Goodwill and Other Intangible Assets (Purchased Intangible Assets) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2020	Aug. 31, 2019
Acquired Intangible Assets by Major Class [Line Items]
Weighted Average Amortization Period (in years)	12 years
Gross Carrying Amount	$ 604,944	$ 594,694
Accumulated Amortization	(395,074)	(337,841)
Net Carrying Amount	209,870	256,853
Trade names
Acquired Intangible Assets by Major Class [Line Items]
Gross Carrying Amount	50,590	50,590
Net Carrying Amount	$ 50,590	50,590
Contractual agreements and customer relationships
Acquired Intangible Assets by Major Class [Line Items]
Weighted Average Amortization Period (in years)	12 years
Gross Carrying Amount	$ 302,314	292,797
Accumulated Amortization	(199,861)	(175,199)
Net Carrying Amount	$ 102,453	117,598
Intellectual property
Acquired Intangible Assets by Major Class [Line Items]
Weighted Average Amortization Period (in years)	8 years
Gross Carrying Amount	$ 174,373	173,771
Accumulated Amortization	(164,671)	(157,606)
Net Carrying Amount	9,702	16,165
Trade names
Acquired Intangible Assets by Major Class [Line Items]
Gross Carrying Amount	77,667	77,536
Accumulated Amortization	(30,542)	(5,036)
Net Carrying Amount	$ 47,125	$ 72,500