James Garfield 'Pythagoras' proof

James Garfield was the 20th president of the USA
for a brief period of time (he was assassinated)

he worked on a proof of the theorem with colleagues, five years before he became president

first, establish that the isosceles triangle is right-angled

then find the area of the trapezium (trapezoid)

relate this to the sum of the three triangles (two of which are congruent):

this involves squaring (a + b)