Butterfly theorem

A formal proof of the theorem is as follows: Let the perpendiculars XX′ and XX″ be dropped from the point X on the straight lines AM and DM respectively.

Similarly, let YY′ and YY″ be dropped from the point Y perpendicular to the straight lines BM and CM respectively.

[3] Proving the butterfly theorem was posed as a problem by William Wallace in The Gentleman's Mathematical Companion (1803).

Three solutions were published in 1804, and in 1805 Sir William Herschel posed the question again in a letter to Wallace.

Thomas Scurr asked the same question again in 1814 in the Gentleman's Diary or Mathematical Repository.