William Chapple (surveyor)

His mathematical discoveries were mostly in plane geometry and include: He was also one of the earliest mathematicians to calculate the values of annuities.

[1] He was a devoted bibliophile,[2] and gained much of his knowledge of mathematics from Ward's The Young Mathematician's Guide: Being a Plain and Easie Introduction to the Mathematicks, in Five Parts.

Although these results are named for Leonhard Euler, who published them in 1765, they were found earlier by Chapple, in a 1746 essay in The Gentleman's Magazine.

This is the triangular case of Poncelet's closure theorem, which applies more generally to polygons of any number of sides and to conics other than circles.

It is the first known mathematical publication on pairs of inscribed and circumscribed circles of polygons, and significantly predates Poncelet's own 1822 work in this area.

[3] In 1749, Chapple published the first known proof of the existence of the orthocentre of a triangle, the point where the three perpendiculars from the vertices to the sides meet.

In this, he became one of the first mathematicians to work on this problem, along with Simpson, Abraham de Moivre, James Dodson, and William Jones.