Freeth’s nephroid is NOT an epicycloid, but rather a strophoid. Thomas Jacob Freeth is a tough fellow to trace. He was born 11 October 1819 in London and named for his grandfather (1758-1826; born in Liverpool, but lived most of his life in London as a silversmith and spoonmaker). Thomas Jacob was the second son and third child of six of Thomas’ fourth son, Charles (1797 – 1869, an agent for Sun Fire and Life Insurance), from a second marriage.
Thomas Jacob studied at University College (London) – he obtained an LL.B in 1841 and LL.D in 1843 (first ever at University College). He then went to Christ’s College, Cambridge, where he was admitted 6 July 1843 and Matriculated Lent 1844. He was mentioned as working as a solicitor in London in 1844 and 1845. He attained a BA in 1849 and an MA in 1853. He was admitted ‘ad eundem’ at Oxford 9 July 1853. The last would be a courtesy degree, but I have not determined if he was a student, a lecturer, or had some other connection. So far, no pictures.
Of interest in our context is a paper he wrote in 1879 describing a curve that could be used to construct the regular heptagon, nonagon and undecagon. None of these can be constructed with a straight edge and compasses.
Freeth, Rev. T. J. May 8, 1878 communication to the London Math. Soc. referenced as “The Nephroid, Heptagon, &c.” Proc. London. Math. Soc. 10, p. 130, 1878. See also the Appendix of vol. 10 on p. 228.