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Acquisitions (Narrative) (Details) - USD ($)
$ in Millions
12 Months Ended
Sep. 03, 2019
Apr. 01, 2019
Feb. 14, 2017
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Feb. 28, 2017
Business Acquisition [Line Items]              
Business Acquisition, Pro Forma Net Income (Loss)       $ 161.6 $ 208.6    
Proceeds from Sales of Business, Affiliate and Productive Assets       166.6 1.0 $ 5.8  
Gain (Loss) on Disposition of Other Assets       (15.9) (23.0) 1.0  
Cash payment, net of cash acquired       303.4 0.0 311.4  
Goodwill       1,800.9 $ 1,738.3 1,759.6  
Royalty Guarantees, Commitments, Amount       22.0      
Senior unsecured 5.00% Notes due on February 14, 2025 [Member]              
Business Acquisition [Line Items]              
Senior unsecured notes             $ 300.0
Breathe [Member]              
Business Acquisition [Line Items]              
Cash payment, net of cash acquired $ 127.6            
Goodwill 60.2            
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net $ 127.6            
Voalte [Member]              
Business Acquisition [Line Items]              
Professional Fees       12.1      
Business Combination, Contingent Consideration Arrangements, Change in Amount of Contingent Consideration, Liability       3.2      
Cash consideration   $ 175.8          
Goodwill   98.4          
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net   181.0          
Business Combination, Contingent Consideration, Liability   5.2          
Business Combination, Contingent Consideration Arrangements, Range of Outcomes, Value, High   $ 15.0          
Mortara [Member]              
Business Acquisition [Line Items]              
Cash consideration     $ 330.0        
Cash payment, net of cash acquired     311.2        
Goodwill     165.5        
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net     $ 311.2        
Architectural Products Business [Member]              
Business Acquisition [Line Items]              
Proceeds from Sales of Business, Affiliate and Productive Assets           4.5  
Volker [Member]              
Business Acquisition [Line Items]              
Gain (Loss) on Disposition of Business       1.0      
Impairment charges relating to non-cash write-downs of long-lived assets and working capital           25.4  
Transaction related costs for businesses to be disposed of           $ 3.0  
Selling, General and Administrative Expenses [Member] | Breathe [Member]              
Business Acquisition [Line Items]              
Professional Fees       6.4      
Restructuring Charges [Member] | Breathe [Member]              
Business Acquisition [Line Items]              
Professional Fees       $ 1.7