My understanding is that in Cartesian geometry, all coordinate axes of an n-dimensional space may intersect at one point. I would like to know how that point--whether (0, 0), (0,0,0), ... -- came to be called "the origin." What else has it been called? How did the use of the word "origin" become commonplace in geometry?
A good place to look for such things is Jeff Miller's Earliest Known Uses of Some of the Words of Mathematics, where we read:
"Boyer (page 404) seems to attribute the term origin to Philippe de Lahire (1640-1718). The term presumably appears in Sections Coniques by Marquis de l'Hopital, since the OED shows a use of the term in English in a 1723 translation of this work".
Boyer writes the following in his History of Mathematics:
"About the only mathematician of stature in France at the time was Philippe de Lahire (1640-1718), a disciple of Desargues and, like his master, an architect. Pure geometry obviously appealed to him, and his first work on conics in 1673 was synthetic, but he did not break with the analytic wave of the future. Lahire kept an eye out for a patron; hence, in his Nouveaux Elemens des Sections Coniques of 1679, dedicated to Jean Baptiste Colbert, the methods of Descartes came to the fore... But Lahire carried over into analytic geometry some of Desargues’ language. The axis of abscissas was the "trunk," points on it were "knots," and ordinates were "branches".
Of his analytic language, only the term “origin” has survived. Perhaps it was because of his terminology that contemporaries did not give proper weight to a significant point in his Nouveaux Elemens. Lahire provided one of the first examples of a surface given analytically through an equation in three unknowns, which was the first real step toward solid analytic geometry. He, like Fermat and Descartes, had only a single reference point or origin on a single line of reference or axis OB, to which he now added the reference or coordinate plane OBA."
l'Hopital's Traité Anlytique des Sections Coniques appeared in 1707. Presumably, he, or his 1723 English translators, borrowed the term "origin" from Lahire.