234 
DISQUISITIONES GENERALES 
atque perpendimus, valores differentialium di, du sic prodeuntium, aequales 
esse debere, independenter a differentialibus doo, dy, quantitatibus Tdx-\~ Udy, 
Udx-\- Vdy resp, inveniemus, post quasdam transformationes satis obvias; 
C 3 T = a A d B b'b'+ y Cb'b' 
— 2a , Abb , — 2d , Bbb , — 2-f , Cbb' 
+ a"A b b + d”B b b + y" C b b 
C 3 U — —aAab'—dB ah'—y Cdb' 
-f- a!A ((a b'-\~b d) -{- d 'B [a b'-j- bd)-\-y'C (a b'-j- 6 d) 
— aAab — d"Bab — y "Cab 
C 3 V — a-¿4 5 aV+y CaV • 
— 2 a'y4a d— 2 d'Bad— 2y'Cad 
-\-a Aaa-\-d"Baa-\~YC aa 
Si itaque brevitatis caussa statuimus 
Aa -\~Bd A~Cy — B (1) 
Aa’+Bd'+Cj = D' (2) 
A a"-f- B d "+ Cy" = B” (3) 
fit 
C 3 T — Db'b'~ 2 l)'bb'A- B"bb 
C S U = -Ddb'A- B\ab'A-bd) — D"ab 
C 3 V — Ddd—2 B'ad-\~B"aa 
Hinc invenimus, evolutione facta, 
C\TV- UU) = (BB"—B'B')[ab'— bd)~ = [BB"-B'B')CC 
et proin formulam pro mensura curvaturae 
j DD"—D'D' 
c (AA+BB + CC)* 
It. 
Formulae modo inventae iam aliam superstruemus, quae inter fertilissima 
theoremata in doctrina de superficiebus curvis referenda est. Introducamus se 
quentes notationes :