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

Table of contents

< >
[411.] THEOREMA V. PROPOS. V.
Page: 311 (291)
[412.] COROLLARIV M.
Page: 312 (292)
[413.] THEOREMA VI. PROPOS. VI.
Page: 313 (293)
[414.] COROLLARIV M.
Page: 315 (295)
[415.] THEOREMA VII. PROPOS. VII.
Page: 315 (295)
[416.] THEOREMA VIII. PROPOS. VIII.
Page: 316 (296)
[417.] SCHOLIV M.
Page: 316 (296)
[418.] PROBLEMA I. PROPOS. IX.
Page: 316 (296)
[419.] THEOREMAIX. PROPOS. X.
Page: 317 (297)
[420.] COROLLARIV M.
Page: 318 (298)
[421.] THEOREMA X. PROPOS. XI.
Page: 318 (298)
[422.] COROLLARIV M.
Page: 320 (300)
[423.] THEOREMA XI. PROPOS. XII.
Page: 320 (300)
[424.] THEOREMA XII. PROPOS. XIII.
Page: 321 (301)
[425.] THEOREMA XIII. PROPOS. XIV.
Page: 323 (303)
[426.] THEOREMA XIV. PROPOS. XV.
Page: 324 (304)
[427.] THEOREMA XV. PROPOS. XVI.
Page: 325 (305)
[428.] THEOREMA XVI. PROPOS. XVII.
Page: 325 (305)
[429.] COROLLARIVM.
Page: 327 (307)
[430.] THEOREMA XVII. PROPOS. XVIII.
Page: 327 (307)
[431.] THEOREMA XVIII. PROPOS. XIX.
Page: 328 (308)
[432.] A. COROLL. SECTIO I.
Page: 328 (308)
[433.] B. SECTIO II.
Page: 329 (309)
[434.] C. SECTIO III.
Page: 329 (309)
[435.] D. SECTIO IV.
Page: 329 (309)
[436.] E. SECTIO V.
Page: 329 (309)
[437.] SCHOLIV M.
Page: 330 (310)
[438.] THEOREMA XIX. PROPOS. XX.
Page: 330 (310)
[439.] COROLLARIVM.
Page: 331 (311)
[440.] THEOREMA XX. PROPOS. XXI.
Page: 331 (311)
< >
page |< < (325) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div782" type="section" level="1" n="463">
          <pb o="325" file="0345" n="345" rhead="LIBER IV."/>
        </div>
        <div xml:id="echoid-div783" type="section" level="1" n="464">
          <head xml:id="echoid-head484" xml:space="preserve">E. SECTIO V.</head>
          <p style="it">
            <s xml:id="echoid-s7811" xml:space="preserve">_T_Andem, quòd, ſi dictorum trilineorum ſecantes ád tángentes eán-
              <lb/>
            demrationem habuerint, omnia quadrata eorundem erunt in tri-
              <lb/>
            plaratione tangentium, vel ſecantium.</s>
            <s xml:id="echoid-s7812" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div784" type="section" level="1" n="465">
          <head xml:id="echoid-head485" xml:space="preserve">THEOREMA XXIX. PROPOS. XXXI.</head>
          <p>
            <s xml:id="echoid-s7813" xml:space="preserve">EXponatur figura Theor. </s>
            <s xml:id="echoid-s7814" xml:space="preserve">antecedentis, & </s>
            <s xml:id="echoid-s7815" xml:space="preserve">intra paralle-
              <lb/>
            logrammum, AC, ducatur vtcunq; </s>
            <s xml:id="echoid-s7816" xml:space="preserve">recta, EF, pa-
              <lb/>
            rallelaipſi, BC, quæ ſumatur pro regula: </s>
            <s xml:id="echoid-s7817" xml:space="preserve">Oſtendemus. </s>
            <s xml:id="echoid-s7818" xml:space="preserve">n.
              <lb/>
            </s>
            <s xml:id="echoid-s7819" xml:space="preserve">om@ia quadrata, AC, demptis omnibus quadratis ſemipa-
              <lb/>
            rabolæ, ABC, ad omnia quadrata, EC, demptis omni-
              <lb/>
            bus quadratis quadrilinei, MEBC, eſſe vt quadratum, A
              <lb/>
            B, ad quadratum, BE.</s>
            <s xml:id="echoid-s7820" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7821" xml:space="preserve">Omnia. </s>
            <s xml:id="echoid-s7822" xml:space="preserve">n. </s>
            <s xml:id="echoid-s7823" xml:space="preserve">quadrata, AC, ad omnia quadrata, EC, demptis
              <lb/>
            omnibus quadratis quadrilinei, EMCB, habent rationem compo-
              <lb/>
            ſitam ex ea, quam habent omnia quadrata, AC, ad omnia qua-
              <lb/>
            drata, EC, ideſt ex ea, quam habet, AB, ad, BE, & </s>
            <s xml:id="echoid-s7824" xml:space="preserve">ex ea,
              <lb/>
              <note position="right" xlink:label="note-0345-01" xlink:href="note-0345-01a" xml:space="preserve">10. l. 2.</note>
            quam habent omnia quadrata, EC, ad reſiduum, demptis ab ijſdem
              <lb/>
              <figure xlink:label="fig-0345-01" xlink:href="fig-0345-01a" number="232">
                <image file="0345-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0345-01"/>
              </figure>
            omnibus quadratis quadrilinei, MEBC,
              <lb/>
            .</s>
            <s xml:id="echoid-s7825" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7826" xml:space="preserve">ex ea, quam habet, AB, ad {1/2}, BE,
              <lb/>
              <note position="right" xlink:label="note-0345-02" xlink:href="note-0345-02a" xml:space="preserve">23. huius.</note>
            duæ autem hæ rationes .</s>
            <s xml:id="echoid-s7827" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s7828" xml:space="preserve">quàm habet,
              <lb/>
            AB, ad, BE, &</s>
            <s xml:id="echoid-s7829" xml:space="preserve">, AB, ad {1/2}. </s>
            <s xml:id="echoid-s7830" xml:space="preserve">BE, com-
              <lb/>
            ponunt rationem quadrati, AB, ad re-
              <lb/>
            ctangulum ſub, EB, & </s>
            <s xml:id="echoid-s7831" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s7832" xml:space="preserve">BE, .</s>
            <s xml:id="echoid-s7833" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7834" xml:space="preserve">ad
              <lb/>
            dimidium quadrati, BE, ergo omnia
              <lb/>
              <note position="right" xlink:label="note-0345-03" xlink:href="note-0345-03a" xml:space="preserve">21. huius.</note>
            quadrata, AC, ad omnia quadrata, E
              <lb/>
            C, demptis omnibus quadratis quadrili-
              <lb/>
            nei, MEBC, erunt vt quadratum, AB,
              <lb/>
            ad dimidium quadrati, BE, ſunt autem omnia quadrata, AC,
              <lb/>
            demptis omnibus quadratis ſemiparabolæ, ABC, dimidium
              <lb/>
            omnium quadratorum, AC, quia omnia quadrata, AC, ſunt du-
              <lb/>
            pla omnium quadratorum ſemiparabolæ, ABC, ergo omnia qua-
              <lb/>
            drata, AC, demptis omnibus quadratis ſemiparabolæ, ABC, ad
              <lb/>
            omnia quadrata, EC, demptis omnibus quadratis quadrilinei, E
              <lb/>
            MCB, erunt vt dimidium quadrati, AB, ad dimidium quadrati,
              <lb/>
            BE, ideſt vt quadratum, AB, ad quadratum, BE, quod erat
              <lb/>
            demonſtrandum.</s>
            <s xml:id="echoid-s7835" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum