Goodwill and Other Intangible Assets (Purchased Intangible Assets) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2019	Aug. 31, 2018
Acquired Intangible Assets by Major Class [Line Items]
Weighted Average Amortization Period (in years)	11 years
Gross Carrying Amount	$ 594,694	$ 586,309
Accumulated Amortization	(337,841)	(307,178)
Net Carrying Amount	256,853	279,131
Trade names
Acquired Intangible Assets by Major Class [Line Items]
Gross Carrying Amount	50,590	123,090
Net Carrying Amount	$ 50,590	123,090
Contractual agreements and customer relationships
Acquired Intangible Assets by Major Class [Line Items]
Weighted Average Amortization Period (in years)	12 years
Gross Carrying Amount	$ 292,797	289,947
Accumulated Amortization	(175,199)	(153,415)
Net Carrying Amount	$ 117,598	136,532
Intellectual property
Acquired Intangible Assets by Major Class [Line Items]
Weighted Average Amortization Period (in years)	6 years
Gross Carrying Amount	$ 173,771	168,181
Accumulated Amortization	(157,606)	(148,672)
Net Carrying Amount	16,165	19,509
Trade names
Acquired Intangible Assets by Major Class [Line Items]
Gross Carrying Amount	77,536	5,091
Accumulated Amortization	(5,036)	(5,091)
Net Carrying Amount	$ 72,500	$ 0