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

Table of contents

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[261.] COROLLARIVM.
Page: 194 (174)
[262.] THEOREMA XXXII. PROPOS. XXXII.
Page: 195 (175)
[263.] COROLLARIVM.
Page: 196 (176)
[264.] THEOREMA XXXIII. PROPOS. XXXIII.
Page: 197 (177)
[265.] COROLLARIVM I.
Page: 198 (178)
[266.] COROLLARIVM II.
Page: 199 (179)
[267.] THEOREMA XXXIV. PROPOS. XXXIV.
Page: 199 (179)
[268.] COROLLARIVM I.
Page: 201 (181)
[269.] COROLLARIVM II.
Page: 201 (181)
[270.] COROLLARIVM III.
Page: 201 (181)
[271.] A. COROLLARII IV. GENERALIS. SECTIO I.
Page: 203 (183)
[272.] B. SECTIO II.
Page: 203 (183)
[273.] C. SECTIO III.
Page: 203 (183)
[274.] D. SECTIO IV.
Page: 204 (184)
[275.] E. SECTIO V.
Page: 204 (184)
[276.] F. SECTIO VI.
Page: 204 (184)
[277.] G. SECTIO VII.
Page: 204 (184)
[278.] H. SECTIO VIII.
Page: 204 (184)
[279.] I. SECTIO IX.
Page: 205 (185)
[280.] K. SECTIO X.
Page: 205 (185)
[281.] L. SECTIO XI.
Page: 206 (186)
[282.] M. SECTIO XII.
Page: 206 (186)
[283.] N. SECTIO XIII.
Page: 207 (187)
[284.] THEOREMA XXXV. PROPOS. XXXV.
Page: 207 (187)
[285.] SCHOLIV M.
Page: 208 (188)
[286.] THEOREMA XXXVI. PROPOS. XXXVI.
Page: 208 (188)
[287.] THEOREMA XXXVII. PROPOS. XXXVII.
Page: 209 (189)
[288.] COROLLARIVM.
Page: 210 (190)
[289.] THEOREMA XXXVIII. PROPOS. XXXVIII.
Page: 210 (190)
[290.] SCHOLIVM.
Page: 211 (191)
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            FI, ad omnia quadrata circuli, vel ellipſis, CFEH, eſſe
              <lb/>
            vt cylindricum ſub, MI, & </s>
            <s xml:id="echoid-s6191" xml:space="preserve">portione, TCFE Y, vna cum,
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            {1/6}, cubi, TY, pro circulo, pro ellipſi verò, vna cum ſæpius
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            dicta parte cubi, TY, vel parallelepipedi ſub, RV, & </s>
            <s xml:id="echoid-s6192" xml:space="preserve">rhom-
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            bo, RZ, ad, {2/3}, parallelepipedi ſub, AD, & </s>
            <s xml:id="echoid-s6193" xml:space="preserve">parallelogram-
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            mo, AQ, ideſt, in circulo ad, {1/6}, cubi, FH.</s>
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            <s xml:id="echoid-s6195" xml:space="preserve">Omnia .</s>
            <s xml:id="echoid-s6196" xml:space="preserve">n. </s>
            <s xml:id="echoid-s6197" xml:space="preserve">quadrata figurę, LCFE G, demptis omnibus quadra-
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            tis trilineorum, CLT, YGE, ad omnia quadrata, AG, ſunt vt cy-
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            lindricus ſub, MI, & </s>
            <s xml:id="echoid-s6198" xml:space="preserve">portione, TCFE Y, vna cum, {1/6}, cubi, TY,
              <lb/>
              <note position="right" xlink:label="note-0269-01" xlink:href="note-0269-01a" xml:space="preserve">22. huius.</note>
            pro circulo, pro ellipſi verò, vna cum ſæpius dicta parte cubi, TY.
              <lb/>
            </s>
            <s xml:id="echoid-s6199" xml:space="preserve">vel dicti parallelepipedi, ad parallelepipedum ſub, LA, & </s>
            <s xml:id="echoid-s6200" xml:space="preserve">paralle-
              <lb/>
            logrammo, AG; </s>
            <s xml:id="echoid-s6201" xml:space="preserve">omnia verò quadraca, AG, ad omnia quadrata,
              <lb/>
            AQ, ſunt vt quadratum, AL, ad quadratum, AD, .</s>
            <s xml:id="echoid-s6202" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6203" xml:space="preserve">ſumpta, A
              <lb/>
              <note position="right" xlink:label="note-0269-02" xlink:href="note-0269-02a" xml:space="preserve">9. Lib. 2.</note>
            P, communi altitudine, vt parallelepipedum ſub, PA, & </s>
            <s xml:id="echoid-s6204" xml:space="preserve">quadra-
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            to, AL, ad parallelepipedum ſub, PA, & </s>
            <s xml:id="echoid-s6205" xml:space="preserve">quadrato, AD, hoc eſt,
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            vt parallelepipedum ſub, LA, & </s>
            <s xml:id="echoid-s6206" xml:space="preserve">parallelogrammo, AG, ad paral-
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            lelepipedum ſub, DA, & </s>
            <s xml:id="echoid-s6207" xml:space="preserve">parallelogrammo, AQ, omnia autem qua-
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            drata, AQ, omnium quadratorum circuli, vel ellipſis, CFEH, ſunt
              <lb/>
              <note position="right" xlink:label="note-0269-03" xlink:href="note-0269-03a" xml:space="preserve">Coroll. 1.
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              huius.</note>
            ſexquialtera .</s>
            <s xml:id="echoid-s6208" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6209" xml:space="preserve">ſunt ad ea, vt parallelepipedum ſub, AD, & </s>
            <s xml:id="echoid-s6210" xml:space="preserve">paral-
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            lelogrammo, AQ, ad eiuſdem, {2/3}, ergo ex æquali omnia quadrata
              <lb/>
            figuræ, LCFE G, demptis ommbus quadratis trilineorum, CLT,
              <lb/>
            YGE, ad omnia quadrata circuli, vel ellipſis, CFEH, erunt vt
              <lb/>
            cylindricus ſub, MI, & </s>
            <s xml:id="echoid-s6211" xml:space="preserve">portione, TCFEY, vna cum, {1/6}, cubi, T
              <lb/>
            Y, pro circulo, pro ellipſi verò, vna cum ſæpius dicta parte cubi, T
              <lb/>
            Y, vel parallelepipedi ſub, RV, & </s>
            <s xml:id="echoid-s6212" xml:space="preserve">rhombo, RZ, ad, {2/3}, parallele-
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            pipedi ſub, AD, & </s>
            <s xml:id="echoid-s6213" xml:space="preserve">parallelogrammo, AQ, .</s>
            <s xml:id="echoid-s6214" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6215" xml:space="preserve">pro circulo ad, {2/3},
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            cubi, AD, vel cubi, FH, quod oſtendere opus erat.</s>
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          <head xml:id="echoid-head366" xml:space="preserve">THEOREMA XXVIII. PROPOS. XXIX.</head>
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            <s xml:id="echoid-s6217" xml:space="preserve">SIparallelogrammo ſit inſcripta figura quæcunque, ita ta-
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            men, vt, ſumpto vno laterum parallelogrammi pro re-
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            gula, &</s>
            <s xml:id="echoid-s6218" xml:space="preserve">, ductis vtcunque ipſiregulæ parallelis intra paralle-
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            logrammum, earum quælibet, vel tota ſit intra figuram in-
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            ſcriptam, vel eiuſdem aliqua parte extra figuram exiſtente,
              <lb/>
            ac ad vnum laterum parallelogrammi terminante, ad latus
              <lb/>
            eiuſdem parallelogrammi prædicto oppoſitum terminet alia
              <lb/>
            portio eiuſdem, regulæ æquidiſtantis, ſint autem duæ </s>
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