Foote was educated at the Albany Institute. He studied law with Judge Daniel Cady in Johnstown, New York. After being admitted to the bar, he settled in western New York, and was district attorney and then judge of the court of common pleas of Seneca County, New York. His specialty was patent law, and he made several valuable inventions. In 1864 he was appointed to the board of appeals at the U. S. Patent Office. On July 28, 1868, he was appointed the eleventh Commissioner of Patents. Foote was the author of several books and papers on mathematics.
Foote was born in Lee, Massachusetts to Elisha Foote (died April 8, 1846) and Delia Battle. On August 12, 1841, he married Eunice Newton (born July 17, 1819). Elisha and Eunice were the parents of Mary Foote Henderson, an artist and writer born July 21, 1842, and Augusta Newton Arnold, born October 1844, a writer who wrote The Sea at Ebb Tide. They had six grandchildren.
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- Goodwin, Nathaniel, "The Foote family: or, The descendants of Nathaniel Foote, one of the first ... " Hartford, Press of Case, Tiffany and company, 1849. p. 159
- Wellman, Judith (October 5, 2004). The Road to Seneca Falls: Elizabeth Cady Stanton and the First Woman's Rights Convention. University of Illinois Press. Retrieved January 31, 2016.
- Goodwin, p. 159
- Reed, Elizabeth Wagner (1992). "Eunice Newton Foote". American women in science before the civil war. Retrieved January 31, 2016.