Gibbs (1881)

Josiah Willard Gibbs was a pioneering American physicist and mathematician, and his work on vector analysis was influential in the development of modern vector calculus. His 1881 pamphlet on vector analysis [37] was one of the earliest texts to present vector analysis in a form similar to what we use today.

The letters $i$, $j$, $k$ are appropriated to the designation of a normal system of unit vectors, i. e., three unit vectors, each of which is at right angles to the other two and determined in direction by them in a perfectly definite manner. We shall always suppose that $k$ is on the side of the $i$-$j$ plane on which a rotation from $i$ to $j$ (through one right angle) appears counter-clock-wise. In other words, the directions of $i$, $j$, and $k$ are to be so determined that if they be turned (remaining rigidly connected with each other) so that $i$ points to the east, and $j$ to the north, $k$ will point upward. When rectangular axes of $X$, $Y$, and $Z$ are employed, their directions will be conformed to a similar condition, and $i$, $j$, $k$ (when the contrary is not stated) will be supposed parallel to these axes respectively.

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