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Stock-based Compensation (Narrative) (Details) - USD ($)		12 Months Ended
		Aug. 31, 2022	Aug. 31, 2021	Aug. 31, 2020
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		384,859
Allocated share-based compensation expense		$ 6,697,000	$ 9,555,000	$ 5,358,000
Employee service share-based, Tax benefit from compensation expense		$ 1,500,000	2,000,000.0	1,200,000
Restricted Stock Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Granted, Number of Shares		23,461
Allocated share-based compensation expense		$ 4,153,000	3,656,000	3,325,000
Employee service share-based, Tax benefit from compensation expense		600,000	$ 1,900,000	$ 1,200,000
Compensation cost not yet recognized		$ 1,400,000
Remaining weighted-average vesting periods		1 year 5 months 12 days
Weighted-average grant date fair value		$ 217.03	$ 208.29	$ 184.43
Total intrinsic value of stock-based awards converted into common shares		$ 3,000,000.0	$ 8,500,000	$ 5,400,000
Market Share Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Granted, Number of Shares		13,195
Allocated share-based compensation expense		$ 2,544,000	2,294,000	2,033,000
Employee service share-based, Tax benefit from compensation expense		900,000	$ 1,300,000	$ 900,000
Compensation cost not yet recognized		$ 3,100,000
Remaining weighted-average vesting periods		1 year 9 months 25 days
Weighted-average grant date fair value		$ 232.99	$ 184.96	$ 216.77
Total intrinsic value of stock-based awards converted into common shares		$ 4,400,000	$ 5,900,000	$ 4,400,000
Expected volatility period		2 years 10 months 20 days	2 years 10 months 17 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		18,684
Allocated share-based compensation expense	[1]		$ 3,605,000
Employee service share-based, Tax benefit from compensation expense		$ 800,000	$ 0	$ 0
Compensation cost not yet recognized		$ 0
Weighted-average grant date fair value		$ 227.24	$ 197.51
Total intrinsic value of stock-based awards converted into common shares		$ 4,000,000.0
Vesting percentage			100.00%
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 year of 2020 was deemed not probable at the end of the fiscal year. DPUs were then discontinued by the Company beginning in fiscal year 2021. PSUs pertaining to the measurement year of fiscal year 2021 vested at 100% since the performance conditions were fully achieved. PSUs pertaining to the measurement year of fiscal year 2022 was deemed not probable at the end of the fiscal year.

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