Earnings per Share and Shareholders' Equity Share Repurchase (Details) - USD ($)	3 Months Ended		6 Months Ended		174 Months Ended
	Feb. 28, 2026	Feb. 28, 2025	Feb. 28, 2026	Feb. 28, 2025	Feb. 28, 2026	Oct. 10, 2025
Equity [Abstract]
Stock Repurchased During Period, Value	$ 65,900,000			$ 14,600,000
Share Repurchase Program, Authorized, Amount						$ 200,000,000
Share Repurchase Program, Remaining Authorized, Amount	$ 134,800,000		$ 134,800,000		$ 134,800,000
Incremental Common Shares Attributable to Dilutive Effect of Share-based Payment Arrangements	420,000	411,000	394,000	491,000
Anti-dilutive securities from stock based compensation plans (excluded from earnings per share calculation)	56,000	192,000	107,000	121,000
Treasury Stock, Value, Acquired, Cost Method	$ 51,025,000				$ 973,500,000
Stock Repurchased During Period, Shares			1,655,307	329,527