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

Page concordance

< >
Scan Original
201 181
202 182
203 183
204 184
205 185
206 186
207 187
208 188
209 189
210 190
211 191
212 192
213 193
214 194
215 195
216
217 197
218 198
219 199
220 200
221 201
222 202
223 203
224 204
225 205
226 206
227 207
228 208
229 209
230 210
< >
page |< < (193) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div488" type="section" level="1" n="294">
          <pb o="193" file="0213" n="213" rhead="LIBER II."/>
          <p>
            <s xml:id="echoid-s4772" xml:space="preserve">Hæc manifeſta eſt, nam habebunt baſes ipſis altitudinibus recipro-
              <lb/>
            cas, quod etiam vniuerſalius oſtenditur Vndecimo Elementorum
              <lb/>
            Propoſ. </s>
            <s xml:id="echoid-s4773" xml:space="preserve">36.</s>
            <s xml:id="echoid-s4774" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div489" type="section" level="1" n="295">
          <head xml:id="echoid-head311" xml:space="preserve">THEOREMA XLII. PROPOS. XLII.</head>
          <p>
            <s xml:id="echoid-s4775" xml:space="preserve">DAta recta linea terminata, vtcumque in puncto diuiſa,
              <lb/>
            poſſibile eſt ipſam ad alteram eiuſdem partium ita
              <lb/>
            producere, vt cubus compoſitæ ex propoſita linea, & </s>
            <s xml:id="echoid-s4776" xml:space="preserve">adiun-
              <lb/>
            cta, ſit æqualis cubo propoſitæ lineæ, ſimul cum cubo com-
              <lb/>
            poſitæ ex adiecta, & </s>
            <s xml:id="echoid-s4777" xml:space="preserve">illi conterminante portione ſectæ lineę.</s>
            <s xml:id="echoid-s4778" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4779" xml:space="preserve">Sit data recta linea, AC, terminata, diuiſaq; </s>
            <s xml:id="echoid-s4780" xml:space="preserve">vtcumque in pun-
              <lb/>
            cto, B, oftendendum eſt poſſibile eſſe ipſam ita producere ad alteram
              <lb/>
            illius partium, vt ad, C, vt cubus compoſitę ex, AC, & </s>
            <s xml:id="echoid-s4781" xml:space="preserve">adiecta, ſit
              <lb/>
            æqualis cubo, AC, cum cubo compoſitæ ex eadem adiecta, & </s>
            <s xml:id="echoid-s4782" xml:space="preserve">ex,
              <lb/>
            BC, portione, AC, adiectæ conterminante. </s>
            <s xml:id="echoid-s4783" xml:space="preserve">Producatur ergo, C
              <lb/>
            A, ad partes, A, vt in, N, ita quod, NB, ſit tripla, BA, ſiat dein-
              <lb/>
            de, vt, NB, ad, BC, ita quadratum, BC, ad quadratum rectæ li-
              <lb/>
            neę, M, ſeorſim poſitæ: </s>
            <s xml:id="echoid-s4784" xml:space="preserve">Vlterius exponatur recta, EF, æqualis com-
              <lb/>
            poſitæ ex, AC, CB, cui applicetur rectangulum æquale quadrato,
              <lb/>
              <figure xlink:label="fig-0213-01" xlink:href="fig-0213-01a" number="128">
                <image file="0213-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0213-01"/>
              </figure>
            M, excedens figura quadrata,
              <lb/>
              <note position="right" xlink:label="note-0213-01" xlink:href="note-0213-01a" xml:space="preserve">29. Sex.
                <lb/>
              lem,</note>
            cuius latus ſit, FH, producatur
              <lb/>
            autem, AC, verſus, C, vt in,
              <lb/>
            D, ita nempè, vt, CD, ſit
              <lb/>
            æqualis, FH. </s>
            <s xml:id="echoid-s4785" xml:space="preserve">Dico cubum to-
              <lb/>
            tius, AD, æquari duobus cubis,
              <lb/>
            AC, BD. </s>
            <s xml:id="echoid-s4786" xml:space="preserve">Cum.</s>
            <s xml:id="echoid-s4787" xml:space="preserve">n. </s>
            <s xml:id="echoid-s4788" xml:space="preserve">ſit, vt, N
              <lb/>
            B, ad, BC, ita quadratum, BC,
              <lb/>
            ad quadratum, M, ideò parallelepipedum ſub altitudine, AB, (qu
              <lb/>
            eſt, {1/3}, prædictę altitudinis, NB,) & </s>
            <s xml:id="echoid-s4789" xml:space="preserve">quadrato, M, æquabitur ter-
              <lb/>
            tiæ parti cubi, BC. </s>
            <s xml:id="echoid-s4790" xml:space="preserve">Quoniam verò quadratum, M, æquatur rectan-
              <lb/>
              <note position="right" xlink:label="note-0213-02" xlink:href="note-0213-02a" xml:space="preserve">E. Cor. 4
                <lb/>
              Gen. 34.
                <lb/>
              huius.</note>
            gulo, EHF, ideſt rectangulo ſub compoſita ex, AD, BC, & </s>
            <s xml:id="echoid-s4791" xml:space="preserve">ſub,
              <lb/>
            CD, ideò parallelepipedum ſub altitudine, AB, & </s>
            <s xml:id="echoid-s4792" xml:space="preserve">baſi rectangulo
              <lb/>
            ſub compoſita ex, AD, BC, & </s>
            <s xml:id="echoid-s4793" xml:space="preserve">ſub, DC, æquabitur tertiæ parti
              <lb/>
            cubi, BC, addatur commune parallelepipedum ſub, BC, & </s>
            <s xml:id="echoid-s4794" xml:space="preserve">baſi re-
              <lb/>
            ctangulo, BDC, erit ex vna parte hoc parallelepipedum cum, {1/3}, cu-
              <lb/>
            bi, BC, ex alia verò hæcſumma; </s>
            <s xml:id="echoid-s4795" xml:space="preserve">ſcilicet parallelepipedum ſub, AB,
              <lb/>
            & </s>
            <s xml:id="echoid-s4796" xml:space="preserve">ſub rectangulo ſub compoſita ex, AD, BC, & </s>
            <s xml:id="echoid-s4797" xml:space="preserve">ſub, DC, vna
              <lb/>
            cum parallelepipedo ſub, BC, & </s>
            <s xml:id="echoid-s4798" xml:space="preserve">rectangulo, BDC, quæ quidem
              <lb/>
            ſumma efficit parallelepipedum ſub, AC, & </s>
            <s xml:id="echoid-s4799" xml:space="preserve">rectangulo, ADC, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum