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In the current era, we label the Cartesian plane in x and y as our basis vectors, but what did the Greeks use to label their axis? The Greeks were around long before Descartes, so did they even use the same axis system? Or how did they graph things?

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    $\begingroup$ Did they graph things? $\endgroup$ – Mary Aug 4 at 3:54
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    $\begingroup$ Ancient Greeks had neither coordinate axes nor letters for variables to label them with. Some prototypes of axes appeared in geometric constructions of Apollonius's Conica, but they were not labeled, only segments on them were labeled (by capital Greek letters A, B, Γ, Δ...). The earliest symbol for variable appears in Diophantus's Arithmetica (c. 250 AD), it was ς, but he did not label anything with it. $\endgroup$ – Conifold Aug 4 at 4:29
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    $\begingroup$ The ancient Greeks named the axes after their favorite stallions, thus... putting the Horse befor DesCartes. //rim shot $\endgroup$ – Carl Witthoft Aug 4 at 11:30
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The ancient Greeks did not use rectangular coordinate systems in their mathematics, so it is unclear what are you asking about. The method of coordinates was introduced to mathematics by Descartes.

However the Greeks used spherical coordinates in astronomy and geography, and they labeled the coordinate circles the same way as we do (or more precisely we do the same as they did). I mean equator, ecliptic, meridians etc. In practical astronomy and geography we use the same coordinates as Ptolemy did, with essentially the same names and labels.

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