Share-Based Compensation (Schedule of Performance Stock Unit Activity) (Details) - Performance Stock Units [Member]	12 Months Ended
	Aug. 31, 2025 $ / shares shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock units outstanding | shares	46,422
Granted, number of stock units | shares	28,280
Vested, number of stock units | shares	(11,729)
Stock units outstanding | shares	62,973
Stock units, weighted-average grant-date fair value | $ / shares	$ 152.67
Granted, weighted-average grant-date fair value | $ / shares	133.29
Vested, weighted-average grant-date fair value | $ / shares	147.74
Stock units, weighted-average grant-date fair value | $ / shares	$ 144.89