## Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER I. tera proportionalia, ideòtriang. HAB, NMT, ſuntæquiangun,
& anguli, AHB, MNT; ABH, MTN, interſe ęquales, ergo
cum anguli, AHG, MNO, ſint æquales, reliqui, BHG, TN
O, erunt æquales, ſunt etiam æquales anguli, HGB, NOT, ergo
trianguli, HBG, NTO, ſunt æquianguli, ergo, BG, ad, GH,
T, ergo ex ęquali, FH, ad, HG, erit vt, QN, ad, NO, ſunt@gi-
tur ipiæ, HF, NQ, ſimiliter diuiſæ, & ad eandem partem in pun-
ctis, G, O, & ipſæ diuidentes, BG, TO, ſunt vt ipſæ, HF, NQ.

### 100.1.

Prima
Def. Sex-
ti Elem.
4. Sexti
Elem.
Ex Defin.
Eucl.
6. Sexti
Elem.
6. Sexei
Elem.

Ducantur nunc inter dictas oppoſitas tangentes elſdem parallelæ
duæ v@cumque, VK, XY, inter circuitum figurarum iam propoſi-
tarum, & rectas, HF, NQ, comprehenſę, ſimiliter ad eandem par-
tem diu@dentes ipſas, HF, NQ, in punctis, K, Y, ſecanteſque ip-
ſas, BE, TP, in punctis, 3, 4, eſt ergo, FK, ad, QY, permutan-
Y, erit vt, FE, ad, QP, & reliqua, EK, ad reliquam, PY, vt, F
K, ad, QY, ideſt vt, FH, ad, QN; Similiter oſtendenius, vt, F
P, componendoque, GE, ad, FK, erit vt, OP, ad, PY, eſt verò,
ſimiliter, quia ipſæ, VK, XY, diuidunt ſimiliter ad eandem partem
ipſas, BC, TS, in punctis, V, X, ac diuiduntur ipſę, GE, OP, in
punctis, K, Y, ideò eodem modo oſtendemus ipſas, V3, X4, eſſe
vt ipſas, CE, SP, ideſt vt ipſas, HF, NQ, erant autem, 3K, 4
X, vt ipſæ, HF, NQ, ergo totæ, VK, XY, erunt vt ipiæ, HF,
NQ, habemus igitur figuras, ADE, MRP, in quibus ductę ſunt
oppoſitæ tangentes, AH, DF, MN, RQ, quibus inciderunt ip-
autem eas, quæ inter dictas, HF, NQ, & circuitum figurarum ei-
ſdem tangentibus vtcumq; ducuntur ęquidiſtantes, & ſecant dictas,
HF, NQ, ſimiliter ad eandem partem, eodem ordine ſumptas, eſſe
vt ipſas, HF, NQ, ergo figuræ, ADE, MRP, quæ erant ſimi-
les iuxta definitionem Euclidis, erunt etiam ſimiles iuxta definitio-
nem meam, & erunt dictæ tangentes regulæ homologarum earum-
dem, & ipſarum, ac dictarum ſimilium figurarum incidentes ipſę, H
F, NQ, quod erat oſtendendum.

Deſin. 10,
huius.

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