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Significant Accounting Policies - Changes of Accumulated Other Comprehensive Loss, Net of Tax (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 31, 2022	Aug. 31, 2021	Aug. 31, 2020
Accumulated Other Comprehensive Loss, Net of Tax [Roll Forward]
Beginning balance	$ 2,044.5	$ 2,127.5	$ 1,918.9
Other comprehensive income (loss) before reclassifications	(32.6)	27.2
Amounts reclassified from accumulated other comprehensive loss	5.0	7.3
Other comprehensive (loss) income items, net of tax	(27.6)	34.5	18.7
Ending balance	1,911.8	2,044.5	2,127.5
Foreign Currency Items
Accumulated Other Comprehensive Loss, Net of Tax [Roll Forward]
Beginning balance	(40.2)	(53.5)
Other comprehensive income (loss) before reclassifications	(33.3)	13.3
Amounts reclassified from accumulated other comprehensive loss	0.0	0.0
Other comprehensive (loss) income items, net of tax	(33.3)	13.3
Ending balance	(73.5)	(40.2)	(53.5)
Defined Benefit Pension Plans
Accumulated Other Comprehensive Loss, Net of Tax [Roll Forward]
Beginning balance	(58.0)	(79.2)
Other comprehensive income (loss) before reclassifications	0.7	13.9
Amounts reclassified from accumulated other comprehensive loss	5.0	7.3
Other comprehensive (loss) income items, net of tax	5.7	21.2
Ending balance	(52.3)	(58.0)	(79.2)
Accumulated Other Comprehensive Loss Items
Accumulated Other Comprehensive Loss, Net of Tax [Roll Forward]
Beginning balance	(98.2)	(132.7)	(151.4)
Other comprehensive (loss) income items, net of tax	(27.6)	34.5	18.7
Ending balance	$ (125.8)	$ (98.2)	$ (132.7)

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

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