulæ, quod in diffinitione aſſumitur contingere
              <lb/>
            tantum ijs, quæ inter circuicum figurarum, & </s>
            <s xml:id="echoid-s1116" xml:space="preserve">ipſas incidentes, eodem
              <lb/>
            ordine ſumptæ, continentur.</s>
            <s xml:id="echoid-s1117" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div131" type="section" level="1" n="91">
          <head xml:id="echoid-head102" xml:space="preserve">COROLLARIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s1118" xml:space="preserve">PAtet etiam ex hac, & </s>
            <s xml:id="echoid-s1119" xml:space="preserve">14. </s>
            <s xml:id="echoid-s1120" xml:space="preserve">huius, omnes ſimiles figuras planas poſſe
              <lb/>
            eſſe alicuius cylindrici, vel fruſti conici, oppoſitas baſes; </s>
            <s xml:id="echoid-s1121" xml:space="preserve">vnde qua
              <lb/>
            pro illis in Coroll. </s>
            <s xml:id="echoid-s1122" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1123" xml:space="preserve">19. </s>
            <s xml:id="echoid-s1124" xml:space="preserve">huius colliguntur, pro omnibus ſimilibus figu-
              <lb/>
            ris planis etiam colligi poſſunt.</s>
            <s xml:id="echoid-s1125" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div132" type="section" level="1" n="92">
          <head xml:id="echoid-head103" xml:space="preserve">LEMMA PRO ANTECED. PROP.</head>
          <p>
            <s xml:id="echoid-s1126" xml:space="preserve">SI in recta linea ſignenturtria puncta, primum, medium, & </s>
            <s xml:id="echoid-s1127" xml:space="preserve">po-
              <lb/>
            ſtremum, à primo autem, & </s>
            <s xml:id="echoid-s1128" xml:space="preserve">medio ducantur ad eandem par-
              <lb/>
            tem duę inuicem parallelę ita ſe habentes, vt educta à primo ad edu-
              <lb/>
            ctam à ſecundo, ſit veluti recta inter primum, & </s>
            <s xml:id="echoid-s1129" xml:space="preserve">poſtremum pun-
              <lb/>
            ctum poſita, ad eam, quę inter medium, & </s>
            <s xml:id="echoid-s1130" xml:space="preserve">idem poſtremum ſita eſt;
              <lb/>
            </s>
            <s xml:id="echoid-s1131" xml:space="preserve">Extrema puncta parallelarum, quę non ſunt in propoſita linea, & </s>
            <s xml:id="echoid-s1132" xml:space="preserve">
              <lb/>
            illius poſtremum, eruntin recta linea.</s>
            <s xml:id="echoid-s1133" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1134" xml:space="preserve">Sit propoſita recta, AC, in qua ſignatis vt-
              <lb/>
              <figure xlink:label="fig-0062-01" xlink:href="fig-0062-01a" number="31">
                <image file="0062-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0062-01"/>
              </figure>
            cumque tribus punctis, C, primo, B, medio,
              <lb/>
            &</s>
            <s xml:id="echoid-s1135" xml:space="preserve">, A, poſtremo, à punctis, C, B, educantur
              <lb/>
            ad eandem partem duę inuicem parallelę, quę
              <lb/>
            ſint, CE, BD, ita ſe habentes, vt, CE, ad,
              <lb/>
            BD, ſit, vt, CA, ad, AB. </s>
            <s xml:id="echoid-s1136" xml:space="preserve">Dico puncta,
              <lb/>
            A, D, E, eſſe in recta linea, ſi enim (iuncta,
              <lb/>
            ED,) ipſa, ED, producta non tranſit per,
              <lb/>
            A, tranſibit ſupra, vel infra, A, ſecans, CA,
              <lb/>
            (nam, BD, eſt minor ipſa, CE, vt eſt, AB,
              <lb/>
            minor, AC,) tranſeat, vt per, M, quia igi-
              <lb/>
            tur, EDM, eſt recta erit, MCE, triangu-
              <lb/>
            lus, in quo lateri, CE, ducitur parallela, B
              <lb/>
            D, ergo trianguli, ECM, DBM, erunt æ-
              <lb/>
              <note position="left" xlink:label="note-0062-01" xlink:href="note-0062-01a" xml:space="preserve">4. Sexti
                <lb/>
              Elem.</note>
            quianguli, & </s>
            <s xml:id="echoid-s1137" xml:space="preserve">circa æquales angulos latera proportionalia, ergo, per-
              <lb/>
            mutando, CE, ad, BD, erit vt, CM, ad, MB, eſt autem vt, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum