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[HM] Geometric roots
Posted:
Dec 23, 2005 11:41 AM
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Dear Colleagues:
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.
Best wishes for peace in your neighborhood.
Barney Hughes
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