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

Table of contents

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[181.] THEOREMA V. PROPOS. V.
Page: 137 (117)
[182.] THEOREMA VI. PROPOS. VI.
Page: 138 (118)
[183.] THEOREMA VII. PROPOS. VII.
Page: 139 (119)
[184.] THEOREMA VIII. PROPOS. VIII.
Page: 140 (120)
[185.] COROLLARIVM.
Page: 140 (120)
[186.] THEOREMA IX. PROPOS. IX.
Page: 140 (120)
[187.] COROLLARIVM.
Page: 141 (121)
[188.] THEOREMA X. PROPOS. X.
Page: 141 (121)
[189.] COROLLARIVM.
Page: 143 (123)
[190.] THEOREMA XI. PROPOS. XI.
Page: 143 (123)
[191.] COROLLARIVM.
Page: 144 (124)
[192.] THEOREMA XII. PROPOS. XII.
Page: 144 (124)
[193.] COROLLARIVM.
Page: 145 (125)
[194.] THEOREMA XIII. PROPOS. XIII.
Page: 145 (125)
[195.] COROLLARIVM.
Page: 146 (126)
[196.] THEOREMA XIV. PROPOS. XIV.
Page: 146 (126)
[197.] COROLLARIVM.
Page: 147 (127)
[198.] THEOREMA XV. PROPOS. XV.
Page: 147 (127)
[199.] A. DEMONSTRATIONIS SECTIO I.
Page: 148 (128)
[200.] B. SECTIO SECVNDA.
Page: 149 (129)
[201.] C. SECTIO III.
Page: 149 (129)
[202.] D. SECTIO IV.
Page: 150 (130)
[203.] E. SECTIO V. ET VLTIMA.
Page: 150 (130)
[204.] COROLLARIVM I.
Page: 151 (131)
[205.] COROLLARIVM II.
Page: 151 (131)
[206.] THEOREMA XVI. PROPOS. XVI.
Page: 151 (131)
[207.] SCHOLIV M.
Page: 152 (132)
[208.] THEOREMA XVII. PROPOS. XVII.
Page: 153 (133)
[209.] A. DEMONSTRATIONIS SECTIO I.
Page: 153 (133)
[210.] B. SECTIO II.
Page: 157 (137)
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            DX, FH, quod producat in parallelepipedo, AP, rectangulum, E
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            V, in parallelepipedo, AM, rectan-
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              <note position="left" xlink:label="note-0208-01" xlink:href="note-0208-01a" xml:space="preserve">Coroll. 6.
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              lib. I.</note>
            gulum, EO, & </s>
            <s xml:id="echoid-s4611" xml:space="preserve">in parallelepipedo,
              <lb/>
            NP, rectangulum, RV, per pla-
              <lb/>
              <note position="left" xlink:label="note-0208-02" xlink:href="note-0208-02a" xml:space="preserve">10. Lib. 1.</note>
            num igitur, EV, diuiduntur paral-
              <lb/>
            lelepipeda, AM, NP, in paralle-
              <lb/>
            pipeda, AR, BM, NQ, OP, eſt
              <lb/>
            autem totum parallelepipedum, A
              <lb/>
            P, æquale parallelepipedis, AR, B
              <lb/>
            M, NQ, OP, & </s>
            <s xml:id="echoid-s4612" xml:space="preserve">eſt parallelepipe-
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            dum, AR, ſub, DS, SO, ideſt ſub,
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            DS, TV, & </s>
            <s xml:id="echoid-s4613" xml:space="preserve">parallelepipedum, B
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            M, ſub, ER, RG, hoc eſt ſub, D
              <lb/>
            S, QH, & </s>
            <s xml:id="echoid-s4614" xml:space="preserve">parallelepipedum, NQ,
              <lb/>
            eſt ſub, ST, TV, &</s>
            <s xml:id="echoid-s4615" xml:space="preserve">, OP, eſt ſub,
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            RQ, QH, hoc eſt ſub, ST, QH,
              <lb/>
            ergo parallelepipedum, AP, ideſt
              <lb/>
            ſub, DT, TH, eſt æquale paralle-
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            lepipedis ſub, DS, &</s>
            <s xml:id="echoid-s4616" xml:space="preserve">, TV, & </s>
            <s xml:id="echoid-s4617" xml:space="preserve">ſub,
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            DS, VP, & </s>
            <s xml:id="echoid-s4618" xml:space="preserve">ſub, ST, TV, & </s>
            <s xml:id="echoid-s4619" xml:space="preserve">ſub,
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            ST, QH, ideſt parallelepipedis ſub
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            fingulis partibus altitudinis, & </s>
            <s xml:id="echoid-s4620" xml:space="preserve">ſingulis partibus baſis content@s.</s>
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          <head xml:id="echoid-head301" xml:space="preserve">SCHOLIV M.</head>
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            <s xml:id="echoid-s4622" xml:space="preserve">_C_Ontineri autem parallelepipedum voco ſub tribus rectis eiuſdem
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            angulum ſolidum continentibus, quarum dua qualibet rectum
              <lb/>
            angulum conſtituunt, ſiue ſub earum quauis, & </s>
            <s xml:id="echoid-s4623" xml:space="preserve">parallelogrammo re-
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            ctangulo ſub reliquis duabus; </s>
            <s xml:id="echoid-s4624" xml:space="preserve">ita vt, cum dico parallelepipedum ſub
              <lb/>
            tali recta linea, & </s>
            <s xml:id="echoid-s4625" xml:space="preserve">tali rectangulo, ſiue ſub talibus tribus rectis lineis,
              <lb/>
            intelligam illud parallelepipedum habere angulum ſolidum rectis an-
              <lb/>
            gulis conſtitutum, veluti in iſtis Theorematibus ipſum aſſumo, igitur
              <lb/>
            patet nos ex tribus rectis parallelepipedum continentibus quamlibet
              <lb/>
            poſſe pro altitudine ſumere, & </s>
            <s xml:id="echoid-s4626" xml:space="preserve">rectangulum ſub reliquis duabus pro
              <lb/>
            baſi.</s>
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          <head xml:id="echoid-head302" xml:space="preserve">THEOREMA XXXVI. PROPOS. XXXVI.</head>
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            <s xml:id="echoid-s4628" xml:space="preserve">SI recta linea in vno puncto ſecta ſit vtcumq; </s>
            <s xml:id="echoid-s4629" xml:space="preserve">parallelepi-
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            pedum ſub tota linea, & </s>
            <s xml:id="echoid-s4630" xml:space="preserve">quadrato vnius factarum par-
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            tium erit æquale parallelepipedo ſub tali parte, & </s>
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