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

Page concordance

< >
Scan Original
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
61 41
62 42
63 43
64 44
65 45
66 46
67 47
68 48
69 49
70 50
< >
page |< < (23) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div87" type="section" level="1" n="65">
          <p>
            <s xml:id="echoid-s687" xml:space="preserve">
              <pb o="23" file="0043" n="43" rhead="LIBER I."/>
            vel, DC, planum per, EM, XR, ductum æquidiſtabit plauo, AC,
              <lb/>
            eſt autem planum, quod tangit cylindricum in, O, æquidiſtans pla-
              <lb/>
            no, AC, & </s>
            <s xml:id="echoid-s688" xml:space="preserve">tranſit per idem punctum, O, per quod tranſit planum
              <lb/>
            per, EM, XR, ductum, ergo illa duo plana fiunt vnum planum,
              <lb/>
            iacet autem, EM, in plano per, EM, XR, ducto, ergo iacet etiam
              <lb/>
            in plano ęquidiſtante ipſi, AC, & </s>
            <s xml:id="echoid-s689" xml:space="preserve">cylindricum, AC, tangente, igi-
              <lb/>
            tur tangit cylindricum in recta, EM. </s>
            <s xml:id="echoid-s690" xml:space="preserve">Eodem pacto ſi in alio pun-
              <lb/>
            cto extra, EM, in ſuperficie cylindracea ſumpto tangeret cylindri-
              <lb/>
            cum, AC, oſtenderemus tangere ipſum in latere, quod per tale pun-
              <lb/>
            ctum tranſiret; </s>
            <s xml:id="echoid-s691" xml:space="preserve">in quo caſu tangeret cylindricum in lateribus vno
              <lb/>
            pluribus, vt contingere poteſt. </s>
            <s xml:id="echoid-s692" xml:space="preserve">Tangat autem ſecundò ipſum in
              <lb/>
            plano, igitur in eo plano ſnmpto vtcumque puncto, tanget cylindri-
              <lb/>
            cum in latere tranſeunte per tale punctum, igitur planum contactus
              <lb/>
            tale eſt, vt in eo omnes ductæ rectæ lineæ æquidiſtantes ipſi, EM,
              <lb/>
            ſint latera cylindrici, AC, & </s>
            <s xml:id="echoid-s693" xml:space="preserve">ſubinde eidem, EM, æqualia, vnde
              <lb/>
            ſuperſicies, in qua iacent erit parallelogrammum, igitur planum
              <lb/>
            contactus in hoc caſu erit parallelogrammum, & </s>
            <s xml:id="echoid-s694" xml:space="preserve">erit æquiangulum
              <lb/>
            parallelogrammo, AC, nam eius latera ſunt parallela lateribus pa-
              <lb/>
            rallelogrammi, AC, & </s>
            <s xml:id="echoid-s695" xml:space="preserve">ideò continent angulos æquales contentis
              <lb/>
            à lateribus parallelogrammi, AC, vnde talia parallelogramma ſunt
              <lb/>
            æquiangula, igitur contactus plani æquidiſtantis plano per latera
              <lb/>
            cylindrici ducto, vel fit in latere, aut lateribus contacti cylindrici,
              <lb/>
            vel in parallelogrammo, ſiue parallelogrammis, in eiuſdem ſuper-
              <lb/>
            ficie iacentibus, & </s>
            <s xml:id="echoid-s696" xml:space="preserve">æquiangulis ei, quod fit a plano per latera ducto,
              <lb/>
            quod oſtendendum erat.</s>
            <s xml:id="echoid-s697" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div89" type="section" level="1" n="66">
          <head xml:id="echoid-head77" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s698" xml:space="preserve">_H_Inc babetur communes ſectiones plani tangentis, & </s>
            <s xml:id="echoid-s699" xml:space="preserve">cylindrici op-
              <lb/>
            poſitarum baſium productorum planorum, quæ ſint, VF, XR,
              <lb/>
            eſſe inter ſe parallelas, & </s>
            <s xml:id="echoid-s700" xml:space="preserve">tangere eaſdem baſes; </s>
            <s xml:id="echoid-s701" xml:space="preserve">ſcilicet, VF, ipſam
              <lb/>
            baſim, EAD, &</s>
            <s xml:id="echoid-s702" xml:space="preserve">, XR, ipſam, MBC.</s>
            <s xml:id="echoid-s703" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div90" type="section" level="1" n="67">
          <head xml:id="echoid-head78" xml:space="preserve">THEOREMA VII. PROPOS. X.</head>
          <p>
            <s xml:id="echoid-s704" xml:space="preserve">SI cylindricus quomodocumque ſecetur per latera, diui-
              <lb/>
            ditur in cylindricos à ſecantibus planis, ſi autem ſecetur
              <lb/>
            planis omnibus eiuſdem lateribus coincidentibus inter ſe
              <lb/>
            parallelis; </s>
            <s xml:id="echoid-s705" xml:space="preserve">ſolidum compræhenſum conceptis in cylindrico
              <lb/>
            figuris, & </s>
            <s xml:id="echoid-s706" xml:space="preserve">incluſa ſuperficie cylindracea, erit cylindricus.</s>
            <s xml:id="echoid-s707" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum