*Axis of abscissas* and *axis of ordinates* are found in 1850 in
*The elements of analytical geometry*
by John Radford Young:
"The distance, *AB*, is denominated the abscissa of the point; *P*, and *BP*, or
its equal, *AC*, is called the ordinate of the same point; hence the axis
*AX* is distinguished from the axis *AY* by the name axis of abscissas, the
latter being called axis of ordinates. The abscissa and ordinate of a point,
when spoken of together, are, for the sake of brevity, called the
coordinates of the point, and, for a like reason, the two axes are referred
to as axes of coordinates. An abscissa is generally denoted by the letter *x*,
and an ordinate by the letter *y*; and often, for shortness, the axis of abscissas
is called the axis of *x*, and the axis of ordinates the axis of *y*."
[University of Michigan Digital Library]

*X-axis* is found in 1852 in *Acoustics* by W. F. Donkin [Google print search].

The terms **X-COORDINATE, Y-COORDINATE,** and **Z-COORDINATE**
appear in a paper published by James Joseph Sylvester in 1863 [James
A. Landau].

**X-INTERCEPT** is found in 1905 in *A Brief Course in the Calculus* by William Cain:
“The *x*-intercept of the tangent is found to be 2*x*_{1}: prove
from this that ‘the segment of any tangent to a hyperbola between the asymptotes, is bisected
by the point of contact.’” [James A. Landau]