254 
DISQUISITIONES GENERALES 
dem linea brevissima DB, pro quo, manente p, characteres q, r, <p', cj/, 8' eadem 
designent, quae q, r, cp, <[», 8 pro puncto B. Ita oritur triangulum inter puncta 
A, B, C, cuius angulos per A, B, C, latera opposita per a, b, c, aream per a 
denotamus; mensuram curvaturae in punctis A, B, C resp. per a, t), y expri 
memus. Supponendo itaque (quod licet), quantitates p, q, q — q' esse positi 
vas, habemus 
A = cp—cp', J5 = <[», C = tz — cp', u = q — q, b = r, c = r, a = 8—8' 
Ante omnia aream a per seriem exprimemus. Mutando in [7] singulas 
quantitates ad B relatas in eas, quae ad C referuntur, prodit formula pro 8', 
unde, usque ad quantitates sexti ordinis obtinemus 
a = ip{q—i)\i—if°{pp-\-qqA-qi-\rii) 
—kV/> {Gpp + 7 n + 7 qq'+ 7 qq) 
— + + 4^^4-4^Y)! 
Haec formula, adiumento seriei [2] puta 
csinJ5 =p[\-~\fqq — ifpqq— i/i 3 *— etc.) 
transit in sequentem 
a = 4-ucsinH 11 — t/°{pp — qq~\~qi~V ii) 
— ihfp (6pp— Sqq-\-7 qiAr 7 H) 
—4w9*$ppq-\-*ppi—* q 3j r 4 q q i A- 4 i 2 V+ 4 i ;i )! 
Mensura curvaturae pro quovis superficiei puncto fit (per art. 1 9, ubi m,p, q 
erant quae hic sunt n, q, p) 
i ddw 
n dç 2 
2f-\- C gq -f-12 hqq + etc. 
i+fqq+ etc. 
— 2f-§gq — [\2h—2ff)qq — etc. 
Hinc fit, quatenus p, q ad punctum B referuntur, 
15 = — 2/°— 2fp — Qc/°q— 2f"pp — 6g’pq — (l 2 A°— %f°f°)qq— etc. 
nec non 
y — —%f°—ïfp — Qg (i i—2f"pp—Qipq--{\2h 0 --2f 0 f 0 )ii— etc. 
a = — 2f°