Goodwill and Other Intangible Assets (Purchased Intangible Assets) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2018	Aug. 31, 2017
Acquired Intangible Assets by Major Class [Line Items]
Weighted Average Amortization Period (in years)	9 years
Gross Carrying Amount	$ 586,309	$ 553,808
Accumulated Amortization	(307,178)	(269,212)
Net Carrying Amount	279,131	284,596
Trade names
Acquired Intangible Assets by Major Class [Line Items]
Gross Carrying Amount	123,090	123,090
Net Carrying Amount	$ 123,090	123,090
Contractual agreements and customer relationships
Acquired Intangible Assets by Major Class [Line Items]
Weighted Average Amortization Period (in years)	11 years
Gross Carrying Amount	$ 289,947	265,148
Accumulated Amortization	(153,415)	(132,691)
Net Carrying Amount	$ 136,532	132,457
Intellectual property
Acquired Intangible Assets by Major Class [Line Items]
Weighted Average Amortization Period (in years)	5 years
Gross Carrying Amount	$ 168,181	160,456
Accumulated Amortization	(148,672)	(131,407)
Net Carrying Amount	19,509	29,049
Trade names
Acquired Intangible Assets by Major Class [Line Items]
Gross Carrying Amount	5,091	5,114
Accumulated Amortization	(5,091)	(5,114)
Net Carrying Amount	$ 0	$ 0