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It was Alexander Macfarlane who promoted this concept in the 1890s as his Algebra of Physics, first through the American Association for the Advancement of Science in 1891, then through his 1894 book of five Papers in Space Analysis, and in a series of lectures at Lehigh University in 1900 (see Historical Review below).
Mathematical physicists James Cockle, William Kingdon Clifford, and Alexander Macfarlane had all employed in their writings an equivalent mapping of the Cartesian plane by operator (cosh a + r sinh a), where a is the hyperbolic angle and r 2 = +1.