Segment Information - Results of Operations and Assets (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Feb. 29, 2024	Feb. 28, 2023	Feb. 29, 2024	Feb. 28, 2023	Aug. 31, 2023
Revenues	$ 545,945	$ 515,085	$ 1,088,161	$ 1,019,900
Operating income	181,942	169,250	370,982	341,145
Capital expenditures	21,917	17,456	38,383	35,416
Assets	3,990,866		3,990,866		$ 3,962,922
Americas
Revenues	352,618	331,121	700,985	654,488
Operating income	81,711	61,181	162,559	128,712
Capital expenditures	20,015	15,589	34,793	31,343
Assets	3,121,172		3,121,172		3,148,192
EMEA
Revenues	139,176	132,508	278,737	263,246
Operating income	62,839	68,941	131,704	136,263
Capital expenditures	295	739	1,256	1,312
Assets	605,954		605,954		558,393
Asia Pacific
Revenues	54,151	51,456	108,439	102,166
Operating income	37,392	39,128	76,719	76,170
Capital expenditures	1,607	$ 1,128	2,334	$ 2,761
Assets	$ 263,740		$ 263,740		$ 256,337