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

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7050GEOMETRIÆ

Sint duæ vtcumque figuræ rectilineæ, ABDEH, MTRPN;
11Prima
Def. Sex-
ti Elem. ſimiles iuxta definitionem E@clidis, ideſt ſingulos habentes angulos
æquales, A, M; B, T; D, R; P, E; HN, & circa æquales angu-
los latera proportionalia. Dico eaidem eſſe ſimiles iuxta meam de-
finitionem: Ducantur duæ vtcum que oppoſitæ earum tangentes,
quæ cum duobus ex lateribus homologis earumdem angulos æqua-
les ab eadem parte contineant, ſint autem ex vna parte tangentes
ipſæ, AH, MN, quæ cum ipſis, HE, NP, lateribus homologis
angulos continent ęquales, AHG, MNO, & ſint ex alia parte tan-
gentes ipſæ, DF, RQ, quæ cum ipſis, HE, NP, productis con-

35[Figure 35] currant in punctis, F, Q, ducantur deinde à
punctis angulorum, qui ſunt, B, E; TP, di-
ctis tangentibus parallelæ, BG, CE, TO, S
P, & iungantur, BH, BE, TN, TP. Quia
ergo anguli, MNQ, AHF, ſunt æquales,
etiam anguli, NQR, HFD, erunt ęquales,
& quia anguli, NPR, HED, ſunt quoque
æquales, etiam anguli, RPQ, DEF, erunt
æquales, & reliqu reliquis, vnde trianguli, R
PQ, DEF, erunt æquianguli, & ideò, QP,
224. Sexti
Elem. ad, PR, erit vt, FE, ad, ED, eſt autem, R
P, ad, PN, vt, DE, ad, EH, ergo, ex ęquali,
33Ex Defin.
Eucl. QP, ad, PN, erit vt, FE, ad, EH, igitur,
NQ, HF, ſunt ſimiliter ad eandem partem
diuiſæ in punctis, E, P, quia verò angulus, NPS, æquatur angu-
lo, NQR. . HFD. . HEC, & , NPR, ipſi, HED, ideo reli-
quus, SPR, æquabitur reliquo, CED, eſt autem angulus, TR
P, ęqualis angulo, BDE, ergo trianguli, PSR, ECD, erunt æ-
quianguli, & ideò, CE, ad, ED, erit vt, SP, ad, PR, & , ED,
ad, EF, erit vt, RP, ad, PQ; ergo ex æquali, & permutando, C
E, ad, SP, erit vt, EF, ad, PQ . i. vt, HF, ad, NQ. S militer
446. Sexti
Elem. quia anguli, BDE, TRP, ſunt æquales, & circa eos latera ſunt
proportionalia, ideò trianguli, BDE, TRP, erunt æquianguli,
vnde anguli, DBE, RTP, & , BED, TPR, erunt ęquales, ſunt
autem ęquales ipſi, CED, SPR, ergo reliqui, BEC, TPS, erunt
æquales, & ideò trianguli, BCE, TSP, erunt ęquianguli, & quia
angulus, BEF, eſt ęqualis ipſi, TPQ, reliquns, BEH, erit ęqua-
lis reliquo, TPN, eſt autem, BGE, ęqual sipſi, TOP, ergo trian-
guli, BGE, TOP, erunt ęquianguli, ergo, BG, ad, TO, erit vt,
BE, ad, TP, ideſt vt, CE, ad, SP, ideſt vt, HF, ad, NQ, per-
mucando, & conuertendo, HF, ad, GB, erit vt, NQ, ad, OT;
quia verò anguli, HAB, NMT, ſunt ęquales, & circa eoſdem

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