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

Scan	Original
71	51
72	52
73	53
74	54
75	55
76	56
77	57
78	58
79	59
80	60
81	61
82	62
83	63
84	64
85	65
86	66
87	67
88	68
89	69
90	70
91	71
92	72
93	73
94	74
95	75
96	76
97	77
98	78
99	79
100	80

5131LIBERI. ergo, SM, æquidiſtans ipſi, TP, regulæ homologarum figurę, A
T, veluti, RK, æquidiſtat ipſi, NL, regulæ homologarum figu-
ræ, F N, & ſecant incidentes, BP, HL, ſimiliter ad eandem par-
tem in punctis, M, K, ergo ipſæ, SV, RI, erunt homologę di-
ctarum figurarum ſimilium, & ęqualium, quę ideò erunt æquales,
ſicut etiam ipſæ, VM, IK. & ſunt ęquidiſtantes, ergo eas iungen-
tes erunt ęquales, & ęquidiſtantes, ſcilicet, SR, VI, MK, eſtau-
tem, MK, parallela, & ęqualis ipſi, PL, ergo, SR, VI, erunt
ęquales, & parallelęipſi, PL: Eodem pacto per, EG, extendentes
planum ęquidiſtans plano, TL, quod ſecet figurarum, AT, FN,
productarum plana in rectis, QE, DG, oſtendemus ipſas, QO, D
C, eſſe homologas figurarum ſimilium, & ęqualium, AT, FN, &
ideò eas eſſe ęquales, vt & ipſas, OE, CG, ergo ſi iungantur, QD,
OC, iſtę erunt ęquales, & parallelę ipfi, EG, ideſt ipſi, PL; ſimi-
liter in cæteris planis procedemus, quæ inter plana, TL, AH, ip-
ſis æquidiſtantia ducuntur, oſtendentes, quæ iungunt extrema ho-
mologarum earundem figurarum, AT, FN, eſſe æquales, & ęqui-
diſtantesipſi, PL, ſi igitur, PL, regula ſtatuatur, erunt omnes di-
ctæ iungentes in ſuperficie quadam, per quam ipſi, PL, properan-
te quadam recta linea æquali ſemper ęquidiſtanter, eiuſdem extrema
11Def.3. iugiter manent in ambitu ſigurarum, AT, FN, ergo hæc erit ſu-
perficies cylindrici, cuius oppoſitę baſes erunt ipſę, AT, FN, ſunt
igitur, AT, FN, cylindrici cuiuſdam (nempè cuius latus eſt quod-
uis ipſorum, QD, SR, VI, OC,) oppoſirę baſes, quod erat no-
bis oſtendendum.

THEOREMA XII. PROPOS. XV.

PVnctus manens, cui in reuolutione innititur latus coni-
ci, eſt vnicus vertex conicireſpectu eiuſdem baſis.

Sit conicus, ABD, baſis, BD, punctus, eui innititur latus co-
22A. Def.4. nici, ABD, in reuolutione, quę ab eo fit per circuitum baſis, BD,

24[Figure 24] ſit, A. Dico, A, eſſe vnicum verticem conici, A
BD, reſpectu baſis, BD. Intelligatur per pun-
ctum, A, ductum planum ęquidiſtans baſi, dico
hoc planum tantummodo in hoc puncto tangere
conicum, ſi enim poſſibile eſt eundem tangat, ſeu
ſecet in duobus punctis, vt in, C, A, iuncta ergo,
AC, illa erit in ſuperficie coniculari, & cum de-
ſcendat à puncto, A, per ipſum tranſiet aliquando
latus conici, vt, AB, igitur, AB, erit in plano ducto per, A,

Page concordance

Text layer

Text normalization

Search

Scan	Original
71	51
72	52
73	53
74	54
75	55
76	56
77	57
78	58
79	59
80	60
81	61
82	62
83	63
84	64
85	65
86	66
87	67
88	68
89	69
90	70
91	71
92	72
93	73
94	74
95	75
96	76
97	77
98	78
99	79
100	80

Scan	Original
71	51
72	52
73	53
74	54
75	55
76	56
77	57
78	58
79	59
80	60
81	61
82	62
83	63
84	64
85	65
86	66
87	67
88	68
89	69
90	70
91	71
92	72
93	73
94	74
95	75
96	76
97	77
98	78
99	79
100	80

Scan	Original
71	51
72	52
73	53
74	54
75	55
76	56
77	57
78	58
79	59
80	60
81	61
82	62
83	63
84	64
85	65
86	66
87	67
88	68
89	69
90	70
91	71
92	72
93	73
94	74
95	75
96	76
97	77
98	78
99	79
100	80