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

Page concordance

< >
Scan Original
311 291
312 292
313 293
314 294
315 295
316 296
317 297
318 298
319 299
320 300
321 301
322 302
323 303
324 304
325 305
326 306
327 307
328 308
329 309
330 310
331 311
332 312
333 313
334 314
335 315
336 316
337 317
338 318
339 319
340 320
< >
page |< < (323) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div776" type="section" level="1" n="458">
          <pb o="323" file="0343" n="343" rhead="LIBER IV."/>
        </div>
        <div xml:id="echoid-div777" type="section" level="1" n="459">
          <head xml:id="echoid-head479" xml:space="preserve">THEOREMA XXVIII. PROPOS. XXX.</head>
          <p>
            <s xml:id="echoid-s7758" xml:space="preserve">SI duæ rectæ lineæ ducantur, quarum altera parabolam
              <lb/>
            tangat, altera verò axi, vel diametro parabolæ æqui-
              <lb/>
            diſtanter ducta eandem ſecet, in idem punctum concurren-
              <lb/>
            tes: </s>
            <s xml:id="echoid-s7759" xml:space="preserve">Omnia quadrata parallelogrammi, regula tangente,
              <lb/>
            erunt ſexcupla omnium quadratorum trilinei ſub dictis tan-
              <lb/>
            gente, & </s>
            <s xml:id="echoid-s7760" xml:space="preserve">ſecante, & </s>
            <s xml:id="echoid-s7761" xml:space="preserve">curua parabolæ ab ijſdem incluſa,
              <lb/>
            comprehenſi.</s>
            <s xml:id="echoid-s7762" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7763" xml:space="preserve">Sit ſemiparabola, ACB, quam tangat lineæ, AD, & </s>
            <s xml:id="echoid-s7764" xml:space="preserve">à pun-
              <lb/>
            cto, A, ducta, AB, axis, vel diameter, integræ parabolæ, dein-
              <lb/>
            de agatur vtcunque, DC, parallela axi, vel diametro, AB, ſecans
              <lb/>
            curuam parabolæ in, C, & </s>
            <s xml:id="echoid-s7765" xml:space="preserve">occurrens tangenti, AD, in, D, duca-
              <lb/>
            tur tandem à puncto, C, ipſi, AD, æquidiſtans, CB, ſecans, AB,
              <lb/>
            in, B, regula autem ſit, AD. </s>
            <s xml:id="echoid-s7766" xml:space="preserve">Dico ergo omnia quadrata parallelo-
              <lb/>
              <figure xlink:label="fig-0343-01" xlink:href="fig-0343-01a" number="230">
                <image file="0343-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0343-01"/>
              </figure>
            grammi, AC, eſſe omnium quadratorum
              <lb/>
            trilinei, ADC, ſexcupla: </s>
            <s xml:id="echoid-s7767" xml:space="preserve">Omnia enim
              <lb/>
            quadrata, AC, ad rectangula ſub, AC,
              <lb/>
              <note position="right" xlink:label="note-0343-01" xlink:href="note-0343-01a" xml:space="preserve">Coroll. 1.
                <lb/>
              26. l. 2.</note>
            & </s>
            <s xml:id="echoid-s7768" xml:space="preserve">ſemiparabola, ABC, ſunt vt, AC, ad
              <lb/>
            ſemiparabolam, ABC, .</s>
            <s xml:id="echoid-s7769" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7770" xml:space="preserve">ſexquialtera
              <lb/>
            .</s>
            <s xml:id="echoid-s7771" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7772" xml:space="preserve">vt 6. </s>
            <s xml:id="echoid-s7773" xml:space="preserve">ad 4. </s>
            <s xml:id="echoid-s7774" xml:space="preserve">omnia autem quadrata, AC,
              <lb/>
              <note position="right" xlink:label="note-0343-02" xlink:href="note-0343-02a" xml:space="preserve">21. huius.</note>
            ad omnia quadrata ſemiparabolę ABC,
              <lb/>
            ſunt dupla .</s>
            <s xml:id="echoid-s7775" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7776" xml:space="preserve">vt 6. </s>
            <s xml:id="echoid-s7777" xml:space="preserve">ad 3. </s>
            <s xml:id="echoid-s7778" xml:space="preserve">ergo omnia qua-
              <lb/>
              <note position="right" xlink:label="note-0343-03" xlink:href="note-0343-03a" xml:space="preserve">Coroll.
                <lb/>
              23. l. 2.</note>
            drata, AC, ad reſiduum demptis omni-
              <lb/>
            bus quadratis ſemiparabolæ, ABC, à re-
              <lb/>
            ctangulis ſub, AC, & </s>
            <s xml:id="echoid-s7779" xml:space="preserve">ſemiparabola, ABC, .</s>
            <s xml:id="echoid-s7780" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7781" xml:space="preserve">ad rectangula ſub
              <lb/>
            ſemiparabola, ABC, & </s>
            <s xml:id="echoid-s7782" xml:space="preserve">trilineo, ADC, erunt in ratione ſex-
              <lb/>
            cuplaideſt vt 6. </s>
            <s xml:id="echoid-s7783" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s7784" xml:space="preserve">ad eadem verò bis ſumpta, vt 6. </s>
            <s xml:id="echoid-s7785" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s7786" xml:space="preserve">quo-
              <lb/>
            niam verò omnia quadrata, AC, ad omnia quadrata ſemipara-
              <lb/>
            bolæ, ABC, ſum vt 6. </s>
            <s xml:id="echoid-s7787" xml:space="preserve">ad 3. </s>
            <s xml:id="echoid-s7788" xml:space="preserve">vt dictum eſt, ideò omnia quadrata,
              <lb/>
            AC, ad omnia quadrata ſemiparabolæ, ABC, cum rectangulis
              <lb/>
            bis ſub ſemiparabola, ABC, & </s>
            <s xml:id="echoid-s7789" xml:space="preserve">trilineo, ADC, erunt vt 6. </s>
            <s xml:id="echoid-s7790" xml:space="preserve">ad 5.
              <lb/>
            </s>
            <s xml:id="echoid-s7791" xml:space="preserve">ergo ad reliquum ſcilicet ad omnia quadrata trilinei, ADC, omnia
              <lb/>
              <note position="right" xlink:label="note-0343-04" xlink:href="note-0343-04a" xml:space="preserve">D. 23. l. 2.</note>
            quadrata, AC, erunt vt 6. </s>
            <s xml:id="echoid-s7792" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s7793" xml:space="preserve">ideſt erunt eorundem ſexcupla,
              <lb/>
            quod oſtendere oportebat.</s>
            <s xml:id="echoid-s7794" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum