This pretty theorem details of the construct of triangles using well known I/GCSE circle theorems (Exterior Angle of Triangle and Cyclic Quadrilateral).  I like the petal effect in the middle.  Never come across the word species in conjunction with triangles before.

Useful facts for I/GCSE pupils (exams v soon!) on SIMULTANEOUS EQUATIONS detailed in Carr’s Victorian text book and alive and well, completely unchanged today.  FP1 students look at the determinant in 59.

Formula and completing the square – basic stuff for School maths students expressed loud and clear in Carr’s Synopsis of Elementary Results in 1880 – find a proof of 45 by using ideas in 47 and teach yourself to be a mathematical genius.

Difference of two squares, staple diet for GCSE maths students, is first proposition in Carr’s book of magic and has ancient geometric roots in Euclid Book II.