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Shareholders' Equity (Narrative) (Details) - USD ($)
$ in Millions
 12 Months Ended
Feb. 14, 2023
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Class of Stock [Line Items]        
Shares of preferred stock authorized for issuance   14,000,000.0    
Preferred stock issued   0 0  
Preferred stock outstanding   0 0  
Shares withheld for tax   17,639    
Shares withheld for tax, fair value   $ 0.8    
Stock repurchased during period, shares 50,000,000.0   499,411  
Common Stock [Member]        
Class of Stock [Line Items]        
Shares withheld for tax       147,092
Shares withheld for tax, fair value       $ 3.0
Open Market Purchases [Member]        
Class of Stock [Line Items]        
Shares withheld for tax     86,125  
Shares withheld for tax, fair value     $ 3.5  
Purchase of treasury shares   $ 34.7 $ 20.3  
Stock repurchased during period, shares   867,873    
Upon Approval of Purchase Plan [Member]        
Class of Stock [Line Items]        
Purchase of treasury shares   $ 34.3    
Stock repurchased during period, shares   857,608