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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            ſolidum ſimilare quodcunque genitum ex parallelogrammo, TV,
              <lb/>
            ad ſibi ſimilare genitum ex figura, TBFHRVQIPX, demptis ſo-
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            lidis ſimilaribus genitis ex oppoſitis hyperbolis, AEC, MON, iux-
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            ta communem regulam, RV; </s>
            <s xml:id="echoid-s11109" xml:space="preserve">eadem verò eſſe oſtendemus ſum-
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            pta pro regula ipſa, VX, & </s>
            <s xml:id="echoid-s11110" xml:space="preserve">reuolutione facta circa axem, GZ.</s>
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          <head xml:id="echoid-head632" xml:space="preserve">SECTIO POSTERIOR.</head>
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            <s xml:id="echoid-s11112" xml:space="preserve">IN Coroll. </s>
            <s xml:id="echoid-s11113" xml:space="preserve">colligitur cylindrum, TV, ad cylindrum, TP, &</s>
            <s xml:id="echoid-s11114" xml:space="preserve">, HV,
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            cum tympano, BFHQIP, eſſe vt cubus, YS, ad parallelepipedũ
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            ſub, KY, & </s>
            <s xml:id="echoid-s11115" xml:space="preserve">quadrato, YS, vna cum parallelepido ſub, KS, & </s>
            <s xml:id="echoid-s11116" xml:space="preserve">com-
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            poſito ex quadrato, SO, & </s>
            <s xml:id="echoid-s11117" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s11118" xml:space="preserve">quadrati, SK; </s>
            <s xml:id="echoid-s11119" xml:space="preserve">& </s>
            <s xml:id="echoid-s11120" xml:space="preserve">ſic ſolida ſimilaria ex
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            elſdem figuris genita iuxta ibi aſſumptam regulam, RV.</s>
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          <head xml:id="echoid-head633" xml:space="preserve">COROLL. XXIX. SECTIO PRIOR.</head>
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            <s xml:id="echoid-s11122" xml:space="preserve">IN Propoſ. </s>
            <s xml:id="echoid-s11123" xml:space="preserve">29. </s>
            <s xml:id="echoid-s11124" xml:space="preserve">viſa eius figura, eaque reuoluta circa axem, &</s>
            <s xml:id="echoid-s11125" xml:space="preserve">Y,
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            vt in anteced. </s>
            <s xml:id="echoid-s11126" xml:space="preserve">conſpicitur, patet ſolidum in reuolutione de-
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            ſcriptum a figura reſidua, demptis à parallelogrammo, T V, qua-
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            tuor hyperbolis, BFH, PIQ, AEC, MON, ad ſolidum deſ@riptum
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            in reuolutione ex figura reſidua, demptis à parallelogrammo, βΩ,
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            quatuor hyperbolis, 9F7, ΦΙΛ, L E ſ, ΣΟ3, eſſe vt parallelepipe-
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            dum ſub QV, & </s>
            <s xml:id="echoid-s11127" xml:space="preserve">quadrato, VZ, vna cum parallelepipedo ſub, QZ,
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            & </s>
            <s xml:id="echoid-s11128" xml:space="preserve">compoſito ex quadrato, SO, & </s>
            <s xml:id="echoid-s11129" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s11130" xml:space="preserve">quadrati, QZ, ab his dempto
              <lb/>
            parallelepipedo ſub, SO, & </s>
            <s xml:id="echoid-s11131" xml:space="preserve">quadrato, OY, & </s>
            <s xml:id="echoid-s11132" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s11133" xml:space="preserve">cubi, OY, ad paral-
              <lb/>
            lelepipedum ſub, ΛΩ, & </s>
            <s xml:id="echoid-s11134" xml:space="preserve">quadrato, Ω4, vna cum parallelepipedo
              <lb/>
            ſub, Λ4, & </s>
            <s xml:id="echoid-s11135" xml:space="preserve">compoſito ex quadrato, SO, & </s>
            <s xml:id="echoid-s11136" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s11137" xml:space="preserve">quadrati, Λ4, dempto
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            parallelepido ſub, SO, & </s>
            <s xml:id="echoid-s11138" xml:space="preserve">quadrato, O6, cum {1/3}. </s>
            <s xml:id="echoid-s11139" xml:space="preserve">cubi, O6: </s>
            <s xml:id="echoid-s11140" xml:space="preserve">Sic etiam
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            patet eſſe quodlibet ſolidum ſimilare genitum ex figura, TBFHR
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            VQIPX, demptis ſolidis ſimilaribus genitis ex opoſitis hyperbolis,
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            AEC, MON, ad ſibi ſimilare genitũ ex figura, B9F72ΩΛΙΦΛ, dem-
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            ptis ſolidis ſimilaribus genitis ex oppoſitis hyperbolis, LEF, ΣΟ3,
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            iuxta communem regulam, RV.</s>
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          <head xml:id="echoid-head634" xml:space="preserve">SECTIO POSTERIOR.</head>
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            <s xml:id="echoid-s11142" xml:space="preserve">IN Coroll. </s>
            <s xml:id="echoid-s11143" xml:space="preserve">colligitur eadem ſolida, genita nempè ex figuris,
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            TBFHRVQIPX β9F72ΩΛ ΙΦΔ, iuxta communem regulam,
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            RV, nihil ab eis dempto, eſſe vt dicta parallelepipeda, nihil pari-
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            @er ab eiſdem dempto.</s>
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