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

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129109LIBER II. metro figuræ, EAG, vna ex ijs, quæ dicuntur omnes lineæ figurę,
EAG, & , NS, clauſa perimetro figuræ, GOS, vna ex omnibus
lineis figurę, GOQ, ſumptis omnibus lineis iam dictis, regula com-
muni, EQ, & recti tranſitus, vti ſemper intelligemus, niſi aliter ex-
plicetur, etiamſi id non exprimatur. Quoniam igitur ſi recta, NS,
ſit minor recta, LM, poteſt indefinitè producta aliquando fieri ma-
ior, ſi hoc intelligamus fieri de cæteris lineis, quæ ab altitudinibus
portiones abſcindunt ęquales verſus regulas, EG, GQ, patet, quod
ſingulę, quę erunt in figura, GOQ, productę fient maiores ijs, quę
erunt in figura, EAG, ſit autem ita facta productio cuiuſuis om-
nium linearum figuræ, GOQ, regula, EQ, vt quæ illi in directum
conſtituitur in figura, EAG, ſit portio eiuſdem productæ, vt ex. gr.
ita ſit producta, SN, verſus, ML, vt ipſam pertranſeat perueniens
verbi gratia vſque ad, T, ita vt, LM, ſit portio ipſius, TS, patet
ergo, quod omnes lineæ figuræ, EAG, erunt pars omnium linea-
rum figuræ, GOQ, ſic productarum, & iſtę erunt totum, nam illę
iſtis claudentur, ſiue in his totæ reperientur, & aliquid amplius . ſ.
quod de omnibus lineis figuræ, GOQ, ſic productis manet extra fi-
guram, EAG, totum autem eſt maius ſua parte, ergo omnes lineę
figuræ, GOQ, ſic productę fuerunt, vt maiores effectę fuerint om-
nibus lineis figuræ, EAG; eadem methodo omnes lineas figurę, E
AG, ſic producemus, vt complectantur omnes lineas figuræ, GO
Q, iam productas, vt dictum eſt, & ideò maiores eiſdem fiant, ma-
gnitudines autem rationem habere inter ſe dicuntur, quæ multipli-
11Diffin. 4.
1. 5. Elem. catæ ſe inuicem ſuperare poſiunt, ergo patet omnes lineas figura-
rum, EAG, GOQ, cum altitudines, A ℟, OP, fuerint æquales,
inter ſe rationem habere.

Non ſint autem æquales, ſed altitudo, A ℟, ſit maior altitudine,
OP, & ab, A ℟, ſit abſciſſa verſus, EG, ipſa, C ℟, ęqualis ipſi, O
P, & per, C, ducta, BD, parallela, EG, intelligatur per, BD, à
figura, EAG, abſciſſa figura, BAD, & ea conſtituta, vt, HFE,
ita vt ſit in eodem plano ad eandem partem cum figuris, EBDG,
(quæ remanſit) & , GOQ, exiſtente, HE, in directum ipſi, EQ,
quod ſi adhuc altitudo, FX, ſit maior altitudine, OP, abſcindatur
illi æqualis, & ſic ſemper fiat, & diſponantur figuræ reſiduæ, vt ea-
rum baſes ſint in directum ipſi, EQ, & figuræ conſtitutæ in eodem
plano, & ad eandem partem cum figuris, EAG, GOQ, in altitu-
dinibus vel ęqualibus, vel non maioribus altitudine, OP, Intelliga-
tur nunc ducta vtcumque in figura, GOQ, recta, NS, parallela,
GQ, quæ erit vna ex omnibus lineis figura, GOQ, regula, GQ,
producaturq; ita, vt pertranſeat omnes ſic diſpoſitas figuras, vt vſq;
in, Z, complectetur ergo, SZ, ipſas, LM, YT, & ſic quæuis

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