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

Table of contents

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[251.] COROLLARIVM II.
Page: 186 (166)
[252.] COROLLARIVM III.
Page: 186 (166)
[253.] THEOREMA XXVII. PROPOS. XXVII.
Page: 187 (167)
[254.] THEOREMA XXVIII. PROPOS. XXVIII:
Page: 188 (168)
[255.] COROLLARIVM.
Page: 189 (169)
[256.] THEOREMA XXIX. PROPOS. XXIX.
Page: 190 (170)
[257.] COROLLARIVM.
Page: 190 (170)
[258.] THEOREMA XXX. PROPOS. XXX.
Page: 191 (171)
[259.] COROLLARIVM.
Page: 192 (172)
[260.] THEOREMA XXXI. PROPOS. XXXI.
Page: 193 (173)
[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)
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          <head xml:id="echoid-head359" xml:space="preserve">THEOREMA XXI. PROPOS. XXII.</head>
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            <s xml:id="echoid-s5840" xml:space="preserve">SI intra parallelogrammum, quod circulo, vel ellipſi ſit
              <lb/>
            circumſcriptum, ducatur lateribus eiuſdem parallela
              <lb/>
            quædam rectalinea, per circuli, vel ellipſis centrum non
              <lb/>
            tranſiens, altero reliquorum laterum regula exiſtente. </s>
            <s xml:id="echoid-s5841" xml:space="preserve">Om-
              <lb/>
            nia quadrata parallelogrammi, quod maiori portioni circu-
              <lb/>
            li, vel ellipſis iam dicti, remanent circumſcriptum, ad om-
              <lb/>
            nia quadrata figuræ compoſitæ ex maiori portione, & </s>
            <s xml:id="echoid-s5842" xml:space="preserve">duo-
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            bus trilineis, quiad baſim eiuſdem hinc inde extra conſtitu-
              <lb/>
            untur, demptis eorundem trilineorum omnibus quadratis,
              <lb/>
            erunt in circulo, vt parallelepipedum ſub baſi parallelo-
              <lb/>
            grammo dictæ portioni maiori circumſcripto, altitudine
              <lb/>
            eiuſdem portionis diametro ad cylindricum ſub baſi eadem
              <lb/>
            maiori portione, altitudine differentia diametrorum maio-
              <lb/>
            ris, acminoris factarum portionum, vna cum ſexta parte cu-
              <lb/>
            bi baſis eiuſdem portionis In ellipſi verò erunt, vt paralle-
              <lb/>
            lepipedum ſub baſi parallelogrammo maiori portioni ſimili-
              <lb/>
            ter circumſcripto, altitudine eiuſdem portionis diametro,
              <lb/>
            ad cylindricum ſub baſi eadem maiori portione, altitudine
              <lb/>
            differentia diametrorum maioris, ac minoris factarum por-
              <lb/>
            tionum, vna cum ea porte cubi baſis eiuſdem portionis, ad
              <lb/>
            quam ſexta pars eiuſdem cubi ſit, vt quadratum primæ dia-
              <lb/>
            metriad quadratum ſecundæ, vel, ſi diametrinon ſint axes,
              <lb/>
            vna cum ea parte parallelepipedi ſub altitudine baſi eiu-
              <lb/>
            ſdem portionis, ac ſub baſi rhombo ab eadem deſcripto, ad
              <lb/>
            quam eiuſdem parallelepipedi pars ſexta ſit, vt quadratum
              <lb/>
            primę diametri ad quadratum ſecundæ.</s>
            <s xml:id="echoid-s5843" xml:space="preserve"/>
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            <s xml:id="echoid-s5844" xml:space="preserve">Sit ergo circulus, vel ellipſis, CFEH, cui ſit circumſcriptum pa-
              <lb/>
            rallelogrammum, AQ, & </s>
            <s xml:id="echoid-s5845" xml:space="preserve">centrum ſit, N, diametriautem tranſeun-
              <lb/>
            tesper puncta contactuum laterum circumſcripti parallelogrammi,
              <lb/>
            & </s>
            <s xml:id="echoid-s5846" xml:space="preserve">per centrum, N. </s>
            <s xml:id="echoid-s5847" xml:space="preserve">ſint, CE, FH; </s>
            <s xml:id="echoid-s5848" xml:space="preserve">ſit autem, FH, regula, cui in-
              <lb/>
            ſiſtens, & </s>
            <s xml:id="echoid-s5849" xml:space="preserve">lateribus, AP, DQ, parallela intra ipſum ducta ſit, LG.
              <lb/>
            </s>
            <s xml:id="echoid-s5850" xml:space="preserve">Dico ergo omnia quadrata parallelogrammi, AG, ad omnia qua-
              <lb/>
            drata figuræ, LCFEG, demptis omnibus quadratis trilineorum,
              <lb/>
            CLI, YGE, eſſe, in circulo, vt parallelepipedum ſub </s>
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