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 |< < (443) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1051" type="section" level="1" n="633">
          <p style="it">
            <s xml:id="echoid-s11437" xml:space="preserve">
              <pb o="443" file="0463" n="463" rhead="LIBER VI."/>
              <figure xlink:label="fig-0463-01" xlink:href="fig-0463-01a" number="318">
                <image file="0463-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0463-01"/>
              </figure>
            etiam parallela, ΚΣ,
              <lb/>
            abſcinditab, LA, ver
              <lb/>
            ſus, A, {4/5}. </s>
            <s xml:id="echoid-s11438" xml:space="preserve">ipſius, LA,
              <lb/>
            ſic ergo puncta notata
              <lb/>
            erunt, Q, γ Ζ, &</s>
            <s xml:id="echoid-s11439" xml:space="preserve">, Φ,
              <lb/>
            Δ, Γ, Π, ℟, Χ, per
              <lb/>
            quæ ſi extend itur cur-
              <lb/>
            ua linea, dico propin-
              <lb/>
            quiſſimè ſic Parabolã
              <lb/>
            delineari, prædictanẽ-
              <lb/>
            pè puncta eſſe in Pa-
              <lb/>
            rabola, cuius diame-
              <lb/>
            ter, A2, & </s>
            <s xml:id="echoid-s11440" xml:space="preserve">baſis, QX,
              <lb/>
            etenim babet bæc pro-
              <lb/>
            prietatem in præbabito Corollario declaratam, vel, vt clarius loquar,
              <lb/>
            XF, ad, E℟, exempligratia babetrationem compoſitam ex ratione, X
              <lb/>
            F, ad, FV, ideſt, propter conſtructionem, ex ratione, FA, ad, AE, & </s>
            <s xml:id="echoid-s11441" xml:space="preserve">ex
              <lb/>
            ratione, VF, ad, E℟, boc eſt adbuc ex ratione, FA, ad, AE, duæ autẽ
              <lb/>
            rationes, F A, ad, AE, componunt ratione quadrati, FA, ad quadra-
              <lb/>
            tum, AE, ergo, XF, ad, E℟, eſt Vt quadratum, FA, ad quadratum, A
              <lb/>
              <note position="right" xlink:label="note-0463-01" xlink:href="note-0463-01a" xml:space="preserve">Corol. 1.
                <lb/>
              1. 4.</note>
            E, ſedſic etiam eſt, FX, ad parallelam ipſi, A2, interiectam inter, A
              <lb/>
            F, & </s>
            <s xml:id="echoid-s11442" xml:space="preserve">Parabolam circa diametrum, A2, in baſi, QX, ergo punctum,
              <lb/>
            ℟, eſt in tali parabola: </s>
            <s xml:id="echoid-s11443" xml:space="preserve">Hoc idem oſtendemus eodem modo de cęteris
              <lb/>
            punctis, Π Γ, Δ, Φ, &</s>
            <s xml:id="echoid-s11444" xml:space="preserve">, Z γ, ergo dicta puncta ſunt omnia in dicta pa-
              <lb/>
            rabola. </s>
            <s xml:id="echoid-s11445" xml:space="preserve">Hic quidẽ modus debuiſſet poni Lib. </s>
            <s xml:id="echoid-s11446" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11447" xml:space="preserve">ſiue in meo Tractatu de
              <lb/>
            Specuio V ſtorio iam in lucem edito, ſed quia oritur bic ex proprietate
              <lb/>
            proximè demonſtrata, nec illud prius menti ſubuenit, propterea idip.
              <lb/>
            </s>
            <s xml:id="echoid-s11448" xml:space="preserve">ſum bic ſubiungere libuit.</s>
            <s xml:id="echoid-s11449" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1053" type="section" level="1" n="634">
          <head xml:id="echoid-head664" xml:space="preserve">THEOREMA X. PROPOS. X.</head>
          <p>
            <s xml:id="echoid-s11450" xml:space="preserve">SI in ſpirali ex prima reuolutione orta ſumatur punctũ,
              <lb/>
            quod non ſit initium, nec terminus eiuſdem ſpiralis,
              <lb/>
            ab initio autem ſpiralis ad dictum punctum agatur recta
              <lb/>
            linea, & </s>
            <s xml:id="echoid-s11451" xml:space="preserve">ſuper initio ſpiralis centro ad diſtantiam dicti pũ-
              <lb/>
            cti deſctibatur circulus, eiuſdem portio comprehenſa du-
              <lb/>
            cta linea, & </s>
            <s xml:id="echoid-s11452" xml:space="preserve">portione eius, quæ dicitur reuolutionis initia-
              <lb/>
            tiua, quam abſcindit circumferentia dicti circuli, & </s>
            <s xml:id="echoid-s11453" xml:space="preserve">circũ-
              <lb/>
            ferentia eiuſdem, quæ eſt ad conſequentia, tripla eſt figu-
              <lb/>
            ræ comprehenſæ ducta linea, & </s>
            <s xml:id="echoid-s11454" xml:space="preserve">portione ſpiralis, quæ eſt
              <lb/>
            ad conſequentia vſquc ad initium ſpiralis.</s>
            <s xml:id="echoid-s11455" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum