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Stock-based Compensation - Narrative (Details) - USD ($)			12 Months Ended
	Jan. 15, 2020	Jan. 15, 2019	Aug. 31, 2020	Aug. 31, 2019	Aug. 31, 2018	Aug. 31, 2017
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation expense			$ 36,579,000	$ 32,400,000	$ 31,516,000
Unrecognized compensation expense			$ 81,900,000
Weighted average period for recognition			2 years 10 months 24 days
Stock-based compensation capitalized			$ 0	$ 0
Exercise price (in dollars per share)			$ 350.40
Employee
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares available for future grant			5,626,000	6,067,000	6,298,000	897,000
Non-employee directors
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares available for future grant			250,000	264,000	282,000	42,000
Director Plan \| Non-employee directors
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock options granted (in shares)	16,080	20,576			18,963
Stock options \| Employee
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock options granted, weighted average exercise price (in dollars per share)			$ 256.43	$ 224.35	$ 190.42
Weighted average estimated fair value (in dollars per share)			$ 60.33	$ 57.12	$ 48.39
Stock options \| LTIP
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Pre-tax intrinsic value of stock options exercised			$ 85,000,000.0	$ 73,000,000.0	$ 50,100,000
Stock options \| LTIP \| Employee
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Expiration period			10 years
Award vesting period			5 years
Stock options \| Director Plan \| Non-employee directors
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Expiration period			7 years
Award vesting period			3 years
Number of shares available for future grant			249,886
Weighted average estimated fair value (in dollars per share)			$ 54.74	$ 42.77	$ 38.76
Restricted stock and PSUs
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unvested and outstanding (in shares)			146,000	124,000	143,000	182,000
Restricted stock and PSUs \| LTIP
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation expense			$ 28,200,000
Weighted average period for recognition			2 years 8 months 12 days
Unvested and outstanding (in shares)			145,897
ESPP
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation expense			$ 2,100,000	$ 2,000,000.0	$ 1,600,000
Purchase period			3 months
Purchase price (as a percent)			85.00%
Percentage of purchases which may not exceed gross compensation			10.00%
Contribution limit			$ 25,000
Number of shares purchased by employees			42,606	48,532	64,230
Stock options granted, weighted average exercise price (in dollars per share)			$ 234.41	$ 205.64	$ 160.34
Number of shares reserved for future issuance			177,804
Weighted average estimated fair value (in dollars per share)			$ 50.69	$ 41.06	$ 31.83