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 |< < (37) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div118" type="section" level="1" n="83">
          <p>
            <s xml:id="echoid-s985" xml:space="preserve">
              <pb o="37" file="0057" n="57" rhead="LIBERI."/>
            fit eas, quæ inter taliter incidentes, & </s>
            <s xml:id="echoid-s986" xml:space="preserve">perimetrum figurarum con-
              <lb/>
            tinentur, eodem ordine ſumptas, eſſe vt ipſas, HP, KN, inciden-
              <lb/>
              <note position="right" xlink:label="note-0057-01" xlink:href="note-0057-01a" xml:space="preserve">A. Def. 10.</note>
            tes, ſunt igitur figuræ planę, BVO, DTF, inter ſe ſimiles, & </s>
            <s xml:id="echoid-s987" xml:space="preserve">ho-
              <lb/>
            mologarum earundem regulæ ipſæ tangentes, dictæ figuræ ſunt in
              <lb/>
            planis æquidiſtantibus, quarum incidentes fibi inuicem ęquidiſtant,
              <lb/>
            & </s>
            <s xml:id="echoid-s988" xml:space="preserve">homologæ earundem figurarum ſunt ad eandem partem inciden-
              <lb/>
            tium, & </s>
            <s xml:id="echoid-s989" xml:space="preserve">ipſarum incidentium partes homologæ pariter ad eandem
              <lb/>
            partem conſtitutæ, igitur figuræ, VBO, TDF, nedum erunt ſimi-
              <lb/>
            les, ſed etiam ſimiliter poſitæ, quod oſtendendum erat.</s>
            <s xml:id="echoid-s990" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div120" type="section" level="1" n="84">
          <head xml:id="echoid-head95" xml:space="preserve">COROLLARIVMI.</head>
          <p style="it">
            <s xml:id="echoid-s991" xml:space="preserve">_E_T quia oſtenſum eſt ipſas tangentes, SP, XN, eſſe bomologárum
              <lb/>
            earundem ſimilium figurarum regulas, & </s>
            <s xml:id="echoid-s992" xml:space="preserve">ductæ ſunt vtcumque,
              <lb/>
            patet ſi duxerimus alias duas eiuſdem baſis oppoſitas tangentes, quæ cum
              <lb/>
            primò ductis angulos efficient æquales, & </s>
            <s xml:id="echoid-s993" xml:space="preserve">per ipſas, & </s>
            <s xml:id="echoid-s994" xml:space="preserve">verticem, A,
              <lb/>
            extenderimus duo plana (quorum & </s>
            <s xml:id="echoid-s995" xml:space="preserve">plani figuræ, BVO, producti com-
              <lb/>
            munes ſectiones erunt aliæ duæ figuræ, BVO, oppoſitæ tangentes) quod
              <lb/>
            eodem modo oſtendemus has ſecundas tangentes eſſe homologarum earun-
              <lb/>
            dem ſimilium figurarum regulas, & </s>
            <s xml:id="echoid-s996" xml:space="preserve">intra ipſas contineri earundem
              <lb/>
            quoq; </s>
            <s xml:id="echoid-s997" xml:space="preserve">incidentes, ſacient autem ſecunda tangentes cum primis angu-
              <lb/>
            los æquales, prima. </s>
            <s xml:id="echoid-s998" xml:space="preserve">n. </s>
            <s xml:id="echoid-s999" xml:space="preserve">ex. </s>
            <s xml:id="echoid-s1000" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1001" xml:space="preserve">tangens figuræ, BVO, quæ eſt, XN, eſt
              <lb/>
            parallela ipſi, SP, primæ tangenti figuræ, DTF, & </s>
            <s xml:id="echoid-s1002" xml:space="preserve">ſecundatangens
              <lb/>
            figuræ, BVO, eſt pariter parallela ſecundæ tangenti figuræ, DTF, nam
              <lb/>
            tum primæ, tum ſecundæ tangentes ſunt communes ſectiones æquidiſtan-
              <lb/>
            tium planorum, ipſarum nempè figurarum, BVO, DTF, productorum
              <lb/>
            planorum, & </s>
            <s xml:id="echoid-s1003" xml:space="preserve">ideò ſunt parallelæ, & </s>
            <s xml:id="echoid-s1004" xml:space="preserve">angulos continent æquales, vnde
              <lb/>
              <note position="right" xlink:label="note-0057-02" xlink:href="note-0057-02a" xml:space="preserve">_10. Vnde-_
                <lb/>
              _cimi El._</note>
            in figuris, quæ à planis baſi conici parallelis producuntur, ſi babeamus
              <lb/>
            bomologas cum àuabus quibuſdam regulis, eaſdem etiam babebimus cum
              <lb/>
            duabus quibaſuis alijs angulos æquales cum prædictis ad eandem partem
              <lb/>
            continentibus.</s>
            <s xml:id="echoid-s1005" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div122" type="section" level="1" n="85">
          <head xml:id="echoid-head96" xml:space="preserve">COROLLARIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s1006" xml:space="preserve">_P_Atet in ſuper ex bac, & </s>
            <s xml:id="echoid-s1007" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1008" xml:space="preserve">ac 12. </s>
            <s xml:id="echoid-s1009" xml:space="preserve">huius ſimilium planarum figu-
              <lb/>
            rarum, quæex ſectione planorum baſi cylindrici, vel conici æqui-
              <lb/>
            diſtantium in illis producuntur, vel ſunt oppoſitæ baſes cylindrici, aut
              <lb/>
            fruſti conici, poſſibile eſſe inuenire incidentes, quæ ſint & </s>
            <s xml:id="echoid-s1010" xml:space="preserve">ductarum vt-
              <lb/>
            cumq; </s>
            <s xml:id="echoid-s1011" xml:space="preserve">oppoſitarum earundem tangentium incidentes, & </s>
            <s xml:id="echoid-s1012" xml:space="preserve">quia punctum,
              <lb/>
            H, ſumptum eſt vtcumque, & </s>
            <s xml:id="echoid-s1013" xml:space="preserve">ab ipſo ducta quælibet incidens, HP, pa-
              <lb/>
            tet, quod, ducta vtcumque in dictis figuris incidente earum </s>
          </p>
        </div>
      </text>
    </echo>
Impressum