Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER IV.
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ita erit alia prædictæ parallela ad diſtantiam parallelarum
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ductarum ab eiuſdem extremitate ſecundò dictæ.</
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<
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">Sit ergo intra curuam parabolicam, ABCDF, ducta vtcunque,
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BF, obliquè ſecans axem, NR, in eandem curuam terminata,
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agatur deinde intra portionem, BNF, reſectam à, BF, recta, C
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D, parallela ipſi, BF; </
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<
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">ducantur inſuperà punctis, B, C, D, F, axi,
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NR, parallelæ, BO, CV, DG, FH, & </
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">à puncto, F, cadat
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0335-01
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ipſi, NR, perpendicularis, F
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A, ſecans parallelas, DG
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R, CV, BO, in punctis, G,
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R, V, O, poterunt ergo dicta-
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rum parallelarum diſtantiæ iumi
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in ipſamet, AF, nam ipſa per-
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pendiculariter dictas parallelas
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ſecat, erit ergo, OF, diſtantia
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parallelarum, BO, FH, ab
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extremis punctis rectæ, BF, ductarum; </
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<
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">pariter, VG, erit diſtan-
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tia parallelarum, CV, DG, ab extremis punctis, CD, ducta-
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rum. </
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">Dico ergo, BF, ad, FO, eſſe vt, CD, ad, VG: </
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tur a puncto, D, ipſi, CV, perpendicularis, DX, ſecans, BF, in,
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M, quoniam ergo anguli, BOF, CXD, ſunt recti, ideò iuntin-
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terſe æ quales, item anguius, OBF, eſt æqualis angulo, VIF, & </
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IF, ipſi angulo, XCD, ergo angulus, OBF, erit æqualis angulo, X
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">46. Elem.</
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CD, & </
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">ideò reliquus, OFB, reliquo, XDC, æqualis erit, & </
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guli, BOF, CXD, ſimiles erunt, vnde, BF, ad, FO, erit vt, C
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D, ad, DX, . </
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<
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">i. </
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<
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<
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dem parallelis, BO, CV, DG, FH, & </
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">ipſa, DX,
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ſiguram plènam deſcribere cum portione, BCDF, com-
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munem habens angulum mixtum ſub, BF, & </
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<
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C, quifit ad punctum, F, ita vt quælibet in deſctipta figu-
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ra recta linea ipſi, BF, æquidiſtanter ducta, ſit diſtantia pa-
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rallelarum axi, quæ ab extremis punctis eiuſdem rectæ li-
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neæ, productæ vſque ad curuam parabolicam, duci poſſunt:
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portionis, ſiue parabolæ, BCDF.</
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