Segment Information - Results of Operations (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Feb. 28, 2021	Feb. 29, 2020	Feb. 28, 2021	Feb. 29, 2020	Aug. 31, 2020
Revenue	$ 391,788	$ 369,780	$ 779,993	$ 736,438
Operating income	116,133	106,257	237,163	219,443
Capital expenditures	10,425	25,119	28,758	51,899
Assets	2,163,507		2,163,507		$ 2,083,388
Americas
Revenue	247,991	232,731	492,327	464,061
Operating income	53,614	41,310	109,989	90,933
Capital expenditures	8,219	15,050	17,779	39,074
Assets	1,094,064		1,094,064		1,111,600
EMEA
Revenue	105,493	102,105	211,270	202,935
Operating income	40,290	42,664	80,924	83,882
Capital expenditures	314	349	633	1,517
Assets	840,679		840,679		757,524
Asia Pacific
Revenue	38,304	34,944	76,396	69,442
Operating income	22,229	22,283	46,250	44,628
Capital expenditures	1,892	$ 9,720	10,346	$ 11,308
Assets	$ 228,764		$ 228,764		$ 214,264