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 |< < (31) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div104" type="section" level="1" n="74">
          <p>
            <s xml:id="echoid-s873" xml:space="preserve">
              <pb o="31" file="0051" n="51" rhead="LIBERI."/>
            ergo, SM, æquidiſtans ipſi, TP, regulæ homologarum figurę, A
              <lb/>
            T, veluti, RK, æquidiſtat ipſi, NL, regulæ homologarum figu-
              <lb/>
            ræ, F N, & </s>
            <s xml:id="echoid-s874" xml:space="preserve">ſecant incidentes, BP, HL, ſimiliter ad eandem par-
              <lb/>
            tem in punctis, M, K, ergo ipſæ, SV, RI, erunt homologę di-
              <lb/>
            ctarum figurarum ſimilium, & </s>
            <s xml:id="echoid-s875" xml:space="preserve">ęqualium, quę ideò erunt æquales,
              <lb/>
            ſicut etiam ipſæ, VM, IK. </s>
            <s xml:id="echoid-s876" xml:space="preserve">& </s>
            <s xml:id="echoid-s877" xml:space="preserve">ſunt ęquidiſtantes, ergo eas iungen-
              <lb/>
            tes erunt ęquales, & </s>
            <s xml:id="echoid-s878" xml:space="preserve">ęquidiſtantes, ſcilicet, SR, VI, MK, eſtau-
              <lb/>
            tem, MK, parallela, & </s>
            <s xml:id="echoid-s879" xml:space="preserve">ęqualis ipſi, PL, ergo, SR, VI, erunt
              <lb/>
            ęquales, & </s>
            <s xml:id="echoid-s880" xml:space="preserve">parallelęipſi, PL: </s>
            <s xml:id="echoid-s881" xml:space="preserve">Eodem pacto per, EG, extendentes
              <lb/>
            planum ęquidiſtans plano, TL, quod ſecet figurarum, AT, FN,
              <lb/>
            productarum plana in rectis, QE, DG, oſtendemus ipſas, QO, D
              <lb/>
            C, eſſe homologas figurarum ſimilium, & </s>
            <s xml:id="echoid-s882" xml:space="preserve">ęqualium, AT, FN, & </s>
            <s xml:id="echoid-s883" xml:space="preserve">
              <lb/>
            ideò eas eſſe ęquales, vt & </s>
            <s xml:id="echoid-s884" xml:space="preserve">ipſas, OE, CG, ergo ſi iungantur, QD,
              <lb/>
            OC, iſtę erunt ęquales, & </s>
            <s xml:id="echoid-s885" xml:space="preserve">parallelę ipfi, EG, ideſt ipſi, PL; </s>
            <s xml:id="echoid-s886" xml:space="preserve">ſimi-
              <lb/>
            liter in cæteris planis procedemus, quæ inter plana, TL, AH, ip-
              <lb/>
            ſis æquidiſtantia ducuntur, oſtendentes, quæ iungunt extrema ho-
              <lb/>
            mologarum earundem figurarum, AT, FN, eſſe æquales, & </s>
            <s xml:id="echoid-s887" xml:space="preserve">ęqui-
              <lb/>
            diſtantesipſi, PL, ſi igitur, PL, regula ſtatuatur, erunt omnes di-
              <lb/>
            ctæ iungentes in ſuperficie quadam, per quam ipſi, PL, properan-
              <lb/>
            te quadam recta linea æquali ſemper ęquidiſtanter, eiuſdem extrema
              <lb/>
              <note position="right" xlink:label="note-0051-01" xlink:href="note-0051-01a" xml:space="preserve">Def.3.</note>
            iugiter manent in ambitu ſigurarum, AT, FN, ergo hæc erit ſu-
              <lb/>
            perficies cylindrici, cuius oppoſitę baſes erunt ipſę, AT, FN, ſunt
              <lb/>
            igitur, AT, FN, cylindrici cuiuſdam (nempè cuius latus eſt quod-
              <lb/>
            uis ipſorum, QD, SR, VI, OC,) oppoſirę baſes, quod erat no-
              <lb/>
            bis oſtendendum.</s>
            <s xml:id="echoid-s888" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div106" type="section" level="1" n="75">
          <head xml:id="echoid-head86" xml:space="preserve">THEOREMA XII. PROPOS. XV.</head>
          <p>
            <s xml:id="echoid-s889" xml:space="preserve">PVnctus manens, cui in reuolutione innititur latus coni-
              <lb/>
            ci, eſt vnicus vertex conicireſpectu eiuſdem baſis.</s>
            <s xml:id="echoid-s890" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s891" xml:space="preserve">Sit conicus, ABD, baſis, BD, punctus, eui innititur latus co-
              <lb/>
              <note position="right" xlink:label="note-0051-02" xlink:href="note-0051-02a" xml:space="preserve">A. Def.4.</note>
            nici, ABD, in reuolutione, quę ab eo fit per circuitum baſis, BD,
              <lb/>
              <figure xlink:label="fig-0051-01" xlink:href="fig-0051-01a" number="24">
                <image file="0051-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0051-01"/>
              </figure>
            ſit, A. </s>
            <s xml:id="echoid-s892" xml:space="preserve">Dico, A, eſſe vnicum verticem conici, A
              <lb/>
            BD, reſpectu baſis, BD. </s>
            <s xml:id="echoid-s893" xml:space="preserve">Intelligatur per pun-
              <lb/>
            ctum, A, ductum planum ęquidiſtans baſi, dico
              <lb/>
            hoc planum tantummodo in hoc puncto tangere
              <lb/>
            conicum, ſi enim poſſibile eſt eundem tangat, ſeu
              <lb/>
            ſecet in duobus punctis, vt in, C, A, iuncta ergo,
              <lb/>
            AC, illa erit in ſuperficie coniculari, & </s>
            <s xml:id="echoid-s894" xml:space="preserve">cum de-
              <lb/>
            ſcendat à puncto, A, per ipſum tranſiet aliquando
              <lb/>
            latus conici, vt, AB, igitur, AB, erit in plano ducto per, A, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum