Share-Based Compensation (Narrative) (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares available for future grant (in shares)	900,000
Closing stock price (in dollars per share)	$ 297.74
Cash received from option exercises	$ 7.9	$ 24.0	$ 19.3
Total tax benefit realized from stock option exercises	8.3
Excess tax benefit from stock option exercises	$ 6.9
Deferred Stock Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of units/shares granted	249,000
Weighted-average grant date fair value (in dollars per share)	$ 283.67
Cash payments made for deferred stock units	$ 2.7	3.6	5.5
Unrecognized compensation costs	$ 71.4
Unrecognized compensation costs, period for recognition, years	1 year 7 months 6 days
Fair value of deferred stock units paid	$ 24.1	$ 45.3	$ 92.9
Deferred Stock Units | Minimum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting or deferral period	2 years
Deferred Stock Units | Maximum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting or deferral period	5 years
Director Deferred Stock Units | Maximum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Period after service in which to elect payment	10 years
Market-Based Deferred Stock Unit
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting or deferral period	3 years
Number of units/shares granted	102,120	85,612	74,364
Weighted-average grant date fair value (in dollars per share)	$ 302.10	$ 502.03	$ 427.23
Time-Based Deferred Stock Unit
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of units/shares granted	146,947	119,954	120,996
Weighted-average grant date fair value (in dollars per share)	$ 270.86	$ 308.91	$ 278.67
Stock Options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Weighted average remaining contractual terms, outstanding	2 months 12 days
Weighted average remaining contractual terms, exercisable	2 months 12 days
Aggregated intrinsic value, outstanding	$ 8.7
Aggregated intrinsic value, exercisable	8.7
Intrinsic value of stock options exercised	35.1	$ 53.5	$ 20.2
Cash received from option exercises	$ 7.9