Mathematical Treasure: Hamilton’s Lectures on Quaternions

William Rowan Hamilton (1805-1865) is best remembered for his discovery of quaternions. His definitive work on this subject was Lectures on Quaternions (1853). Unsatisfied with this presentation, Hamilton attempted to write a more detailed and “user friendly” version of the work, but never succeeded in completing the task. Note the written inscription “from the author” on the title page. Hamilton was the first foreign elected member of the American National Academy of Science that was founded in 1863.

The concept of the “Cross Product” of unit vectors is considered on page 70.

The beginning of “Lecture V” (pages 186-87) provides an example of Hamilton’s lecture style. He discussed the associativity of his vector multiplication, i.e. his “Dot Product.”

This material is obtained through the courtesy of the Peabody Library of Johns Hopkins University. A complete copy of the work can be viewed in the Internet Archive.

Index to Mathematical Treasures