During Davies' early years, the family moved to St Lawrence County, New York, where he was educated in local schools.

He entered the US Military Academy at West Point in December 1813, through the influence of General Joseph Swift, who had met Davies' father during the War of 1812.

[2] Davies had earned praise for the services rendered to General James Wilkinson's army in the Descent of the St. Lawerence during the fall of 1813.

He served a year in garrison at New England posts till August 31, 1816, when he was transferred to the Corps of Engineers.

From 1839 till 1841, he was a professor at Trinity College in Hartford, Connecticut, wherein he established a connection with Alfred Smith Barnes for publication of his books.

[2] Mathematical historian Florian Cajori wrote of his books as being "perspicuous, clear, and logically arranged.