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Comprehensive Income (Changes in Components of Accumulated Other Comprehensive Income (Loss) Items) (Details) - USD ($) $ in Millions	3 Months Ended						9 Months Ended
	May 31, 2019	Feb. 28, 2019	Nov. 30, 2018	May 31, 2018	Feb. 28, 2018	Nov. 30, 2017	May 31, 2019	May 31, 2018
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance	$ 1,801.8	$ 1,750.9	$ 1,716.8	$ 1,635.8	$ 1,726.1	$ 1,665.6	$ 1,716.8	$ 1,665.6
Net current period other comprehensive (loss) income	(7.4)	6.3	(6.2)	(5.7)	4.3	(8.9)
Reclassification of stranded tax effects of TCJA					0.0
Ending balance	1,884.9	1,801.8	1,750.9	1,600.4	1,635.8	1,726.1	1,884.9	1,600.4
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance	(114.7)	(121.0)	(114.8)	(115.4)	(108.6)	(99.7)	(114.8)	(99.7)
Other comprehensive (loss) income before reclassifications							(11.7)	(15.6)
Amounts reclassified from accumulated other comprehensive loss							4.4	5.3
Net current period other comprehensive (loss) income	(7.4)	6.3	(6.2)	(5.7)	4.3	(8.9)	(7.3)	(10.3)
Reclassification of stranded tax effects of TCJA					(11.1)			(11.1)
Ending balance	(122.1)	$ (114.7)	(121.0)	(121.1)	$ (115.4)	(108.6)	(122.1)	(121.1)
Foreign Currency Items
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance			(53.9)			(28.7)	(53.9)	(28.7)
Other comprehensive (loss) income before reclassifications							(12.6)	(15.6)
Amounts reclassified from accumulated other comprehensive loss							0.0	0.0
Net current period other comprehensive (loss) income	(8.7)			(7.6)			(12.6)	(15.6)
Reclassification of stranded tax effects of TCJA								0.0
Ending balance	(66.5)			(44.3)			(66.5)	(44.3)
Defined Benefit Pension Plans
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance			$ (60.9)			$ (71.0)	(60.9)	(71.0)
Other comprehensive (loss) income before reclassifications							0.9	0.0
Amounts reclassified from accumulated other comprehensive loss							4.4	5.3
Net current period other comprehensive (loss) income	1.3			1.9			5.3	5.3
Reclassification of stranded tax effects of TCJA								(11.1)
Ending balance	$ (55.6)			$ (76.8)			$ (55.6)	$ (76.8)

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Amount of increase (decrease) in accumulated other comprehensive income (AOCI) for reclassification to retained earnings of tax effect from remeasurement of deferred tax pursuant to Tax Cuts and Jobs Act.

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Amount after tax, before reclassification adjustments of other comprehensive income (loss).

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Amount after tax and reclassification adjustments of other comprehensive income (loss).

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