Stock-based Compensation (Narrative) (Details)	12 Months Ended
Aug. 31, 2020 USD ($) item $ / shares shares	Aug. 31, 2019 USD ($) $ / shares	Aug. 31, 2018 USD ($) $ / shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of plans \| item	1
Number of shares authorized under stock plan \| shares	1,000,000
Number of shares available for grant \| shares	627,742
Allocated share-based compensation expense	$ 5,400,000	$ 4,400,000	$ 4,200,000
Employee service share-based, Tax benefit from compensation expense	1,200,000	1,000,000.0	1,100,000
Restricted Stock Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Employee service share-based, Tax benefit from compensation expense	1,200,000	$ 1,400,000	$ 700,000
Compensation cost not yet recognized	$ 600,000
Remaining weighted-average vesting periods	1 year 4 months 24 days
Weighted-average grant date fair value \| $ / shares	$ 184.43	$ 163.93	$ 111.71
Total intrinsic value of stock-based awards converted into common shares	$ 5,400,000	$ 6,000,000.0	$ 2,800,000
Market Share Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Employee service share-based, Tax benefit from compensation expense	900,000	$ 900,000	$ 800,000
Compensation cost not yet recognized	$ 3,000,000.0
Remaining weighted-average vesting periods	1 year 10 months 24 days
Weighted-average grant date fair value \| $ / shares	$ 216.77	$ 177.82	$ 101.93
Total intrinsic value of stock-based awards converted into common shares	$ 4,400,000	$ 4,000,000.0	$ 3,000,000.0
Expected volatility period	2 years 10 months 24 days	2 years 10 months 24 days	2 years 10 months 20 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]
Compensation cost not yet recognized	$ 0
Weighted-average grant date fair value \| $ / shares	$ 183.62	$ 160.37	$ 110.65
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
High Level Employees [Member] \| Deferred Performance Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	1 year
Minimum [Member] \| Market Share Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of original target number of vested shares	0.00%
Minimum [Member] \| Deferred Performance Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of original target number of vested shares	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] \| Deferred Performance Units [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percent of original target number of vested shares	100.00%

Amount of expense for award under share-based payment arrangement. Excludes amount capitalized.

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The weighted average fair value at grant date for nonvested equity-based awards issued during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

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The estimated dividend rate (a percentage of the share price) to be paid (expected dividends) to holders of the underlying shares over the option's term.

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