Comprehensive Income - Changes in Components of Accumulated Other Comprehensive Income (Loss) Items (Details) - USD ($) $ in Millions	3 Months Ended						9 Months Ended
	May 31, 2022	Feb. 28, 2022	Nov. 30, 2021	May 31, 2021	Feb. 28, 2021	Nov. 30, 2020	May 31, 2022	May 31, 2021
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance	$ 2,104.3	$ 2,072.9	$ 2,044.5	$ 1,932.5	$ 1,937.0	$ 2,127.5	$ 2,044.5	$ 2,127.5
Other comprehensive loss before reclassifications							(8.9)	30.4
Amounts reclassified from accumulated other comprehensive loss							3.6	4.9
Net current period other comprehensive income	(0.6)	6.0	(10.7)	20.7	8.4	6.2	(5.3)	35.3
Ending balance	1,918.6	2,104.3	2,072.9	2,039.1	1,932.5	1,937.0	1,918.6	2,039.1
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance	(102.9)	(108.9)	(98.2)	(118.1)	(126.5)	(132.7)	(98.2)	(132.7)
Net current period other comprehensive income	(0.6)	6.0	(10.7)	20.7	8.4	6.2
Ending balance	(103.5)	$ (102.9)	(108.9)	(97.4)	$ (118.1)	(126.5)	(103.5)	(97.4)
Foreign Currency Items
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance			(40.2)			(53.5)	(40.2)	(53.5)
Other comprehensive loss before reclassifications							(8.9)	33.6
Amounts reclassified from accumulated other comprehensive loss							0.0	0.0
Net current period other comprehensive income							(8.9)	33.6
Ending balance	(49.1)			(19.9)			(49.1)	(19.9)
Defined Benefit Pension Plans
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance			$ (58.0)			$ (79.2)	(58.0)	(79.2)
Other comprehensive loss before reclassifications							0.0	(3.2)
Amounts reclassified from accumulated other comprehensive loss							3.6	4.9
Net current period other comprehensive income							3.6	1.7
Ending balance	$ (54.4)			$ (77.5)			$ (54.4)	$ (77.5)