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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          <head xml:id="echoid-head762" xml:space="preserve">COROLLARIVM V.</head>
          <p style="it">
            <s xml:id="echoid-s13573" xml:space="preserve">_C_olligitur quintò, ſi ſupponamus, BIE, bifariam ſecare dictas
              <lb/>
            ipſi, DF, parallelas in figura, BGEN, & </s>
            <s xml:id="echoid-s13574" xml:space="preserve">deinde illis adiungi,
              <lb/>
            BNEO, figuram in eiſdem parallelis cum, BGEN, conſtitutam; </s>
            <s xml:id="echoid-s13575" xml:space="preserve">rectan-
              <lb/>
            gulum ſolidum ſub, BGEO, & </s>
            <s xml:id="echoid-s13576" xml:space="preserve">ſub, BNEO, hoc eſt vnum ſub, BGEL,
              <lb/>
            ſeu, BIEN, & </s>
            <s xml:id="echoid-s13577" xml:space="preserve">ſub, BNEO, indiuiſa, aliud ſub, BIEO, & </s>
            <s xml:id="echoid-s13578" xml:space="preserve">ſub, BNE
              <lb/>
            O, cum quadrato ſolido, BIEN, ( quod iunctum rectangulo ſolido ſub,
              <lb/>
            BIEN, BNEO, facit rectangulum ſolidum ſub, BIEN, BIEO, per Cor.
              <lb/>
            </s>
            <s xml:id="echoid-s13579" xml:space="preserve">2.) </s>
            <s xml:id="echoid-s13580" xml:space="preserve">æquari quadrato ſolido, BIEO, per Cor. </s>
            <s xml:id="echoid-s13581" xml:space="preserve">I. </s>
            <s xml:id="echoid-s13582" xml:space="preserve">hoc eft rectangulum ſo-
              <lb/>
            lidam ſub figura compoſita ex propoſita, BGEN, & </s>
            <s xml:id="echoid-s13583" xml:space="preserve">adiecta, BNEO, & </s>
            <s xml:id="echoid-s13584" xml:space="preserve">
              <lb/>
            ſub adiecta, BNEO, cum quadrato ſolido, BIEN, dimidiæ ipſius propo-
              <lb/>
            ſitæ, æquari quadrato ſolido, BIEO, compoſitæ ex dimidia, BIEN, & </s>
            <s xml:id="echoid-s13585" xml:space="preserve">
              <lb/>
            adiecta, BNEO.</s>
            <s xml:id="echoid-s13586" xml:space="preserve"/>
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          <head xml:id="echoid-head763" xml:space="preserve">COROLLARIVM VI.</head>
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            <s xml:id="echoid-s13587" xml:space="preserve">_C_olligitur ſextò, in eadem fig. </s>
            <s xml:id="echoid-s13588" xml:space="preserve">BGEO, poſito, quod per lineam tan-
              <lb/>
            tum, BNE, ſecentur dictæ parallelæ ipſi, DF, quad. </s>
            <s xml:id="echoid-s13589" xml:space="preserve">ſolidum fi-
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            guræ, BGEO, cum quadrato ſolido figuræ, BN
              <lb/>
            EO, æquari rectangulo ſolido bis ſub, BGEO, &</s>
            <s xml:id="echoid-s13590" xml:space="preserve">,
              <lb/>
            BNEO, figuris contento, cum quadrato ſolido
              <lb/>
            reliquæ figuræ, BGEN. </s>
            <s xml:id="echoid-s13591" xml:space="preserve">Nam quadratum
              <lb/>
            ſolidum, BGEO, æquatur quadratis ſolidis, BG
              <lb/>
            EN, BNEO, cum duobus rectangulis ſolidis
              <lb/>
            ſub eiſdem figuris, addito ergo quadrato ſolido communi, BNEO, fient
              <lb/>
            quadrata ſolida figuraxum, BGEO, BNEO, æqualia duobus rectangulis
              <lb/>
            ſolidis ſub figuris, BGEN, BNEO, cum duobus quadratis ſolidis, BN
              <lb/>
            EO, hoc eſt duobus rectangulis ſolidis ſub, BGEO, BNEO, cum qua-
              <lb/>
            drato ſolido, BGEN.</s>
            <s xml:id="echoid-s13592" xml:space="preserve"/>
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          <head xml:id="echoid-head764" xml:space="preserve">COROLLARIVM VII.</head>
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            <s xml:id="echoid-s13593" xml:space="preserve">_C_olligitur ſeptimò, ſi propoſitæ figuræ, B G E N, diuidatur per li-
              <lb/>
            neam, B I E, dictas quoq; </s>
            <s xml:id="echoid-s13594" xml:space="preserve">parallelas ipſi, D F, ſecantem, rectan-
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            gulum ſolidum quater ſub, B G E N, B I E N, cum quadrato ſolido,
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            B G E I, æquari quadrato ſolido figuræ compoſitæ ex, B G E N, & </s>
            <s xml:id="echoid-s13595" xml:space="preserve">
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            figura, B I E N, ſeu illi homologa, quæ ſit, B N E O. </s>
            <s xml:id="echoid-s13596" xml:space="preserve">Duo enim
              <lb/>
            rectangula ſolida ſub, B G E N, B I E N, cum quadrato ſolido, B GEI,
              <lb/>
            æquantur duobus quadratis ſolidis, B G E N, B I E N, ex Cor. </s>
            <s xml:id="echoid-s13597" xml:space="preserve">ant.</s>
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