Euclid described it best in the Elements as a balance of proportion between two lines:
“A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the
greater segment, so is the greater to the less.” INTERFERENCE - A Grand Scientific Musical Theory, Richard Merrick, 2011, Third Edition
See Also
Golden Mean
Golden Number
PHI
Proportion
Propositions of Geometry
Ratio