It's my understanding that the convention of using letters from the end of the alphabet ($x$, $y$, $z$) to represent $variables$, and letters from the start of the alphabet ($a$, $b$, $c$) to represent $constants$ came to us from F. Vieta (who proposed vowels and consonants) by way of Descartes.

However, I was curious to know if there was ever any debate around subscript notation for the same distinction, i.e. $x$ vs. $x_o$, where the first is considered a variable and the second, an unknown constant.

I can imagine many reasons for $x_a$ being more popular than $a_x$; but, does anyone know where this notation got its start? &nd was there any contention?

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    Not from Torricelli but from Descartes' Géométrie (1637). – Mauro ALLEGRANZA Mar 24 '17 at 6:56
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    Cauchy in his Résumé (1823) used $x_0, y_0$ to denote a chosen value for the variable $x,y$. – Mauro ALLEGRANZA Mar 24 '17 at 7:05
  • I see $x,$ $y,$ $z$ used as subscripts all the time in physics and multivariable calculus. But maybe these examples are cheating. – Dave L Renfro Mar 24 '17 at 14:38
  • @MauroALLEGRANZA thanks for the flag on that fact - of course you're right, except that it was Vieta (Viète) first with vowels / consonants and then Descartes' contribution was start / end of alphabet. Edited to reflect this point. – Rax Adaam Apr 4 '17 at 17:05
  • I don't understand the question. What is $x_a$ a notation for? What is $a_x$ a notation for? What convention are you referring to? In what context is $x_a$ "more popular than" $a_x$? – Ben Crowell Apr 6 '17 at 2:42

If we write $0_x$ then it looks like a special kind of 0, since the 0 is above the baseline for typography. So we would expect $0_x+1_x=1_x$ etc. With the $x_0$ notation it is clear that $x_0$ is a special kind of $x$, or at any rate the same kind of thing as $x$.

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