Earliest Known Uses of Some of the Words of Mathematics (X)
X-AXIS. Axis of x appears in "On the Attractions of Homogeneous Ellipsoids" by James Ivory, Philosophical Transactions of the Royal Society of London, Vol. 99. (1809), pp. 345-372. [JSTOR].
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 2x1: 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]