Hamilton, William Rowan | Lectures on quaternions, Dublin, 1853, first edition

Hamilton, Sir William Rowan

Lectures on quaternions. Dublin: Hodges & Smith, 1853

First edition of Hamilton’s seemingly spontaneous discovery of quaternions, 

Hamilton’s longstanding contemplation on complex numbers and multi-dimensional geometry came to fruition, as a metaphorical “electric circuit seemed to close, and a spark flashed forth” whilst walking with his wife alongside the Royal Canal on October 16, 1843. In hopes of keeping this mathematical spark alive, Hamilton wrote the fundamental equation for quaternions on a nearby brick part of Broome Bridge—now commemorated with a plaque.

Hamilton’s discovery of quaternions, a significant departure from the constraints of commutative law of multiplication, gives basis to vector calculus, which would later supersede it. 

8vo (212 x 135 mm). Lacking half-title, in-text diagrams; a few spots, title marginally toned. Modern red morocco over marbled boards, spine in six compartments with raised bands, gilt-lettered and dated, edges sprinkled red; upper edge dust-soiled. 

REFERENCES

PMM 344; Bruno Math and Mathematicians, pp. 207-10; Hamilton, William Rowan. “Letter from Sir W. R. Hamilton to Rev. Archibald H. Hamilton, August 5, 1865.” In Letters Describing the Discovery of Quaternions. Trinity College Dublin. Accessed September 16, 2026. Broome Bridge Letters.

PROVENANCE

Brown University Library (stamp in blind to title)—Janus Foundation (bookplate to front pastedown)