Viviani, Vincenzo - De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Scan	Original
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
111	87
112	88
113	89
114	90
115	91
116	92
117	93
118	94
119	95
120	96
121	97
122	98
123	99
124	100
125	101
126	102
127	103
128	104
129	105
130	106

11086 ipſa HM producta omnino ſecabit ſectionem CBA, vel ſupra contingentem
CEA, vt in N, vel in ipſo occurſu A, vel infra ad partes AL; ſi in N, vel in
A, patet interiorem ſectionem totam cadere infra applicatas ex N, vel ex A,
& nunquam infra N, vel A ſectioni BNA occurrere, ne priùs ſecet propriam
aſymptoton HM.

Si verò HM ſecet exteriorẽ

76[Figure 76] BA infra contingentem CAE,
vt in hac ipſa figura; item pa-
tet ſectiones BA, ED infra LD
nunquam ſimul conuenire, ſin
aliter propriam aſymptoton
ſecaret.

Præterea indirectũ produ-
cta communi diametro EBG,
ſumptiſque in ea punctis V, T,
quæ ſint extrema tranſuerſo-
rum laterum datarum ſectio-
num, ductiſque regulis TX,
VZ; ipſę vti ſuperiùs oſtenſum
fuit, inter ſe æquidiſtabunt.
Ampliùs ſumpto in portione
ED quolibet puncto K, per ip-
ſum applicetur KY vtranque Hyperbolen ſecans in P, K; regulas verò in
Z, X.

Iam, vel recta VZ eſt regula interioris ſectionis DEF, & TX exterioris;
vel ipſæ ſimul congruunt, ſi tamen puncta V, T, in vnum conueniant; vel è
contra VZ eſt regula exterioris, TX verò interioris. Si primum, cum in ſe-
ctione ABC quadratum applicatæ PY æquale ſit rectangulo BYX, & 11Coroll.
1. huius. Hyperbola DEF quadratum KY ſit æquale rectangulo EYZ, ſitque rectan-
gulum BYX maius EYZ, cum ſub maioribus lateribus contineatur, erit quo-
que quadratum PY, maius quadrato KY: vnde punctum K eſt intra ſectio-
nem ABC. Si ſecundum nempe ſit VZ vtriuſque ſectionis communis regu-
la, erit quadratum PY æquale rectangulo BYZ, & quadratum KY æquale
rectangulo EYZ, ſed rectangulum BYZ maius eſt EYZ, cum altitudo BY
maior ſit altitudine EY, quare quadratum PY maius eſt quadrato KY, ſiue
punctum K eſt intra ſectionem ABC. Si denique interior recta VZ fuerit re-
gula exterioris ſectionis ABC, & exterior TX, regula interioris DEF, erit
HE ipſi HT æqualis, ſed eſt ablata HB minor ablata GV (cum ponatur GB,
quæ maior eſt HB, æqualis GV) ergo reliqua BE maior erit reſiduis ſegmen-
tis GH, VT, & eò maior vnico ſegmento VT, ſed eſt EY minor VY, quare
BE ad EY maiorem habebit rationẽ quàm TV ad VY, vel quàm XZ ad ZY,
& componendo BY ad YE maiorem habebit rationem quàm XY ad YZ, vn-
de rectangulum BYZ ſiue quadratum PY maius erit rectangulo EYX 22ibidem.3316. ſept.
Pappi. quadrato KY, hoc eſt punctum K incidet intra ſectionem ABC, & ſic 44Coroll.
1. huius. quolibet alio puncto portionis DEF; Quare huiuſmodi ſimiles Hyperbolæ,
neque infra applicatam LF, neque inter lineas LF, AC ſimul conueniunt,
vnde ſunt in totum nunquam coeuntes. Quod ſextò, & c.

Page concordance

Text layer

Text normalization

Search

Scan	Original
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
111	87
112	88
113	89
114	90
115	91
116	92
117	93
118	94
119	95
120	96
121	97
122	98
123	99
124	100
125	101
126	102
127	103
128	104
129	105
130	106

Scan	Original
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
111	87
112	88
113	89
114	90
115	91
116	92
117	93
118	94
119	95
120	96
121	97
122	98
123	99
124	100
125	101
126	102
127	103
128	104
129	105
130	106

Scan	Original
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
111	87
112	88
113	89
114	90
115	91
116	92
117	93
118	94
119	95
120	96
121	97
122	98
123	99
124	100
125	101
126	102
127	103
128	104
129	105
130	106