266 L. EULEUI OPERA POSTHUMA. Arithmeiica. 



90. 



Theorema. Si proposita fueril haec formula zz = aa-+-'2.abx-t-max'^-+-'idex'^~^eea'^, in qua sit 



m = bb-i-dd — //, 

 tnm eadem forma sequentibus modis repraesentari potest: 



1) zz=:{a-i-bx)'^-i-xx{ex-i-d~t-f}{ex-+-d — f) 



2) zz == XX {ex -4- d)'^ ■+- (a -t- {b -t- f) x) (a -+■ {b — f) x), 



unde sequitur z = a-t-bx si fuerit vel x = -, vel x = ^ . Ex altera 



^ e e 



zz=x{ex~h-d) si fuerit vel x = r — j., vel x- 



Praeter hos quatuor valores operationes vulgares praebent adhuc sequenles sex valores 



. 2ae-¥-ff—dd ., 2a (& — d) ... 1ae-*-ff—dd ,^ _ 2a (6 -*- d) 



*• ^— 2e{a-b) ♦ "• ^ — 2ae-t-ff-by "*' ^— 2e{d^b] ' *^' ^ — _ 2ae -H/y- 66» 



y 3aadeH-4a6(/ y— dd) „ [ff—bbf—^aaee^ 



' ^ {ff—dd)^—^aaee ' ^ Safccen- 4de (/jr— 66)' 



A. m. T. III. p. 163. 



