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

List of thumbnails

< >
341
341 (321) 		342
342 (322)
343
343 (323) 		344
344 (324)
345
345 (325) 		346
346 (326)
347
347 (327) 		348
348 (328)
349
349 (329) 		350
350 (330)
< >
page |< < (321) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div765" type="section" level="1" n="451">
          <pb o="321" file="0341" n="341" rhead="LIBER IV."/>
        </div>
        <div xml:id="echoid-div767" type="section" level="1" n="452">
          <head xml:id="echoid-head472" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s7711" xml:space="preserve">_H_Inc patet, ſi àuæ rectæ lineæ ad axem obliquæ parabolas conſtitue-
              <lb/>
            rint, ſumpta pro regula conſtitutæ parabolæ recta eam conſtituen-
              <lb/>
            te, quoniam rectangula ſub dictis parabolis, & </s>
            <s xml:id="echoid-s7712" xml:space="preserve">figuris diſtantiarum ea-
              <lb/>
            rundem ad omnia quadrata parabolæ, cuius baſis ſit ad axim recta (quæ
              <lb/>
            pro eadem ſumatur pro regula) ſunt, vt quadrata diametrorum earun-
              <lb/>
            dem ad quadratum axis illius tertia parabolæ; </s>
            <s xml:id="echoid-s7713" xml:space="preserve">quod ideò illa rectangula
              <lb/>
            erunt inter ſe, vt diametrorum earundem parabolarum quadrata fuerint
              <lb/>
            quoq; </s>
            <s xml:id="echoid-s7714" xml:space="preserve">inter ſe.</s>
            <s xml:id="echoid-s7715" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div768" type="section" level="1" n="453">
          <head xml:id="echoid-head473" xml:space="preserve">THEOREMA XXVII. PROPOS. XXIX:</head>
          <p>
            <s xml:id="echoid-s7716" xml:space="preserve">OMnia quadrata parabolarum, regulis baſibus ſuntin-
              <lb/>
            terſe, vt omnia quadrata parallelogrammorum, in
              <lb/>
            eiſdem baſibus, & </s>
            <s xml:id="echoid-s7717" xml:space="preserve">circa eoſdem axes, veldiametros exi-
              <lb/>
            ſtentium, regulis eiſdem baſibus.</s>
            <s xml:id="echoid-s7718" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7719" xml:space="preserve">Manifeſta eſt hæc propoſitio, nam omnia quadrata dictarum
              <lb/>
            parabolarum ſunt ſubdupla omnium quadratorum eorundem pa-
              <lb/>
              <note position="right" xlink:label="note-0341-01" xlink:href="note-0341-01a" xml:space="preserve">21. huius</note>
            rallelogrammorum, endemregulis aſſumptis, ſcilicet parabolarum
              <lb/>
            baſibus iam dictis.</s>
            <s xml:id="echoid-s7720" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div770" type="section" level="1" n="454">
          <head xml:id="echoid-head474" xml:space="preserve">A. COROLL. SECTIO I.</head>
          <note position="right" xml:space="preserve">A</note>
          <p style="it">
            <s xml:id="echoid-s7721" xml:space="preserve">_H_Inc colligimus concluſiones, quæ de omnibus quadratis parallelo-
              <lb/>
            grammorum collectæ ſuntin Theorematibus _9. </s>
            <s xml:id="echoid-s7722" xml:space="preserve">10. </s>
            <s xml:id="echoid-s7723" xml:space="preserve">11. </s>
            <s xml:id="echoid-s7724" xml:space="preserve">12. </s>
            <s xml:id="echoid-s7725" xml:space="preserve">13._
              <lb/>
            </s>
            <s xml:id="echoid-s7726" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s7727" xml:space="preserve">_2._ </s>
            <s xml:id="echoid-s7728" xml:space="preserve">regulis ibidem aſſumptis, ſuppoſitis quibuſdam conditionibus
              <lb/>
            circa altitudines, vel latera æqualiter baſibus inclinata, & </s>
            <s xml:id="echoid-s7729" xml:space="preserve">quadrata
              <lb/>
            baſium, vel ipſas baſes, veriſicarietiam de omnibus quadratis parabo-
              <lb/>
            larum, ſuppoſitis eiſdem conditionibus circa axes, vel altitudines, vel
              <lb/>
            circa diametros æqualiter baſibus inclinatas, & </s>
            <s xml:id="echoid-s7730" xml:space="preserve">circa quadrata baſium,
              <lb/>
            vel eaſdem baſes; </s>
            <s xml:id="echoid-s7731" xml:space="preserve">nam his conditionibus axibus, vel altitudmibus, vel
              <lb/>
            diametris, & </s>
            <s xml:id="echoid-s7732" xml:space="preserve">quadratis baſium, vel ipſis baſibus competentibus, etiam
              <lb/>
            altitudinibus, vel lateribus parallelogrammorum, æqualiter baſibus
              <lb/>
            inclinatis, & </s>
            <s xml:id="echoid-s7733" xml:space="preserve">quadratis baſium, vel eiſdem baſibus, pariter conueniunt,
              <lb/>
            quæ quidem parallelogramma ſint in eiſdem baſibus, & </s>
            <s xml:id="echoid-s7734" xml:space="preserve">circa eoſdem
              <lb/>
            axes vel diametros cum parabolis; </s>
            <s xml:id="echoid-s7735" xml:space="preserve">& </s>
            <s xml:id="echoid-s7736" xml:space="preserve">ideò dictæ concluſiones, quæ </s>
          </p>
        </div>
      </text>
    </echo>
Impressum