Shareholders' Equity (Narrative) (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Equity [Abstract]
Common shares, authorized (in shares)	300,000,000.0	300,000,000.0	300,000,000
Shares available for future awards (in shares)	3,400,000	3,400,000
Preferred shares, par value (in usd per share)	$ 0.01	$ 0.01	$ 0.01
Preferred shares, outstanding (in shares)			0
Treasury Stock, Shares, Acquired		1,600,000
Treasury Stock, Value, Acquired, Cost Method		$ 58.5	$ 75.2	$ 125.3
Shares available for repurchase under authorization		3.0
Common Stock, Dividends, Per Share, Declared	$ 0.15
Preferred shares, authorized (in shares)	10,000,000	10,000,000	10,000,000.0
Dividends declared to common shareholders		$ 30.6	$ 31.7	32.6
Dividends paid to common shareholders		$ 30.7	$ 31.5	$ 32.6
Shares purchased to satisfy tax withholding		200,000