Significant Accounting Policies - Changes of Accumulated Other Comprehensive Loss, Net of tax (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 31, 2021	Aug. 31, 2020	Aug. 31, 2019
Accumulated Other Comprehensive Loss, Net of Tax [Roll Forward]
Beginning balance	$ 2,127.5	$ 1,918.9	$ 1,716.8
Other comprehensive income (loss) before reclassifications	27.2	11.3
Amounts reclassified from accumulated other comprehensive loss	7.3	7.4
Other comprehensive income (loss) items, net of tax	34.5	18.7	(36.6)
Ending balance	2,044.5	2,127.5	1,918.9
Foreign Currency Items
Accumulated Other Comprehensive Loss, Net of Tax [Roll Forward]
Beginning balance	(53.5)	(65.4)
Other comprehensive income (loss) before reclassifications	13.3	11.9
Amounts reclassified from accumulated other comprehensive loss	0.0	0.0
Other comprehensive income (loss) items, net of tax	13.3	11.9
Ending balance	(40.2)	(53.5)	(65.4)
Defined Benefit Pension Plans
Accumulated Other Comprehensive Loss, Net of Tax [Roll Forward]
Beginning balance	(79.2)	(86.0)
Other comprehensive income (loss) before reclassifications	13.9	(0.6)
Amounts reclassified from accumulated other comprehensive loss	7.3	7.4
Other comprehensive income (loss) items, net of tax	21.2	6.8
Ending balance	(58.0)	(79.2)	(86.0)
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Loss, Net of Tax [Roll Forward]
Beginning balance	(132.7)	(151.4)	(114.8)
Other comprehensive income (loss) items, net of tax	34.5	18.7	(36.6)
Ending balance	$ (98.2)	$ (132.7)	$ (151.4)