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Stock-based Compensation (Narrative) (Details) - USD ($)		12 Months Ended
		Aug. 31, 2021	Aug. 31, 2020	Aug. 31, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares authorized under stock plan		1,000,000
Number of shares available for grant		543,700
Allocated share-based compensation expense		$ 9,555,000	$ 5,358,000	$ 4,446,000
Employee service share-based, Tax benefit from compensation expense		$ 2,000,000.0	1,200,000	1,000,000.0
Restricted Stock Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Granted, Number of Shares		17,244
Allocated share-based compensation expense		$ 3,656,000	3,325,000	2,876,000
Employee service share-based, Tax benefit from compensation expense		1,900,000	$ 1,200,000	$ 1,400,000
Compensation cost not yet recognized		$ 500,000
Remaining weighted-average vesting periods		1 year 7 months 6 days
Weighted-average grant date fair value		$ 208.29	$ 184.43	$ 163.93
Total intrinsic value of stock-based awards converted into common shares		$ 8,500,000	$ 5,400,000	$ 6,000,000.0
Market Share Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Granted, Number of Shares		13,701
Allocated share-based compensation expense		$ 2,294,000	2,033,000	1,570,000
Employee service share-based, Tax benefit from compensation expense		1,300,000	$ 900,000	$ 900,000
Compensation cost not yet recognized		$ 2,800,000
Remaining weighted-average vesting periods		1 year 9 months
Weighted-average grant date fair value		$ 184.96	$ 216.77	$ 177.82
Total intrinsic value of stock-based awards converted into common shares		$ 5,900,000	$ 4,400,000	$ 4,000,000.0
Expected volatility period		2 years 10 months 17 days	2 years 10 months 24 days	2 years 10 months 24 days
Percent of original target number of vested shares		100.00%
Expected dividend yield		0.00%	0.00%	0.00%
Deferred Performance Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Granted, Number of Shares		0
Compensation cost not yet recognized		$ 0
Performance Share Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Granted, Number of Shares		19,468
Allocated share-based compensation expense	[1]	$ 3,605,000
Compensation cost not yet recognized		$ 0
Weighted-average grant date fair value		$ 197.51
Vesting percentage		100.00%
Converted units to common shares		0
Key Executives [Member] | Restricted Stock Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period		3 years
High Level Employees [Member] | Restricted Stock Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period		3 years
High Level Employees [Member] | Market Share Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period		3 years
Minimum [Member] | Performance Share Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting percentage		0.00%
Maximum [Member] | Market Share Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of original target number of vested shares		200.00%
Maximum [Member] | Performance Share Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting percentage		100.00%
[1] PSU awards, similar to DPU awards that were replaced by PSUs in fiscal year 2021, contain performance conditions for which accrual of expense is based on the probable outcome of the performance conditions. Vesting of DPUs related to the measurement years of both fiscal year 2020 and 2019 was deemed not probable at the end of each fiscal year. DPUs were then discontinued by the Company prior fiscal year 2021. PSUs pertaining to the measurement year of fiscal year 2021 vested at 100% since the performance conditions were fully achieved.

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