Alexander Macfarlane FRSE LLD (21 April 1851 – 28 August 1913) was a Scottish logician, physicist, and mathematician.

His doctoral thesis "The disruptive discharge of electricity"[1] reported on experimental results from the laboratory of Peter Guthrie Tait.

In 1878 Macfarlane spoke at the Royal Society of Edinburgh on algebraic logic as introduced by George Boole.

His proposers were Peter Guthrie Tait, Philip Kelland, Alexander Crum Brown, and John Hutton Balfour.

Macfarlane was caught up in the revolution in geometry during his lifetime,[6] in particular through the influence of G. B. Halsted who was mathematics professor at the University of Texas.

In 1894 he published his five earlier papers[9] and a book review of Alexander McAulay's Utility of Quaternions in Physics.

Macfarlane reached this idea or ratios of areas while considering the basis for hyperbolic angle which is analogously defined.

In 1900 Alexander published "Hyperbolic Quaternions"[14] with the Royal Society in Edinburgh, and included a sheet of nine figures, two of which display conjugate hyperbolas.