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

Table of contents

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[431.] THEOREMA XVIII. PROPOS. XIX.
Page: 328 (308)
[432.] A. COROLL. SECTIO I.
Page: 328 (308)
[433.] B. SECTIO II.
Page: 329 (309)
[434.] C. SECTIO III.
Page: 329 (309)
[435.] D. SECTIO IV.
Page: 329 (309)
[436.] E. SECTIO V.
Page: 329 (309)
[437.] SCHOLIV M.
Page: 330 (310)
[438.] THEOREMA XIX. PROPOS. XX.
Page: 330 (310)
[439.] COROLLARIVM.
Page: 331 (311)
[440.] THEOREMA XX. PROPOS. XXI.
Page: 331 (311)
[441.] THEOREMA XXI. PROPOS. XXII.
Page: 332 (312)
[442.] THEOREMA XXII. PROPOS. XXIII.
Page: 333 (313)
[443.] COROLLARIVM.
Page: 334 (314)
[444.] THEOREMA XXIII. PROPOS. XXIV.
Page: 334 (314)
[445.] PROBLEMA II. PROPOS. XXV.
Page: 335 (315)
[446.] COROLLARIVM.
Page: 336 (316)
[447.] THEOREMA XXIV. PROPOS. XXVI.
Page: 337 (317)
[448.] THEOREMA XXV. PROPOS. XXVII.
Page: 337 (317)
[449.] COROLLARIVM I.
Page: 339 (319)
[450.] COROLLARIVM II.
Page: 339 (319)
[451.] THEOREMA XXVI. PROPOS. XXVIII.
Page: 340 (320)
[452.] COROLLARIVM.
Page: 341 (321)
[453.] THEOREMA XXVII. PROPOS. XXIX:
Page: 341 (321)
[454.] A. COROLL. SECTIO I.
Page: 341 (321)
[455.] B. SECTIO II.
Page: 342 (322)
[456.] C. SECTIO III.
Page: 342 (322)
[457.] D. SECTIO IV.
Page: 342 (322)
[458.] E. SECTIO V.
Page: 342 (322)
[459.] THEOREMA XXVIII. PROPOS. XXX.
Page: 343 (323)
[460.] A. COROLL. SECT IO I.
Page: 344 (324)
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            ad ſibi ſimilare genitum ex triangulo, DBF, iuxta communem re-
              <lb/>
            gulam, DF.</s>
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        <div xml:id="echoid-div963" type="section" level="1" n="574">
          <head xml:id="echoid-head599" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s10761" xml:space="preserve">_Q_V oniam verò ex Propoſ. </s>
            <s xml:id="echoid-s10762" xml:space="preserve">45. </s>
            <s xml:id="echoid-s10763" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s10764" xml:space="preserve">Primi habetur, quod ſi quæ
              <lb/>
            cunque conois byperbolica, im cuius baſi ſit cylindrus, & </s>
            <s xml:id="echoid-s10765" xml:space="preserve">conus
              <lb/>
            & </s>
            <s xml:id="echoid-s10766" xml:space="preserve">circa eundem axem, vel diametrum ſecetur planis baſi æquidiſtan-
              <lb/>
            tibus, quibus pariter ſecentur cylindrus, & </s>
            <s xml:id="echoid-s10767" xml:space="preserve">conus, fient conceptæ in
              <lb/>
            ſolidis figuræ ſimiles baſi, ideò omnia plana eorundem regula baſi erũt
              <lb/>
              <note position="left" xlink:label="note-0432-01" xlink:href="note-0432-01a" xml:space="preserve">_45. l. 1._
                <lb/>
              _Elicitur ex_
                <lb/>
              _45. l. 1. pſo_
                <lb/>
              _Conoide_
                <lb/>
              _Hyperb. &_
                <lb/>
              _ex Cor. 3_
                <lb/>
              _34. l. 2. pro_
                <lb/>
              _Cylindro._
                <lb/>
              _& Cono-_</note>
            omnes figuræ ſimiles dictorum ſolidorum, in quibus ſi ducatur pla-
              <lb/>
            num per axem, producet in ipſis figuras genitrices earundem, nempè
              <lb/>
            parallelogrammum in cylindro, hyperbolam in conoide, & </s>
            <s xml:id="echoid-s10768" xml:space="preserve">trian-
              <lb/>
            gulum in cono, dicta autem ſolida erunt ſimilaria genita ex his figu.
              <lb/>
            </s>
            <s xml:id="echoid-s10769" xml:space="preserve">ris genitricibus iuxta communem regulam ipſam baſim, & </s>
            <s xml:id="echoid-s10770" xml:space="preserve">ideò eorũ
              <lb/>
            ratio nota erit, quia ſcimus quam rationem habeant inter ſe omnia
              <lb/>
            quadrata dictarum genitricium figurarum, regula baſi. </s>
            <s xml:id="echoid-s10771" xml:space="preserve">Hæc autem
              <lb/>
            ſimiliter pro ſequentibus memoria teneantùr, in quibus ſiet noſtrum
              <lb/>
            ſolitum exemplum per reuolutionem ſigurarum circa ſuos axes, Vt
              <lb/>
            habeamus omnes figuras ſimiles genitorum ſolidorum, quæ ſint circuli
              <lb/>
            diametros in figuris genitricibus, quibus ſint erecti, ſitas habentes,
              <lb/>
            licet eadem Verificentur ſſumptis non axibus, ſed tantum diametris,
              <lb/>
            Vt alibi pluriés repetitum eſt, ex dictis autem infraſcripta habentur
              <lb/>
            Corollaria.</s>
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        <div xml:id="echoid-div965" type="section" level="1" n="575">
          <head xml:id="echoid-head600" xml:space="preserve">COROLLARIVM I.</head>
          <p>
            <s xml:id="echoid-s10773" xml:space="preserve">VTigitur fiat noſtrum exemplum in Prop. </s>
            <s xml:id="echoid-s10774" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10775" xml:space="preserve">reuoluatur pa-
              <lb/>
            rallelogrammum, AF, circam manentem axim, BE, vt fiat
              <lb/>
              <figure xlink:label="fig-0432-01" xlink:href="fig-0432-01a" number="290">
                <image file="0432-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0432-01"/>
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            ex parallelogrammo, AF, cylindrus, A
              <lb/>
            F, ex hyperbola, DBF, conois, DBF,
              <lb/>
            & </s>
            <s xml:id="echoid-s10776" xml:space="preserve">ex triangulo, DBF, conus, DBF, col-
              <lb/>
            ligitur ergo cylindrum, AF, ad conoidé,
              <lb/>
            DBF, eſſe vt, OE, ad compoſitam ex,
              <lb/>
            NB, & </s>
            <s xml:id="echoid-s10777" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10778" xml:space="preserve">BE, conoidem autem, DBF,
              <lb/>
            ad conum, DBF, eſſe vt compoſitam
              <lb/>
            ex ſexquialtera, OB, & </s>
            <s xml:id="echoid-s10779" xml:space="preserve">ex, BE, ad OE;
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            </s>
            <s xml:id="echoid-s10780" xml:space="preserve">& </s>
            <s xml:id="echoid-s10781" xml:space="preserve">ita eſſe ſolida quæcunque ſimilaria
              <lb/>
            genita ex eiſdem figuris .</s>
            <s xml:id="echoid-s10782" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s10783" xml:space="preserve">ex parallelo-
              <lb/>
            grammo, AF, hyperbola, DBF, & </s>
            <s xml:id="echoid-s10784" xml:space="preserve">triã-
              <lb/>
            gulo, DBF, iuxta communem regulam,
              <lb/>
            DF, vt ſupra dictum eſt, quę declarare oportebat.</s>
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