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en.wikipedia.org/wiki/Horizontal_and_vertical

In the three-dimensional case, the situation is more complicated as now one has horizontal and vertical planes in addition to horizontal and vertical lines. Consider a point P and designate a direction through P as vertical. A plane which contains P and is normal to the designated direction is the horizontal plane at P.

Horizontal like the word horizon .... a line from left to right that is like the earth with the sun rising above it. The horizon. Now, vertical is the opposite it's a line from top to bottom (up and down).

www.vocabulary.com/dictionary/vertical

When you're standing up, you're vertical, as opposed to when you lie down in a horizontal position on the couch. The terms vertical and horizontal often describe directions: a vertical line goes up and down, and a horizontal line goes across. You can remember which direction is vertical by the letter, "v," which points down.

Length can be measured either way. The actual definition of length is the longest dimension. A shape that is two units horizontal and three units vertical will have a length of 3, and in this case ...

english.stackexchange.com/.../x-y-z-horizontal-vertical-and

If x and y are horizontal, z is vertical; if x and z are horizontal, y is vertical. The words horizontal and vertical are generally used in a planar (2-dimensional) sense, not spatial (3-dimensional). Which is the reason you may not find a word corresponding to the third dimension along with horizontal and vertical.

researchmaniacs.com/FAQ/WhichWayIsHorizontal.html

Which way is horizontal is a common question. Horizontal is left to right or east to west, or flat on the surface. Many people remember it by thinking about looking out over the horizon, which is flat, or goes from side to side, and horizon sounds like horizontal.

researchmaniacs.com/FAQ/WhichWayIsVertical.html

Which way is vertical is a common question. Vertical is up to down, or south to north. It is a pole that stands up straight. You can remember vertical by looking at the first letter of this word: V.