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

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8060GEOMETRIÆ in, X, ducatur in plano, NOP, recta, QR, à puncto, Q, perpen-
dicularis ipſi, OP, & iungatur, HR, triangulumque, HRQ, ſe-
cet duo triangula, VST, KST, in rectis, YX, ZX. Quia ergo
1116. Vnd.
Elem. triangula, VST, NOP, ſunt parallela, erunt etiam ipſę, ZX, R
Q, parallelæ, ſed & , ST, OP, ſunt parallelę, ergo anguli, ZXS,
RQO, erunt æquales, rectus ergo eſt etiam ipſe, ZXS, ſed etiam,
2210.Vnd.
Elem. SXH, rectus eſt, ergo, SX, eſt duabus, ZX, XH, perpendicula-
ris, & ſubinde plano per ipſas tranſeunti, & conſequenter, SXY, eſt
334.Vndec.
Elem. rectus, vnde, HXZ, erit inclinatio planorum, HST, KST, & , H
XY, inclinatio planorum, HST, SVT, hæc autem eſt æqualis in-
clinationi planorum, HOP, NOP, ex hypoteſi, ideſt angulo, H

42[Figure 42] QR, ideſt angulo, H
XZ, ergo angulus, H
XY, qui eſt totum, eſt
ęqualis augulo, HXZ,
eiuſdem parti, quod eſt
abſurdũ, ergo abſurdum
etiam eſt dicere trian-
gulum, VST, non æ-
quidiſtare ipſi, NOP,
æquidiſtat ergo, & ip-
ſæ, VS, VT, ſunte-
4416. Vnd.
Elem. tiam parallelæ ipſis, N
O, NP, & triangula,
VHS, ipſi, NHO, V
HT, ipſi, NHP, nec-
non, VST, ipſi, NOP, ſunt ſimilia, ergo pyramides, HVST,
HNOP, ſunt ſimiles, eſt autem pyramis, HVST, ſimilis, immo
& ęqualis, ipſi, ACDB, ergo pyramides, ACDB, HNOP, in-
ter ſe ſimiles erunt, & anguli, ACB, HVT, ACD, HVS, inter
ſe æquales, ergo, AC, HV, rectę lineę ſtantes in ſublimi, & cum
ipſis, CD, CB, VS, VT, angulos æquales continentes (à quibus
etiam contenti anguli, DCB, SVT, ſunt ęquales) erunt ad plana
5535. Vnd.
Elem. triangulorum, CDB, NOP, æqualiter inclinata, & ſunt ipſæ py-
ramides, ACDB, HNOP, ſimiles, vt propoſitum fuit demon-
ſtrare.

Si verò rectæ lineæ angulos æquales cum ipſis, DA, AB, OH,
HP, continentes eſſent ipſæ, AT, Η Λ, quarum, Λ Η, eſſet paral-
lela plano, VST, probaremus etiam, TA, eſſe parallelam plano,
CDB, alioquin ſi cum ipſo producta concurreret, etiam, Λ Η, ex
ſupra oſtenſis, producta concurreret cum plano trianguli, VST. Vel
præintellectis duabus iam datis, AC, HN, & ſuppoſita

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101	81
102	82
103	83
104	84
105	85
106	86
107	87
108	88
109	89
110	90
111	91
112	92
113	93
114	94
115	95
116	96
117	97
118	98
119	99
120	100
121	101
122	102
123	103
124	104
125	105
126	106
127	107
128	108
129	109
130	110

Scan	Original
101	81
102	82
103	83
104	84
105	85
106	86
107	87
108	88
109	89
110	90
111	91
112	92
113	93
114	94
115	95
116	96
117	97
118	98
119	99
120	100
121	101
122	102
123	103
124	104
125	105
126	106
127	107
128	108
129	109
130	110

Scan	Original
101	81
102	82
103	83
104	84
105	85
106	86
107	87
108	88
109	89
110	90
111	91
112	92
113	93
114	94
115	95
116	96
117	97
118	98
119	99
120	100
121	101
122	102
123	103
124	104
125	105
126	106
127	107
128	108
129	109
130	110