Acquisitions (Schedule of Fair Value of Assets Acquired and Liabilities Assumed) (Details) - USD ($) $ in Millions		12 Months Ended
	Feb. 14, 2017	Sep. 30, 2018	Sep. 30, 2017	Sep. 30, 2016
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Net [Abstract]
Goodwill		$ 1,738.3	$ 1,759.6	$ 1,584.4
Business Combination, Consideration Transferred, Including Equity Interest in Acquiree Held Prior to Combination [Abstract]
Cash payment, net of cash acquired		$ 0.0	$ 311.4	$ 25.3
Mortara [Member]
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Net [Abstract]
Trade receivables	$ 16.4
Inventory	21.5
Other current assets	2.8
Property, plant and equipment	18.2
Goodwill	165.5
Other noncurrent assets	4.8
Current liabilities	(22.8)
Noncurrent liabilities	(1.2)
Total purchase price, net of cash acquired	311.2
Business Combination, Consideration Transferred, Including Equity Interest in Acquiree Held Prior to Combination [Abstract]
Cash payment, net of cash acquired	311.2
Mortara [Member] | Trade names [Member]
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Net [Abstract]
Intangibles (finite-lived)	$ 15.8
Finite-Lived Intangible Assets, Net [Abstract]
Weighted-average useful life	7 years
Mortara [Member] | Customer relationships [Member]
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Net [Abstract]
Intangibles (finite-lived)	$ 37.9
Finite-Lived Intangible Assets, Net [Abstract]
Weighted-average useful life	8 years
Mortara [Member] | Developed technology [Member]
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Net [Abstract]
Intangibles (finite-lived)	$ 52.3
Finite-Lived Intangible Assets, Net [Abstract]
Weighted-average useful life	7 years