Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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licet non ſint rectangula, tamen erunt æquiangula, vndeæquiangu-
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lum erit parallelogrammi, HP, ipſi, FG, & </
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TMI, erunt circa, AC, KM,
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æquales diametros, ita vt ſi ſuper-
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ponerentur ad inuicem iſti ellipſes,
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vt, KM, eſſet in, AC, ipſa, TI,
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eſſet in, BD, & </
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<
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xml:space
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">ideò eodem mo-
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do oſtendemus, vt ſupra ellipſes,
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ABCD, STVI, eſſe inter ſe, vt
<
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parallelogramma illis eircumſcri-
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pta, FG, ER, & </
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<
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">quia illa ſunt
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ęquiangula habebunt rationem ex
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ratione laterum compoſitam, ſed
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etiam parallelogramma rectangu-
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">6.Lib.2.</
note
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la ſub eiſdem lateribus habent ra-
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tionem cõpoſitam ex ratione eo-
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rundem laterum, ergo ellipſis, A
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BCD, ad ellipſim, STVI, erit
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vt parallelogrammum, FG, ad
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parallelogrammum, ER, ſibiæ-
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quiangulum. </
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<
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xml:space
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">vt rectangulum ſub,
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FL, LG, vel ſub, BD, AC, dia-
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metris, ad rectangulum ſub, TI,
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SV, diametris, patetigitur circu-
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lum, vel ellipſim, ABCD, ad cir-
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eulum, vel cllipſim, STVI, eſſe vt rectangulum ſub axibus, vel dia-
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metris, AC, BD, ad rectangulum ſub axibus, vel diametris, SV,
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TI, quæ diametri æquè ad inuicem inclinantur, quod oſtendere
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opuserat.</
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<
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">_H_INC ergo colligitur, quod quando circulos comparatur ad cir-
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culum, illi ſunt interſe, vt rectangula ſub eorum axibus. </
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<
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quadrata axium, & </
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">ideò ſunt in dupla ratione axium, ſiue diametro-
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rum, quando verò circulus comparatur ad ellipſim, erit ad illum, vt
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ſui axis quadratum adrectangulum ſub axibus ellipſis. </
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lipſis comparetur ad ellipſim, erit ad illum, vt rectangulum ſub axibus
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illius ad rectangulum ſub axibus alterius, vel vt rectangulum ſub dia-
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metris (coniugatis ſemper intellige, niſi aliud addatur) illius ad rectan-
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gulum ſub diametris alterins, quæ vt prædicti æqualiter ad inuicem
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ſunt inclinatæ; </
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<
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