Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ ſit in parallelis, E6, Y4, etiam reſidua figura, vel reſiduarum ag-
gregatum, ipſius, CβΛ, (quod ſit ipſi fruſta, ΙΓΛ, 785,) erit in eiſdẽ
parallelis; E6, Y4, ſi enim non pertingeret hinc inde ad parallelas,
E6, Y4, vt ex. g. ſi pertingeret quidem vſq; ad, E6, non tamen vſq; ad, Y4, ſed tantum vſque ad, LΣ, conceptis rectis lineis in fruſto,
Q℟β59R, ipſi, AD, parallelis non reſponderent in reſiduo figuræ,
CβΛ, ſeu ex reſiduis aggregato, aliæ rectæ lineæ, vt ſuperius neceſ-
ſe eſſe probatum eſt, ſunt ergo hæc reſidua, vel reſiduorum aggre-
gata in eiſdem parallelis, & in illis conceptæ parallelarum ipſis, A
D, Y4, portiones inter ſe ſunt æquales, vt ſupra oſtendimus, ergo
reſidua, ſeu reſiduorum aggregata, ſunt eius conditionis, cuius ip-
ſas, BZ& , CβΛ, figuras iam eſſe ſuppoſitum fuit, ideſt æqualiter
analoga. Fiat ergo denuo reſiduorum ſuperpoſitio, ita tamen vt
parallelæ, GH, & β, ſuper parallelas, HK, β4, ſint conſtitutæ, & congruat pars, VΔΛ, fruſti, H℟597, parti, VΔΛ, fruſti, ΙΓΛ, oſten-
demus ergo vt ſupra, dum vnius habetur reſiduum haberi etiam al-
terius, & hæc reſidua, ſiue reſiduorum aggregata, eſſe in eiſdem
parallelis, ſit autem ad figuram, BZ& , ſpectans reſiduum, ΚVΛ3
ΠΧ, ad figuram autem, CβΛ, ſint pertinentia reſidua, ΙΓΔV, 785,
quorum aggregatum eſt in eiſdem parallelis cum reſiduo, ΚVΛ3
ΠΧ, nem pè in parallelis, E6, Y4, ſi ergo horum reſiduorum fiat
denuò ſuperpoſitio, ita tamen vt parallelæ, in quibus exiſtunt, ſint
ſemper ad inuicem ſuperpoſitę, & hoc ſemper fieri intelligatur, do-
nec tota figura, BZ& , fuerit ſuperpoſita, dico totam debere ipſi,
CβΛ, congruere, alioquin ſi eſſet aliquod reſiduum vt figurę, CβΛ,
cui nihil eſſet ſuperpoſitum, eſſet etiam aliquod reſiduum figurę,

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