Leases (Supplemental Cash Flow) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2022
Leases [Abstract]
Operating Lease, Payments	$ 12,119	$ 13,153	$ 14,166
Right-of-Use Asset Obtained in Exchange for Operating Lease Liability	$ 3,075	$ 1,654	$ 4,584
Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]	Other Assets, Noncurrent	Other Assets, Noncurrent