132 
DE FORMIS SECUNDI GRADUS. 
(a^-f-^y'— yfi'— 8d) l mm = AbbUU 
(a y' — y d) (fi 8' — 8fi')mm = acUU 
(a8'-J-fi y' — yfi' — 8d) (fi8' — 8fi')mm =■ 2bcUU 
(fi8' — 8fi'fmm = ccZTZJ 
Hinc adiumento aequationis [14] et huius 5i«-|-2596-(-(£c — m, facile 
deducitur (multiplicando primam, secundam, quartam; secundam, tertiam, quin 
tam; quartam, quintam, sextam, resp. per 51,53, (£ addendoque producta): 
(ay'— yd)TJmm = maUU 
(a 8' -f- fi y' — yfi' — 8 a) Umm — 2mbUU 
(fi8' — 8fi')Umm = mcUU 
atque hinc, dividendo per mU # ) 
ali — (ay’ — y a ')m [19] 
2bU = (a8'-\-fiy'—yfi'—8d)m [20] 
cU = (fi8' — 8fi')m [21] 
ex quarum aequationum aliqua U multo facilius quam ex [14] deduci potest. — 
Simul hinc colligitur, quomodocunque 5i, 59, (£ determinentur (quod infinitis mo 
dis diversis fieri potest), tum T tum U eundem valorem adipisci. 
lam si aequatio 18 multiplicatur per a, 19 per 2 fi, 20 per —a, fit per 
additionem 
2aeT 2 (fi a — a b)U= 2 (a 8 — fiy) dm = 2 eam 
Simili modo fit ex fi [18] -j- fi [20] — 2 a [21] 
2fieT-\- 2 (fib — ac) U — 2 (a 8 — fiy) fi'm — 2 efi'm 
Porro ex y | 1 81 -f- 2 8 [19] — y [20l fit 
2 ye T-\- 2 (3« — y b) U = 2 (a 8 — fi y) y 'm — 2eym 
Tandem ex 8 [18] -(-£[20] — 2 y [21 i prodit 
2 8 e T -(- 2 (8 b — y c) U — 2 (a 8 — fi y) 8'm = 2 e 8'm 
*) Hoc non liceret, si esset U = o : tunc vero aequationum 19, 20, 21 veritas statim ex prima, tertia 
et sexta praecedentium sequeretur.