An Elementary Treatise on Elliptic Functions

An Elementary Treatise on Elliptic Functions is a book by Arthur Cayley, a prominent 19th-century English mathematician. The work focuses on elliptic functions, which originated from studying integrals that could not be explicitly evaluated using standard functions.12

These integrals, often arising from calculations like the length of an ellipse's arc, were extensively studied by mathematicians like Adrien-Marie Legendre. However, the field was transformed by Niels Henrik Abel and Carl Jacobi, who showed that by considering complex variables, these integrals could define new functions with properties generalizing the periodicity of trigonometric functions. Cayley's book draws from Carl Jacobi's perspective on this widely studied subject.21