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

Table of contents

< >
[31.] VIII.
[32.] IX.
[33.] SCHOLIVM.
[34.] A. X.
[35.] B.
[36.] C.
[37.] D. IV.
[38.] E.
[39.] APPENDIX PRIOR Pro explicatione Definit. 10. antecedentis.
[40.] A. XI.
[43.] APPENDIX POSTERIOR Pro declaratione Definit. II.
[44.] SCHOLIVM.
[45.] XII.
[46.] XIII.
[47.] XIV.
[48.] XV.
[49.] POSTVLATA I.
[50.] II.
[51.] PROBLEMA I. PROPOS. 1.
[52.] COROLLARIVM.
[53.] PROBLEMA II. PROPOS. II.
[54.] PROBLEMA III. PROPOS. III.
[55.] SCHOLIVM.
[56.] THEOREMA I. PROPOS. IV.
[57.] COROLLARIVM I.
[58.] COROLLARIVM II.
[59.] THEOREMA II. PROPOS. V.
[60.] THEOREMA III. PROPOS. VI.
< >
page |< < (8) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div41" type="section" level="1" n="38">
          <p>
            <s xml:id="echoid-s390" xml:space="preserve">
              <pb o="8" file="0028" n="28" rhead="GEOMETRIÆ"/>
            ſimilium figurarum incidentes. </s>
            <s xml:id="echoid-s391" xml:space="preserve">Tales figuræ dicentur bi-
              <lb/>
            næ ſimiles, & </s>
            <s xml:id="echoid-s392" xml:space="preserve">ſimiliter inter ſe poſitę primò dictæ, ac ſecun-
              <lb/>
            dò dictæ, & </s>
            <s xml:id="echoid-s393" xml:space="preserve">earum, ac exremarum tangentium etiam dicen-
              <lb/>
            tur incidentes, quæ in tangentium extremas terminan-
              <lb/>
            tur.</s>
            <s xml:id="echoid-s394" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div42" type="section" level="1" n="39">
          <head xml:id="echoid-head49" xml:space="preserve">APPENDIX PRIOR
            <lb/>
          Pro explicatione Definit. 10. antecedentis.</head>
          <p style="it">
            <s xml:id="echoid-s395" xml:space="preserve">_S_Int duæ figuræ planæ. </s>
            <s xml:id="echoid-s396" xml:space="preserve">ABCD, KLγP, in quibus ſupponantur
              <lb/>
            ductæ oppoſitæ tangentes, AE, CG, in figura, ABCD, & </s>
            <s xml:id="echoid-s397" xml:space="preserve">KQ,
              <lb/>
              <note position="left" xlink:label="note-0028-01" xlink:href="note-0028-01a" xml:space="preserve">_B.Def.1._</note>
            γ℟, in fig. </s>
            <s xml:id="echoid-s398" xml:space="preserve">KLγP, quibus incidant duæ rectæ lineæ, EG, Q℟, ad
              <lb/>
            eundem angulum ex eadem parte, ſiue ſecent figuras, ſiue non, du-
              <lb/>
            ctis autem vtcumq dictis tangentibus parallelis, BF, L&</s>
            <s xml:id="echoid-s399" xml:space="preserve">, quæ
              <lb/>
            in puctis F, &</s>
            <s xml:id="echoid-s400" xml:space="preserve">, diuidant ſimiliter ad eandem partem ipſas, EC,
              <lb/>
            Q℟, & </s>
            <s xml:id="echoid-s401" xml:space="preserve">circuitus figu-
              <lb/>
              <figure xlink:label="fig-0028-01" xlink:href="fig-0028-01a" number="6">
                <image file="0028-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0028-01"/>
              </figure>
            rarum in punctis, B, I,
              <lb/>
            S, D, L, T, X, P. </s>
            <s xml:id="echoid-s402" xml:space="preserve">repe-
              <lb/>
            riamus, DF, ad, P&</s>
            <s xml:id="echoid-s403" xml:space="preserve">,
              <lb/>
            eſſe vt, EC, ad, Q℟,
              <lb/>
            & </s>
            <s xml:id="echoid-s404" xml:space="preserve">ita eſſe, SF, ad, X&</s>
            <s xml:id="echoid-s405" xml:space="preserve">,
              <lb/>
            IF, ad, T&</s>
            <s xml:id="echoid-s406" xml:space="preserve">, BF, ad
              <lb/>
            L&</s>
            <s xml:id="echoid-s407" xml:space="preserve">, ita nempè, vt, quæ
              <lb/>
            ſunt ad eandem partem
              <lb/>
            ipſarum, EG, Q℟, eo-
              <lb/>
            dem ordine ſumptæ, ſint,
              <lb/>
            vt ipſæ, EG, Q℟, ſic
              <lb/>
            etiam tangentes, AE, KQ, CG, γ℟, ſint vt, FQG, ℟, & </s>
            <s xml:id="echoid-s408" xml:space="preserve">ſic cæ-
              <lb/>
            teræ conſimiliter ſumptæ, tunc voco figuras, ABCD, KLγP ſimi-
              <lb/>
              <note position="left" xlink:label="note-0028-02" xlink:href="note-0028-02a" xml:space="preserve">_A Def.10._</note>
            les, & </s>
            <s xml:id="echoid-s409" xml:space="preserve">ipſas, EG, Q℟, incidentes ſimiles figurarum, ABCD, KLγP,
              <lb/>
              <note position="left" xlink:label="note-0028-03" xlink:href="note-0028-03a" xml:space="preserve">_B.Def.10._</note>
            & </s>
            <s xml:id="echoid-s410" xml:space="preserve">oppoſitarum tangentium, AE, CG, KQ, γ℟; </s>
            <s xml:id="echoid-s411" xml:space="preserve">ipſas, BI, SD,
              <lb/>
            LT, XP, quæ clanduntur perimetris figurarum, & </s>
            <s xml:id="echoid-s412" xml:space="preserve">diuidunt pro-
              <lb/>
            ductæ, ſiopus ſit, ipſas, EG, Q℟. </s>
            <s xml:id="echoid-s413" xml:space="preserve">ſimiliter ad eandem partem,
              <lb/>
            voco, homologas earumdem figurarum, quarum dictæ oppoſitæ
              <lb/>
              <note position="left" xlink:label="note-0028-04" xlink:href="note-0028-04a" xml:space="preserve">_C.Def.10_</note>
            tangentes dicuntur tangentes, ſiue regulæ.</s>
            <s xml:id="echoid-s414" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s415" xml:space="preserve">Cum verò figuræ, ABCD, KLγP, fuerint in eodem plano, </s>
          </p>
        </div>
      </text>
    </echo>