The horns of a dilemma. (or Syllogismum cornutum); at my wits' and; a puzzling question. Dulcarnein is the Arabic dhulkarnein (double-horned, having two horns). Hence the 47th proposition of the First Book of Buclid is called the Dulcarnon, as the 5th is the pons asinorum. Alexander the Great is called Iscander Dulcarnein, and the Macedonian æra the æra of Dulcarnein. Chaucer uses the word in Troylus and Cryseyde, book iii. 126, 127.
The horns of the 47th proposition are the two squares which contain the right angle.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894