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

List of thumbnails

< >
491
491 (473) 		492
492 (474)
493
493 (473) 		494
494 (474)
495
495 (475) 		496
496 (476)
497
497 (477) 		498
498 (478)
499
499 (479) 		500
500 (480)
< >
page |< < (478) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1123" type="section" level="1" n="673">
          <pb o="478" file="0498" n="498" rhead="GEOMETRIÆ"/>
        </div>
        <div xml:id="echoid-div1124" type="section" level="1" n="674">
          <head xml:id="echoid-head704" xml:space="preserve">THEOREMA XXIV. PROPOS. XXXI.</head>
          <p>
            <s xml:id="echoid-s12249" xml:space="preserve">SI in ſpatio helico primi circuli ſpiralium conicus in
              <lb/>
            eadem altitudine cum apice parabolico, in baſi dicto
              <lb/>
            circulo exiſtente, ſit conſtitutus; </s>
            <s xml:id="echoid-s12250" xml:space="preserve">apex parabolicus erit
              <lb/>
            ſexquialter dicti conici.</s>
            <s xml:id="echoid-s12251" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12252" xml:space="preserve">Patet hæc Propoſitio, nam ſi in dicto circulo, vt in baſi, & </s>
            <s xml:id="echoid-s12253" xml:space="preserve">cir-
              <lb/>
              <note position="left" xlink:label="note-0498-01" xlink:href="note-0498-01a" xml:space="preserve">Coroll. 8
                <lb/>
              Prop. 51.
                <lb/>
              l. 4. ſect. 1.
                <lb/>
              22. huius.</note>
            ca eundem axim cum dictis ſolidis ſit cylindrus conſtitutus, hic
              <lb/>
            erit ſexcuplus apicis parabolici, & </s>
            <s xml:id="echoid-s12254" xml:space="preserve">nonuplus dicti primi conici, er-
              <lb/>
            go apex parabolicus ad cylindrum erit, vt 3. </s>
            <s xml:id="echoid-s12255" xml:space="preserve">ad 18. </s>
            <s xml:id="echoid-s12256" xml:space="preserve">& </s>
            <s xml:id="echoid-s12257" xml:space="preserve">conicus ad
              <lb/>
            ipſum, vt 2. </s>
            <s xml:id="echoid-s12258" xml:space="preserve">ad 18. </s>
            <s xml:id="echoid-s12259" xml:space="preserve">vnde apex adconicum erit, vt 3. </s>
            <s xml:id="echoid-s12260" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s12261" xml:space="preserve">ideſt in
              <lb/>
            ratione ſexquialtera, quod erat oſtendendum.</s>
            <s xml:id="echoid-s12262" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1126" type="section" level="1" n="675">
          <head xml:id="echoid-head705" xml:space="preserve">THEOREMA XXV. PROPOS. XXXII.</head>
          <p>
            <s xml:id="echoid-s12263" xml:space="preserve">SI circa diametrum baſis ſemianuli ſtricti parabolici
              <lb/>
            tanquam circa propriam diametrum ſphæra, vel ſphę-
              <lb/>
            rois, fuerit conſtituta, cuius ſecunda diamet@er ſit æqualis
              <lb/>
            altitudine, ſiue axi, eiuſdem ſemianuli; </s>
            <s xml:id="echoid-s12264" xml:space="preserve">dicta ſphæra, vel
              <lb/>
            ſphærois ipſi ſemianulo æqualis erit.</s>
            <s xml:id="echoid-s12265" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12266" xml:space="preserve">Hæc etiam patet, nam cylindrus in eadem baſi cum ſemianulo
              <lb/>
            dicto, & </s>
            <s xml:id="echoid-s12267" xml:space="preserve">eadem altitudine, eſt eiuſdem ſexquialter, eſt autem etiã
              <lb/>
              <note position="left" xlink:label="note-0498-02" xlink:href="note-0498-02a" xml:space="preserve">Corol. 10.
                <lb/>
              51. lib. 4
                <lb/>
              ſect. poiſe
                <lb/>
              rior.</note>
            ſexquialter d ctæ ſphæræ, vel ſphæroidis, & </s>
            <s xml:id="echoid-s12268" xml:space="preserve">ideò dicta ſphæra, vel
              <lb/>
            ſphærois, erit æqualis dicto ſemianulo, quod oſtendendum erat.</s>
            <s xml:id="echoid-s12269" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Coroll. 1.
            <lb/>
          34. l. 3.</note>
        </div>
        <div xml:id="echoid-div1128" type="section" level="1" n="676">
          <head xml:id="echoid-head706" xml:space="preserve">THEOREMA XXVI. PROPOS. XXXIII.</head>
          <p>
            <s xml:id="echoid-s12270" xml:space="preserve">SI cylindrus, & </s>
            <s xml:id="echoid-s12271" xml:space="preserve">conus, hæmiſphærium, vel hæmiſphę-
              <lb/>
            roides, conoides parabolicum, apex parabolicus, & </s>
            <s xml:id="echoid-s12272" xml:space="preserve">
              <lb/>
            ſphæralis, fuerint in baſi eodem circul
              <unsure/>
            o, & </s>
            <s xml:id="echoid-s12273" xml:space="preserve">circa eundem
              <lb/>
            axim, infraſcriptam rationem inter ſe habebunt -</s>
          </p>
          <p>
            <s xml:id="echoid-s12274" xml:space="preserve">Sit cylindrus, BE, in baſi circulo, CE, circa axem, FD, in qui-
              <lb/>
            bus ſint etiam hæmiſphærium, vel hæmiſphæroides, CFE, conoi-
              <lb/>
            d@s parabolicum, CRFkE, conus, CFE, apex parabolicus, CVF
              <lb/>
            ZE, & </s>
            <s xml:id="echoid-s12275" xml:space="preserve">apex ſphæralis, vel ſphæroidalis, CXFYE, qualium igitur
              <lb/>
            partium cylindrus, BE, eſt 126. </s>
            <s xml:id="echoid-s12276" xml:space="preserve">talium hæmilphærium eſt 84. </s>
            <s xml:id="echoid-s12277" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum