"[E]arly analytic geometers—Descartes in particular—did not accept that geometry could be based on numbers or algebra. Perhaps the first to take the idea of arithmetizing geometry seriously was Wallis... [(1657) Mathesis universalis. Opera 1, 11-228.] Chs. XXIII and XXV, gave the first arithmetic treatment of Euclid's Books II and V, and he had earlier given purely algebraic treatment of s [(1655) De sectionibus conicus. Opera 1, 291-364.]. He initially derived equations from classical definitions by sections of the cone but then proceeded to derive their properties from the equations, "without the embranglings of the cone," as he put it."
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, Mathematics and Its History (1989, 2002) 2nd edition, p. 115.
https://en.wikiquote.org/wiki/Euclid%E2%80%99s_Elements
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Euclid’s Elements
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