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Common Stock (Narrative) (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended 73 Months Ended
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Sep. 30, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Share Price $ 105.23     $ 105.23
Stock Repurchase Program, Number of Shares Authorized to be Repurchased   $ 340.0    
Stock Repurchase Program, Number of Shares Authorized to be Repurchased $ 170.0      
Share-based Payment Arrangement, Noncash Expense 34.4 28.1 $ 23.0  
Effective Income Tax Rate Reconciliation, Tax Expense (Benefit), Share-based Payment Arrangement, Amount 5.2 16.1 8.9  
Remaining availability 217.5     $ 217.5
Payments for Repurchase of Common Stock 117.2 0.0 50.0  
Payment, Tax Withholding, Share-based Payment Arrangement $ 4.7 $ 14.1 10.6  
Treasury stock (in shares) 21,832,623 21,201,522   21,832,623
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Authorized 15,300,000     15,300,000
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Available for Grant 1,800,000     1,800,000
Employee Tax Withholding For Restricted and Deferred Stock Distributions [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Payments for Repurchase of Common Stock     $ 10.6  
Treasury Stock, Shares, Acquired (48,908) 158,182 158,668  
Share-based Payment Arrangement, Option [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Maximum contractual term 10 years      
Total intrinsic value of options exercised $ 17.7 $ 54.7 $ 19.4  
Share-based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount $ 6.3     $ 6.3
Share-based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition 2 years 2 months 12 days      
Share-based Payment Arrangement, Option [Member] | Minimum [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting period 3 years      
Share-based Payment Arrangement, Option [Member] | Maximum [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting period 4 years      
Restricted Stock Units (RSUs) [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Total vest date fair value of shares that vested $ 16.6 21.9 14.5  
Share-based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount $ 19.5     19.5
Share-based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition 1 year 9 months 18 days      
Restricted Stock Units (RSUs) [Member] | Minimum [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting period 1 year      
Restricted Stock Units (RSUs) [Member] | Maximum [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting period 4 years      
Performance Shares [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Total vest date fair value of shares that vested $ 8.0 16.4 $ 14.2  
Share-based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount $ 10.8     10.8
Common Stock [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Shares repurchased (in shares) 1,200,000   800,000  
Value of shares repurchased $ (117.2)   $ 50.0 292.5
Pension Plan [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Defined Benefit Plan, Plan Assets, Contributions by Employer 9.0 1.1    
Pension Plan [Member] | Cash [Member]        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Assets for Plan Benefits, Defined Benefit Plan $ 4.2 $ 4.0   $ 4.2