Share-Based Compensation (Narrative) (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares available for future grant	1,300,000
Closing stock price (in dollars per share)	$ 283.40
Cash received from option exercises	$ 24.0	$ 19.3	$ 10.6
Total tax benefit realized from stock option exercises	12.5
Excess tax benefit from stock option exercises	$ 11.7
Deferred Stock Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of units/shares granted	206,000
Weighted-average grant date fair value (in dollars per share)	$ 389.34
Cash payments made for deferred stock units	$ 3.6	5.5	5.2
Unrecognized compensation costs	$ 75.3
Unrecognized compensation costs, period for recognition, years	1 year 7 months 6 days
Fair value of deferred stock units paid	$ 45.3	$ 92.9	$ 88.0
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	85,612	74,364	77,251
Weighted-average grant date fair value (in dollars per share)	$ 502.03	$ 427.23	$ 235.48
Time-Based Deferred Stock Unit
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of units/shares granted	119,954	120,996	110,555
Weighted-average grant date fair value (in dollars per share)	$ 308.91	$ 278.67	$ 282.48
Stock Options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Weighted average remaining contractual terms, outstanding	8 months 12 days
Weighted average remaining contractual terms, exercisable	8 months 12 days
Aggregated intrinsic value, outstanding	$ 47.9
Aggregated intrinsic value, exercisable	47.9
Intrinsic value of stock options exercised	53.5	$ 20.2	$ 29.0
Cash received from option exercises	$ 24.0