# Why $x_a$ (or $x_o$) and not $a_x$? (conventions for algebraic quantities)

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?

• Not from Torricelli but from Descartes' Géométrie (1637). – Mauro ALLEGRANZA Mar 24 '17 at 6:56
• 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 $$x$$.
Leibniz is the inventor of the index notation. Today we would write $$D_1, D_2$$ etc. for the indexed points $$D$$. Leibniz does this differently: he writes the numbers in front of the letter and he does not set them lower. (In the case of this figure he does not write the numbers smaller [so he wrote $$1D, 2D$$ etc.]. But he does in other cases. Sometimes he also sets the numbers lower, but he never writes the numbers smaller and sets them lower at the same time. ...)