In the United States, the first analytical geometry textbook I am aware of
is Charles Davies, _Elements of Analytical Geometry_, New York, 1836.
Analytical geometry is listed among the subjects to be taught at West Point
in 1816, but I don't know that there was a textbook available. (Perhaps the
treatises by Biot and Bourdon consulted by Davies?) Most colleges did not
include analytical geometry in the mathematical course but taught
conic sections, mensuration, and surveying alongside the plane and solid
geometry course (which was recitation of Euclid or Legendre). One reason
was that these subjects were included in compendia by Charles Hutton, John
Bonnycastle (both English), and Samuel Webber (U.S.). Colleges relied
on compendia before textbook series by Jeremiah Day, John Farrar, and Davies
appeared in the 1810s and 1820s.
Geometry became an entrance requirement at Harvard in 1844. I think it was
several years before any other institutions followed--there just wasn't a
system of secondary education comprehensive enough to guarantee students had
received the rigorous mental training colleges liked. "Davies' Legendre," a
translation of Legendre's _Elements de geometrie_ was still taught in
some colleges c. 1900.
--- Amy Ackerberg-Hastings