Omar Khayyam · Mathematics
In the second part of his Euclid commentary, Khayyam reexamined the theory of ratios in Book V of the <em>Elements</em> and pressed a revolutionary idea: that a ratio - even between incommensurable magnitudes - is itself a kind of number. In treating irrational magnitudes as numbers, he took an early step on the road to the real numbers.
You learned that Khayyam scrutinized Euclid’s Book V theory of proportion, connected it to an older definition based on the process now linked to continued fractions, and argued that ratios of magnitudes - including incommensurable ones - are genuine numbers. Explain why treating irrational ratios as numbers was…
Leads to Euclid.
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