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

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

10282GEOMETRI Æ

Sit conus, cuius vertex, A, baſis circulus, CEFD, ſecetur autem
prius plano per axem, quod in eo producat triangulum, ACF, ſe-
1116, huius. cetur deinde altero plano baſim ſecante ſecundum rectam, ED, per-
pendicularem ipfi, CF, cuius in cono concepta ſit figura, BED,
22Ex antec. erit ergo hæc figura circa axem, vel diametrum, BV, quę ſit paral-
lela ipſi, AF, cuius vertex reſpectu ipſius, ED, erit, B; ducaturà
puncto, M, qui non ſit punctus, B, ſed vtcumque ſumptus in linea,
EBD, extra baſim, ED, ipſi, ED, recta ęquidiſtans, MO, pro-
ducta vſq; ad ambientem ſuperficiem, cui occurrat in, O, igitur hęc
erit vna ex ordinatim applicatis ad axim, vel diametrum, BV, ęqui-
diſtans ipſi, ED, quę bifariam diuidetur ab ipſa, BV, in puncto, N,
ducatur per, N, ipſi, CF, parallela, HR, eſt verò etiam, MO, ipſi,
ED, parallela, ergo planum tranſiens per, HR, MO, æquidiſta-
3315. Vnde-
cim. El. bit baſi, CEFD, & quatuor puncta, H, M, R, O, erunt in circuli

56[Figure 56] periphæria, cuius diameter, HR, quem
4415. huius. ſecat, MO, perpendiculariter, nam an-
gulus, HNM, æquatur angulo, CVE,
5514. Secun.
Elem. quirectus eſt, ergo quadratum, MN, æ-
quatur rectangulo, HNR, & quadra-
tum, EV, rectangulo, CVF, eſt autem
rectangulum, CVF, ad rectangulum, H
NR, (quia eorum altitudines, VF, NR,
ſunt æ quales, cum ſint parallelogrammi,
NF, oppoſita latera) vt baſis, CV, ad,
HN, ex prima Sexti Elem. vel ex quinta
libro ſequentis independénter ab hac de-
monſtrata, & quia, HN, eſt parallela
ipſi, CV, trianguli, BHN, BCV, ſunt æquianguli, ideò, vt, C
664. Sexti
Elem. V, ad, HN, ita, VB, ad, BN, ergo rectangulum, CVF, ad re-
ctangulum, HNR, ideſt quadratum, EV, ad quadratum, MN,
erit vt, VB, ad, BN, eſt autem quadratum, ED, quadruplum
quadrati, EV, nam eſt æquale quadratis, EV, VD, & rectangulis
774. Secun.
Elem. fub, EVD, bis, ideſt duobus quadratis, EV, quæ cum prædictis
conficiunt quatuor quadrata, EV, & eadem ratione quadratum, M
O, eſt quadruplum quadrati, MN, ergo quadratum, ED, ad qua-
dratum, MO, erit vt, BV, ad, BN, quæſunt abſciſſæ ab ipſa axi,
vel diametro, BV, verſus verticem, B, per ipſas, ED, MO, ordi-
natim adipſam, BV, applicatas, quod oſtendere opus erat; hęc au-
tem vocatur ab Apolonio Parabola.

Page concordance

Text layer

Text normalization

Search

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

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