Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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xml:space
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">in eiſdem parallelis conſtitutę,
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in quibus, ductis quibuſcunq; </
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<
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">eiſdem parallelis ęqui-
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diſtantibus rectis lineis, conceptæ cuiuſcumq; </
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<
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">rectæ lineæ
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portiones ſunt æquales, etiam inter ſe æquales erunt: </
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<
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figuræ ſolidæ quæcumq; </
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<
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xml:space
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">in eiſdem planis parallelis conſti-
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tutæ, in quibus, ductis quibuſcunq; </
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<
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xml:space
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">planis eiſdem planis
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parallelis æquidiſtantibus, conceptæ cuiuſcunq; </
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<
s
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">ſic ducti
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plani in ipſis ſolidis figuræ planæ ſunt æquales, pariter in-
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terſe æquales erunt. </
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<
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">Dicantur autem figuræ æqualiter
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analogæ, tum planæ, tum ipſæ ſolidæ interſe comparatæ,
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ac etiam iuxta regulas lineas, ſeu plana parallela, in qui-
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bus eſse ſupponuntur, cum hoc fuerit opus explicare.</
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<
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</
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<
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<
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">Sint quæcunq; </
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<
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">planę figuræ, BZ&</
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<
s
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xml:space
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">, CβΛ, in eiſdem parallelis,
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AD, Y4, conſtitutæ, ductis autem ipſis, AD, Y4, quibuſcunque
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parallelis, E6, LΣ, portione ex. </
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<
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">g. </
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<
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">ipſius, E6, in figuris conceptę,
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nempè, FG, HI, inter ſe ſint æquales, necnon ipſius, LΣ, portio-
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nes, MN, OP, ſimul ſumptæ (ſit enim figura, BZ&</
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<
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<
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<
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ua ſecundum ambitum, {12/ }, N, {13/ }, O,) ipſi, SV, ſint pariter ęqua-
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les, & </
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<
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<
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">alijs ipſi, AD, æquidiſtanti-
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bus. </
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<
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">Dico figuras, BZ&</
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<
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<
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ergo alterutra figurarum, BZ&</
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<
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<
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">, cum paralle-
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larum, AD, Y4, portionibus ipſi conterminantibus, nempè cum,
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AB, Y&</
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<
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">, ſuperponatur reliquæ figuræ, CβΛ, ita tamen vt ipſæ, A
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B, Y&</
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<
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<
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CβΛ, & </
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<
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">ita cum ſibi congruant æquales erunt, vel non, aliqua
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tamen pars eſto, quod congruerit alicui parti, vt, CΙγβ587, pars
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figuræ, BZ&</
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<
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<
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">Manifeſtum eſt
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autem ſuperpoſitione figurarum taliter effecta, vt portiones pa-
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rallelarum, AD, Y4, ipſius figuris conterminantes ſint inuicem
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ſuperpoſitæ, quod quæcumq; </
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<
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ſibi in Birectum, manent etiam ſibi in directum, vt ex. </
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<
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N, OP, eſſent in directum ipſi, SV, dicta ſuperpoſitione facta, ma-
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nent etiam ſibi in directum, nempè, QR, ST, in directum ipſi, SV,
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eſt enim diſtantia ipſarum, MN, OP, ab, AD, æqualis diſtantiæ,
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SV, ab eadem, AD, vnde quotieſcunque, AB, extendatur ſuper, B
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D, vbicunque hoc fiat, ſemper, MN, OP, manebunt in </
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