Accumulated Other Comprehensive Income (Loss) - Components (Details) - USD ($) $ in Millions	3 Months Ended
Nov. 30, 2019	Nov. 30, 2018	Nov. 30, 2017	Nov. 30, 2016
Accumulated Other Comprehensive Income (Loss) [Line Items]
Restructuring Reserve, Translation and Other Adjustment	$ 17.9
Accumulated Other Comprehensive Income (Loss), Net of Tax	(138.8)	$ (122.4)	$ (125.3)	$ (138.5)
Accumulated Foreign Currency Adjustment Attributable to Parent [Member]
Accumulated Other Comprehensive Income (Loss) [Line Items]
Accumulated Other Comprehensive Income (Loss), Net of Tax	(19.0)	(32.6)	(23.1)	(29.6)
Accumulated Defined Benefit Plans Adjustment Attributable to Parent [Member]
Accumulated Other Comprehensive Income (Loss) [Line Items]
Accumulated Other Comprehensive Income (Loss), Net of Tax	$ (119.8)	$ (89.8)	$ (102.2)	$ (108.9)

Accumulated change in equity from transactions and other events and circumstances from non-owner sources, net of tax effect, at period end. Excludes Net Income (Loss), and accumulated changes in equity from transactions resulting from investments by owners and distributions to owners. Includes foreign currency translation items, certain pension adjustments, unrealized gains and losses on certain investments in debt and equity securities, other than temporary impairment (OTTI) losses related to factors other than credit losses on available-for-sale and held-to-maturity debt securities that an entity does not intend to sell and it is not more likely than not that the entity will be required to sell before recovery of the amortized cost basis, as well as changes in the fair value of derivatives related to the effective portion of a designated cash flow hedge.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 11
-URI http://asc.fasb.org/extlink&oid=114867106&loc=d3e637-108580

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 14A
-URI http://asc.fasb.org/extlink&oid=114867106&loc=SL7669686-108580

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section 45
-Paragraph 14
-URI http://asc.fasb.org/extlink&oid=114867106&loc=d3e681-108580

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant