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

Table of Notes

< >
[Note]
Page: 79
[Note]
Page: 79
[Note]
Page: 79
[Note]
Page: 79
[Note]
Page: 79
[Note]
Page: 80
[Note]
Page: 80
[Note]
Page: 80
[Note]
Page: 80
[Note]
Page: 80
[Note]
Page: 81
[Note]
Page: 81
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 82
[Note]
Page: 84
[Note]
Page: 84
[Note]
Page: 84
[Note]
Page: 84
[Note]
Page: 84
[Note]
Page: 85
[Note]
Page: 85
[Note]
Page: 85
[Note]
Page: 85
[Note]
Page: 85
[Note]
Page: 85
[Note]
Page: 85
[Note]
Page: 85
[Note]
Page: 85
< >
page |< < (182) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div449" type="section" level="1" n="270">
          <p style="it">
            <s xml:id="echoid-s4459" xml:space="preserve">
              <pb o="182" file="0202" n="202" rhead="GEOMETRI Æ"/>
            ſecantium, & </s>
            <s xml:id="echoid-s4460" xml:space="preserve">baſium, quæ figuræ genitrices in cylindricis erunt paral-
              <lb/>
              <note position="left" xlink:label="note-0202-01" xlink:href="note-0202-01a" xml:space="preserve">_Cor. 6. l. I._
                <lb/>
              _16. lib. l._</note>
            lelogramma in conicis triangula, & </s>
            <s xml:id="echoid-s4461" xml:space="preserve">in fruſtis conicis trapezia; </s>
            <s xml:id="echoid-s4462" xml:space="preserve">igitur
              <lb/>
            verum eſt quodlibet ſolidum ſimilare genitum ex parallelogrammo iuxta
              <lb/>
            regulam vnum laterum eſſe cylindricum, & </s>
            <s xml:id="echoid-s4463" xml:space="preserve">genitum ex triangulo iux-
              <lb/>
            taregulam vnum laterum eſſe conicum, & </s>
            <s xml:id="echoid-s4464" xml:space="preserve">ex trapezio eſſe fruſtum co-
              <lb/>
            nicum; </s>
            <s xml:id="echoid-s4465" xml:space="preserve">& </s>
            <s xml:id="echoid-s4466" xml:space="preserve">vice verſa, quemlibet cylindrum eſſe ſolidum ſimilare geni-
              <lb/>
            tum ex parallelogrammo in ipſo producto per planum per latera ductum,
              <lb/>
            genitum inquam iuxta communem ſectionem eius, & </s>
            <s xml:id="echoid-s4467" xml:space="preserve">baſis cylindrici;
              <lb/>
            </s>
            <s xml:id="echoid-s4468" xml:space="preserve">& </s>
            <s xml:id="echoid-s4469" xml:space="preserve">quemlibet conicum eſſe ſolidum ſimilare genitum ex triangulo in eo-
              <lb/>
              <figure xlink:label="fig-0202-01" xlink:href="fig-0202-01a" number="119">
                <image file="0202-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0202-01"/>
              </figure>
            dem producto per traiectio-
              <lb/>
            nem plani per latera, geni-
              <lb/>
            tum, inquam iuxta commu-
              <lb/>
            nem ſectionem eius, & </s>
            <s xml:id="echoid-s4470" xml:space="preserve">baſis
              <lb/>
            dicticonici; </s>
            <s xml:id="echoid-s4471" xml:space="preserve">& </s>
            <s xml:id="echoid-s4472" xml:space="preserve">quodlibet fru-
              <lb/>
            ſtum conicum eſſe ſolidum ſi.
              <lb/>
            </s>
            <s xml:id="echoid-s4473" xml:space="preserve">milare genitum ex trapezio in
              <lb/>
            ipſo producto per traiectionem
              <lb/>
            plani per latera eiuſdem fru-
              <lb/>
            ſti, genitum inquam iuxtare-
              <lb/>
            gulam communem ſectionem-
              <lb/>
            eius, & </s>
            <s xml:id="echoid-s4474" xml:space="preserve">vnius baſium eiu-
              <lb/>
            ſdem: </s>
            <s xml:id="echoid-s4475" xml:space="preserve">Siue ergo, expoſito pa-
              <lb/>
            rallelogrammo, & </s>
            <s xml:id="echoid-s4476" xml:space="preserve">triangulo intellexeris iuxta diffin 8. </s>
            <s xml:id="echoid-s4477" xml:space="preserve">huius, deſcribi
              <lb/>
            omnes figuras ſimiles eis quæ deſcribuntur à baſibus dicti parallelogram-
              <lb/>
            mi, & </s>
            <s xml:id="echoid-s4478" xml:space="preserve">trianguli, & </s>
            <s xml:id="echoid-s4479" xml:space="preserve">ſic conceperis effici ſolidum, cuius illæ ſunt omnia
              <lb/>
            plana; </s>
            <s xml:id="echoid-s4480" xml:space="preserve">ſiue intellexeris latus dicti parallelogrammi, vel trianguli in-
              <lb/>
              <note position="left" xlink:label="note-0202-02" xlink:href="note-0202-02a" xml:space="preserve">_Diff. 3. &_
                <lb/>
              _4. lib. I._</note>
            definitè productum reuolui per circuitum figurarum à baſibus deſcripta-
              <lb/>
            rum, vt babeas ſolidum dicta ſuperficie deſcripta, & </s>
            <s xml:id="echoid-s4481" xml:space="preserve">baſi, vel baſibus
              <lb/>
            comprehenſum, idem vtroque modo tibi obuenit ſolidum, poteſt autem
              <lb/>
            prior vocarigeneratio ſolidorum per deſcriptionem figurarum; </s>
            <s xml:id="echoid-s4482" xml:space="preserve">poſteriov
              <lb/>
            autem, generatio ſolidorum per reuolutionem facta, quæ maioris diluci-
              <lb/>
            dationis gratia bic appoſui, vt ex hac declaratione aliqualiter pateat,
              <lb/>
            in plurimis etiam alijs vtramq; </s>
            <s xml:id="echoid-s4483" xml:space="preserve">gener ationemritè nos imaginari poſſe,
              <lb/>
            vt in ſpbęra, ſphęroide, & </s>
            <s xml:id="echoid-s4484" xml:space="preserve">conoidibus, & </s>
            <s xml:id="echoid-s4485" xml:space="preserve">eiuſdem fruſtis, & </s>
            <s xml:id="echoid-s4486" xml:space="preserve">alijs quam-
              <lb/>
            plurimis, vt ſuo loco animaduertetur.</s>
            <s xml:id="echoid-s4487" xml:space="preserve"/>
          </p>
          <figure number="120">
            <image file="0202-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0202-02"/>
          </figure>
        </div>
      </text>
    </echo>
Impressum