Quod erat demonstrandum

The two outer vertical arrows are isomorphisms the one on the right by [BBM] Proposition 2.3.12, the one on the left by Proposition 4.3.1. Thus any element in the upper middle group which maps to zero in the group below it also maps to zero in the group on the left. Hence it comes from an element on the right. Quod erat demonstrandum. ... 

Abbreviation for quod erat demonstrandum, used to denote the end of a proof, quadrangle... 

Control nevertheless is important in science—tremendously so—not as an end but as a component of proof. The ability to control is the strongest possible demonstration of true understanding. Many doubted whether Becquerel, Curie, Bohr, Oppenheimer and the rest really understood what causes what inside the atom. But after July 16, 1945, when the day dawned prematurely to the northwest of Alamagordo, at White Sands, New Mexico, no one could possibly doubt any more, for the atom bomb was plainer than the sun. With a demonstrated abdity to control, the good scientist may sign off hke the mathematician at the end of a proof Quod erat demonstrandum. (Huber 1991)... 

---