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

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4929LIBER I. milium. Ducantur plana oppoſita tangentia cylindrici, AM, re-
11Coroll. 1.
huius. ſpectu plani, BF, in eo ducti, vnius quorum, & planorum figura-
rum, YNO, TDF, productorum, communes ſectiones ſint, XS,
MG, alterius autem, & eorundem planorum ſint rectæ, YP, TQ,
indefinitè ambæ productæ, ſumpto autem in, YP, vtcumque pun-
cto, P, ducatur per, P, ipſi, CF, æquidiſtans, PQ, & ab eodem
in plano per, YP, XS, tranſeunte vſquead, XS, ducatur vtcum-
queipſa, PS, per ipſas autem, QP, PS, intelligatur extenſum pla-
num, quod ſecetaliud tangens planum in, SG, & planum per, T

22[Figure 22] Q, MG, ductum in, QG, producan-
tur autem ipſæ, NO, DF, verſus, P
S, QG, quibus occurrant in, V, R,
& iungatur, VR, erunt igitur, VR,
PQ, communes ſectiones æquidiſtan-
tium planorum, YQ, NR, & plani,
PR, & ideò erunt parallelæ, vt & ip-
ſæ, PV, QR, & , PR, erit paralle-
logrammum: Similiter, vt in Prop. 11.
oſtendemus eſſe parallelogramma ip-
ſa, VG, PG, NF, OR, NR, & an-
gulum, PSX, æqualem eſſe angulo,
QGM, & tandem, PS, QG, eſſe in-
22B. Def. 10.
huius. cidentes ſimilium figurarum, YNO,
TDF, & oppofitarum tangentium, YP, XS, TQ, MG, & tan-
gentes eſſe homologarum earundem regulas, & quia eiſdem æqui-
diſtant ipſæ, NO, DF, & productæ ſimiliter, & ad eandem par-
tem ipſas incidentes, PS, QG, diuidunt; nam, PV, æquatur ipſi,
QR, & , VS, ipſi, RG, ideò ipſæ, NO, DF, erunt lineæ homo-
logæ figurarum, YNO, TDF, ſimilium, quæ in plures homolo-
gas ſecari contingere poteſt, prout ſe habet ambitus ſuperficiei cy-
lindraceæ huius cylindrici, AM, ſunt lineæ homologæ inquam, ſi
33C. Def. 10.
huius. ſint intra ambitum figurarum, quarum ſunt homologæ, ſunt verò
latera homologa, ſi ſint in earundem ambitu, veluti contingeret ſi
planum per latera ductum eſſet planum contactus vnius oppoſito-
rum tangentium, veluti ſi cylindricus fuiſſet, cuius oppoſitæ baſes
ſunt, ABC, TDF, excluſis reſiduis figuris, quæ ab ipſis, BC, D
F, abſcinduntur, tunc enim eodem modo facta fuiſſet demonſtra-
tio, vt conſideranti facilè patebit; idem oſtendemus in recta, BC,
& in quibuſuis alijs, quæ ſunt communes ſectiones planorum baſi-
bus æquidiſtantium, & parallelogrammi, BF, probantes ſcilicet
eaſdem eſſe lineas, vellatera homologa figurarum in cylindrico per
baſibus æquidiſtantia plana productarum, quod oſtendere opus erat.

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Scan	Original
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
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129	109
130	110
131	111
132	112
133	113
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136	116
137	117
138	118
139	119
140	120

Scan	Original
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
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129	109
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131	111
132	112
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