Through the thoghtful ness of Jens Hoyrup, I have been reading offprints of his articles for nearly 25 years. In one of them (most probably dealing with Babylonian mathematics), he wrote to the effect that in the expression, say a square and four roots, the roots are actually unit rectangles. Analogically in algebra: x^2 = 4x = x + x + x + x. All the x's are rectangles dimensionally, 1 by x.
While checking my translation of Fibonacci's "De practica geometrie", exactly this concept appears in Chapter 3. The Latin is . . . embadum eius equatur quatuor radicibus quarum una est quadrilatera ae, secunda . . . As is obvious from figure 3.52 (in Boncompagni's transcription), the root is the unit rectangle ae. Hence, Fibonaccis concept of a geometric root differs from his idea of a numerical root (which is the common one we have), and a Babylonian idea purdured into the thirteenth century.