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

Table of contents

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[591.] SECTIO POSTERIOR.
Page: 439 (419)
[592.] COROLLARIVM XVII.
Page: 439 (419)
[593.] COROLLARIVM XVIII.
Page: 440 (420)
[594.] COROLL. XIX. SECTIO PRIOR.
Page: 440 (420)
[595.] SECTIO POSTERIOR.
Page: 440 (420)
[596.] COROLLARIVM XX.
Page: 441 (421)
[597.] COROLLARIVM XXL
Page: 441 (421)
[598.] COROLL. XXII. SECTIO PRIMA.
Page: 442 (422)
[599.] SECTIO II.
Page: 442 (422)
[600.] SECTIO III.
Page: 442 (422)
[601.] COROLLARIVM XXIII.
Page: 442 (422)
[602.] COROLLARIVM XXIV.
Page: 443 (423)
[603.] COROLLARIVM XXV.
Page: 443 (423)
[604.] COROLLARIVM XXVI.
Page: 443 (423)
[605.] COROLLARIVM XXVII.
Page: 444 (424)
[606.] COROLL. XXVIII. SECTIO PRIOR.
Page: 444 (424)
[607.] SECTIO POSTERIOR.
Page: 445 (425)
[608.] COROLL. XXIX. SECTIO PRIOR.
Page: 445 (425)
[609.] SECTIO POSTERIOR.
Page: 445 (425)
[610.] SCHOLIV M.
Page: 446 (426)
[611.] Finis Quinti Libri.
Page: 446 (426)
[612.] GEOMETRIAE CAVALER II LIBER SEXTVS. In quo de Spatijs Helicis, & Solidis in-de genitis, ac alijs quibuſdam ex ſuperioribus deductis, ſpecula-tio inſtituitur. DEFINITIONES, I.
Page: 447 (427)
[613.] II.
Page: 447 (427)
[614.] III.
Page: 448 (428)
[615.] IV.
Page: 448 (428)
[616.] SCHOLIVM.
Page: 448 (428)
[617.] THEOREMA I. PROPOS. I.
Page: 449 (429)
[618.] THEOREMA II. PROPOS. II.
Page: 449 (429)
[619.] THEOREMA III. PROPOS. III.
Page: 449 (429)
[620.] COROLLARIVM I.
Page: 450 (428)
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            <s xml:id="echoid-s11068" xml:space="preserve">
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            drum, FC, in figura Coroll. </s>
            <s xml:id="echoid-s11069" xml:space="preserve">23. </s>
            <s xml:id="echoid-s11070" xml:space="preserve">demptis oppoſitis conoidibus, F
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            AD, EVC, ad tympanum hyperbolicum genitum ex figura, EVC
              <lb/>
            DAF, in figura Coroll. </s>
            <s xml:id="echoid-s11071" xml:space="preserve">24. </s>
            <s xml:id="echoid-s11072" xml:space="preserve">ſcilicet ad tympanum hyperbolicum,
              <lb/>
            EVCDAF, habere rationem compoſitam ex ratione rectanguli,
              <lb/>
            AOZ, bis cum {2/3}. </s>
            <s xml:id="echoid-s11073" xml:space="preserve">quadrati, VZ, ad rectangulum, AZO, & </s>
            <s xml:id="echoid-s11074" xml:space="preserve">ex ra-
              <lb/>
            tione rectanguli ſub, DC, vel, RZ, & </s>
            <s xml:id="echoid-s11075" xml:space="preserve">ſub, EC, ad quadratum, A
              <lb/>
            V, cum {1/3}. </s>
            <s xml:id="echoid-s11076" xml:space="preserve">quadrati, KI, vel cum rectangulo ſub, AZ, & </s>
            <s xml:id="echoid-s11077" xml:space="preserve">ſexqui.
              <lb/>
            </s>
            <s xml:id="echoid-s11078" xml:space="preserve">tertia, ZV, & </s>
            <s xml:id="echoid-s11079" xml:space="preserve">ſic eſſe quodlibet ſolidum ſimilare genitum ex, FC,
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            de@nptis ſolidis ſimilaribus genitis ex oppoſitis hyperbolis, FAD,
              <lb/>
            EVC, iuxta communem regulam, EC, ad ſolidum ſimilare ſibi
              <lb/>
            genitum ex figura, EVCDAF, iuxta regulam, CD.</s>
            <s xml:id="echoid-s11080" xml:space="preserve"/>
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        <div xml:id="echoid-div1012" type="section" level="1" n="605">
          <head xml:id="echoid-head630" xml:space="preserve">COROLLARIVM XXVII.</head>
          <p>
            <s xml:id="echoid-s11081" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s11082" xml:space="preserve">27. </s>
            <s xml:id="echoid-s11083" xml:space="preserve">conſpecta figura Coroll. </s>
            <s xml:id="echoid-s11084" xml:space="preserve">21. </s>
            <s xml:id="echoid-s11085" xml:space="preserve">intelligantur deſcri-
              <lb/>
            ptæ ſectiones, BIG, kMP, quæ dicuntur coniugatæ ſectioni-
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            bus, DAF, CVE, ex quibus in reuolutione genitæ fuerint oppoſi-
              <lb/>
            tæ conoides, B G, kMP, patet igitur cylindrum, DE, ad tympa-
              <lb/>
            num hyperbolicum, DAF, EVC, demptis oppoſitis conoidibus,
              <lb/>
            BIG, KMP, eſſe vt parallelepipedum ſub, ZC, & </s>
            <s xml:id="echoid-s11086" xml:space="preserve">ſub quadrato, Z
              <lb/>
            Q (quæ habetur extenſa, ZC, ad aſymptoton producta .</s>
            <s xml:id="echoid-s11087" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s11088" xml:space="preserve">ad, OS,
              <lb/>
            cu@occurrat in, Q,) a@ parallele ipedum bis ſub, XM, & </s>
            <s xml:id="echoid-s11089" xml:space="preserve">quadra-
              <lb/>
            to, MO, cum cubo, MO, & </s>
            <s xml:id="echoid-s11090" xml:space="preserve">amplius {1/3}. </s>
            <s xml:id="echoid-s11091" xml:space="preserve">eiuſdem cubi; </s>
            <s xml:id="echoid-s11092" xml:space="preserve">& </s>
            <s xml:id="echoid-s11093" xml:space="preserve">ſic eſſe
              <lb/>
            quodlibet ſolidum ſimilare genitum ex, FC, ad ſibi ſimlare g@nitũ
              <lb/>
            ex figura, DAFEVC, demptis ſolidis ſimilaribus genitis ex oppo-
              <lb/>
            ſitis hyperbolis, BIG, KMP, iuxta cõmunẽ regulam, FE, vel, AV.</s>
            <s xml:id="echoid-s11094" xml:space="preserve"/>
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        <div xml:id="echoid-div1013" type="section" level="1" n="606">
          <head xml:id="echoid-head631" xml:space="preserve">COROLL. XXVIII. SECTIO PRIOR.</head>
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            <s xml:id="echoid-s11095" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s11096" xml:space="preserve">28. </s>
            <s xml:id="echoid-s11097" xml:space="preserve">illius aſſumpta figu-
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            ra, eadem reuoluatur circa axẽ,
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            &</s>
            <s xml:id="echoid-s11098" xml:space="preserve">Y, vel, GZ, ſit autem reuolutio
              <lb/>
            circa, &</s>
            <s xml:id="echoid-s11099" xml:space="preserve">Y; </s>
            <s xml:id="echoid-s11100" xml:space="preserve">patet ergo cylindrum ge-
              <lb/>
            nitum ex, TV, nempè, TV, ad reli-
              <lb/>
            quum, ab eodem demptis ſolidis ge
              <lb/>
            nitis ex quatuor hyperbolis coniu-
              <lb/>
            gatis, BFH, PIQ, AEC, MON, eſſe
              <lb/>
            vt cubus, ZV, vel, SY, ad parallele-
              <lb/>
            pipedum ſub, QV, & </s>
            <s xml:id="echoid-s11101" xml:space="preserve">quad. </s>
            <s xml:id="echoid-s11102" xml:space="preserve">ZV, vna
              <lb/>
            cum parallelepipedo ſub, ZQ, & </s>
            <s xml:id="echoid-s11103" xml:space="preserve">ſub
              <lb/>
            compoſito ex {1/3}. </s>
            <s xml:id="echoid-s11104" xml:space="preserve">quadrati, ZQ, & </s>
            <s xml:id="echoid-s11105" xml:space="preserve">
              <lb/>
            qua@rato, SO, ab his tamen dempto
              <lb/>
            parallelepipedo ſub, SO, & </s>
            <s xml:id="echoid-s11106" xml:space="preserve">quadra
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            to, OY, cum {1/3}. </s>
            <s xml:id="echoid-s11107" xml:space="preserve">cubi, OY, & </s>
            <s xml:id="echoid-s11108" xml:space="preserve">ſic </s>
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