Prepared in connection with his lectures as Professor of Perspective at the Royal Academy, Turner’s diagram of various geometrical figures is based on an illustration in Samuel Cunn’s *Euclid’s Elements of Geometry *(London 1759, book 1, plate 1, Propositions 1 and 4). The left figure illustrates Proposition 1, ‘Problem: To describe an equilateral triangle upon a given finite right line’, while the right describes Proposition 4:

Theorem: If there are two triangles that have two sides of the one equal to two sides of the other, each to each, and the angle contained by those equal sides in one triangle equal to the angle contained by the correspondent sides in the other triangle; then the base of one of the triangles shall be equal to the base of the other, the whole triangle equal to the whole triangle, and the remaining angles of one equal to the remaining angles of the other, each to each, which subtend the equal sides.

1There are sketches of both Propositions in Turner’s lecture notes.

2