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I think the Elements would have been a lot more concise if he did.

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    $\begingroup$ Euclid wrote in a rhetorical manner simply because symbolic expressions had not yet been developed. I believe that this remained the case until renaissance Europe. The Greeks sometimes used the letters of the alphabet as numerals in a manner similar to the ancient Hebrew method - a decimal, non-positional system which used the first nine letters of the alphabet to represent the numbers 1 to 9. Numbers were sometimes written with a bar or dot over the letter in order to distinguish numbers from words. Various superscripts were used to write "large" numbers. $\endgroup$ – Nick Dec 26 '19 at 16:02
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    $\begingroup$ Because he did not take an undergraduate course of Analytic geometry. $\endgroup$ – Alexandre Eremenko Dec 26 '19 at 23:05
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    $\begingroup$ Euclid did not use degrees, of course. (Can you explain what's a degree, in a simple way and with Euclidean rigor? Without Calculus, which Euclid did not now.) Concerning $\angle ABC$ vs "angle ABC", there is really no much difference. $\endgroup$ – Alexandre Eremenko Dec 27 '19 at 3:11
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    $\begingroup$ @AlexandreEremenko. But Ptolemy (and his sources) did use degrees, without knowledge of calculus, $\endgroup$ – fdb Dec 29 '19 at 23:31
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    $\begingroup$ @fdb: Ptolemy was an applied mathematician. He was concerned with numerical approximations. Babylonians also used degree. But they had no concept of rigorous mathematics. While Euclid's Elements is pure mathematics, with rigorous proofs. $\endgroup$ – Alexandre Eremenko Dec 29 '19 at 23:35

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