The Work of Tschirnhaus, La Hire and Leibniz on Catacaustics and the Birth of the Envelopes of Lines in the 17th Century

The aim of this paper is to examine the work of Tschirnhaus, La Hire and Leibniz on the theory of caustics, a subject whose history is closely linked to geometrical optics. The curves in question were examined by the most eminent mathematicians of the 17th century such as Huygens, Barrow and Newton and were subsequently studied analytically from the time of Tschirnhaus until the 19th century.