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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            prædicta omnia quadrata, vel rectangula, vt ſupra ad inuicem
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            comparata.</s>
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        <div xml:id="echoid-div985" type="section" level="1" n="587">
          <head xml:id="echoid-head612" xml:space="preserve">COROLLARIVM XIII.</head>
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            <s xml:id="echoid-s10908" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s10909" xml:space="preserve">13. </s>
            <s xml:id="echoid-s10910" xml:space="preserve">habetur ſimiles conoides hyperbolicas eſſe in tri-
              <lb/>
              <note position="left" xlink:label="note-0438-01" xlink:href="note-0438-01a" xml:space="preserve">Eliciture 1
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              Coro. 50.
                <lb/>
              l. 1.</note>
            pla ratione axium, vel diametrorum earundem, quippe quæ
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            ex ſimilibus hyperbolis naſcuntur: </s>
            <s xml:id="echoid-s10911" xml:space="preserve">lgitur in anteced. </s>
            <s xml:id="echoid-s10912" xml:space="preserve">Corollarij
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            figura, ſi ſupponantur ſimiles hyperbolæ, BAD, HMQ, vt fiant
              <lb/>
            ex illis ſimiles conoides hyperbolicæ, FEG, HTS, iſtæ erunt inter
              <lb/>
            ſe in tripla ratione axium, AC, MP, & </s>
            <s xml:id="echoid-s10913" xml:space="preserve">ſic erit quodlibet ſolidum
              <lb/>
              <note position="left" xlink:label="note-0438-02" xlink:href="note-0438-02a" xml:space="preserve">Coro. 50.
                <lb/>
              l. 1.</note>
            ſimilare genitum ex hyperbola, FEG, ad ſibi ſimilare genitum ex
              <lb/>
            hyperbola, HTS, iuxta regulas, FG, HS.</s>
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        <div xml:id="echoid-div987" type="section" level="1" n="588">
          <head xml:id="echoid-head613" xml:space="preserve">COROLLARIV M XIV.</head>
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            <s xml:id="echoid-s10915" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s10916" xml:space="preserve">14. </s>
            <s xml:id="echoid-s10917" xml:space="preserve">expoſita eius figura, vt fiat exem plum, reuolua-
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              <figure xlink:label="fig-0438-01" xlink:href="fig-0438-01a" number="299">
                <image file="0438-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0438-01"/>
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            tur circa axim, DG, vt ex, EG, fiat
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            cylindrus, EF, & </s>
            <s xml:id="echoid-s10918" xml:space="preserve">ex trilineo, DGB, ſo-
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            lidum, DBGF, quod vocetur: </s>
            <s xml:id="echoid-s10919" xml:space="preserve">Apex
              <lb/>
            hyperbolicus; </s>
            <s xml:id="echoid-s10920" xml:space="preserve">patet ergo cylindrum, E
              <lb/>
            F, ad apicem, BDF, eſſe vt, BD, ad ſui
              <lb/>
            reliquum, dempta ab eodem ſemihy-
              <lb/>
            perbola, BED, vna cum exceſſu, quo
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            ipſa ſuperat {1/3}. </s>
            <s xml:id="echoid-s10921" xml:space="preserve">parall: </s>
            <s xml:id="echoid-s10922" xml:space="preserve">logrammi, BD, & </s>
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              <lb/>
            {1/6}. </s>
            <s xml:id="echoid-s10924" xml:space="preserve">BM; </s>
            <s xml:id="echoid-s10925" xml:space="preserve">& </s>
            <s xml:id="echoid-s10926" xml:space="preserve">ſic eſſe patet, quodlibet ſoli-
              <lb/>
            dum ſimilate genitum ex, BD, ad ſibi
              <lb/>
            ſimilare genitum ex ſemihyperbola, BE
              <lb/>
            D, iuxta communem regulam, ED.</s>
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        <div xml:id="echoid-div989" type="section" level="1" n="589">
          <head xml:id="echoid-head614" xml:space="preserve">COROLLARIVM XV.</head>
          <p>
            <s xml:id="echoid-s10928" xml:space="preserve">IN Propoſ. </s>
            <s xml:id="echoid-s10929" xml:space="preserve">15. </s>
            <s xml:id="echoid-s10930" xml:space="preserve">expoſita
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            eius figura, vt fiat exẽ-
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            p@u@n, eadem voluatur cir-
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            ca axim, GD, vt ex, FD,
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            fiat cylindrus, FH, & </s>
            <s xml:id="echoid-s10931" xml:space="preserve">ex
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            hyperbola, CBD, ſolidum,
              <lb/>
            CBDNH, quod voeetur:
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            </s>
            <s xml:id="echoid-s10932" xml:space="preserve">Sem anulus ſtr@ctus hyper-
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            bolicus: </s>
            <s xml:id="echoid-s10933" xml:space="preserve">@ntelligantur autẽ
              <lb/>
            ſe@nper hæc ſolida ſecari
              <lb/>
            per axem, vt ijs producan-
              <lb/>
            tur figuræ, quæ in </s>
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