''Dulcarnon'' or ''dulcarnoun'' is a term used in the

Middle English Middle English (abbreviated to ME) is a form of the English language that was spoken after the Norman conquest of 1066, until the late 15th century. The English language underwent distinct variations and developments following the Old English p ...

poem ''

Troilus and Criseyde ''Troilus and Criseyde'' () is an epic poem by Geoffrey Chaucer which re-tells in Middle English the tragic story of the lovers Troilus and Criseyde set against a backdrop of war during the siege of Troy. It was written in '' rime royale'' an ...

'' by

Geoffrey Chaucer Geoffrey Chaucer (; – 25 October 1400) was an English poet, author, and civil servant best known for ''The Canterbury Tales''. He has been called the "father of English literature", or, alternatively, the "father of English poetry". He wa ...

, in a line given to

Criseyde Cressida (; also Criseida, Cresseid or Criseyde) is a character who appears in many Medieval literature, Medieval and Renaissance literature, Renaissance retellings of the story of the Trojan War. She is a Trojan woman, the daughter of Calchas, a ...

: "at dulcarnoun, right at my wittes ende". It became proverbial. The etymology is from an Arabic phrase ''dhū-al-qarnayn'' meaning "two-horned", and the term was in use in medieval Latin. Dulcarnon was used to refer to the exposition of the

Pythagorean theorem In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite t ...

in the ''

Elements of Euclid The ''Elements'' ( grc, Στοιχεῖα ''Stoikheîa'') is a mathematics, mathematical treatise consisting of 13 books attributed to the ancient Greek mathematics, Greek mathematician Euclid in Alexandria, Ptolemaic Egypt 300 BC. It is a colle ...

'', considered baffling. In Chaucer's poem, Pandarus conflates it with the

Pons asinorum In geometry, the statement that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the ''pons asinorum'' (, ), typically translated as "bridge of asses". This statement is Proposition 5 of Book 1 in Eu ...

, an earlier result in Euclid on the

isosceles triangle In geometry, an isosceles triangle () is a triangle that has two sides of equal length. Sometimes it is specified as having ''exactly'' two sides of equal length, and sometimes as having ''at least'' two sides of equal length, the latter versio ...

Alexander Neckam Alexander Neckam (8 September 115731 March 1217) was an English magnetician, poet, theologian, and writer. He was an abbot of Cirencester Abbey from 1213 until his death. Early life Born on 8 September 1157 in St Albans, Alexander shared his b ...

had used it for the Pythagorean theorem, though in a way that allowed for the confusion;

Richard of Wallingford Richard of Wallingford (1292–1336) was an English mathematician, astronomer, horologist, and cleric who made major contributions to astronomy and horology while serving as abbot of St Albans Abbey in Hertfordshire. Biography Richard was bor ...

applied it to the Pythagorean theorem. By the 17th century to be "at Dulcarnon" was to be at the end of one's wits, or in a dilemma in the sense of a predicament.

John Selden John Selden (16 December 1584 – 30 November 1654) was an English jurist, a scholar of England's ancient laws and constitution and scholar of Jewish law. He was known as a polymath; John Milton hailed Selden in 1644 as "the chief of learned ...

made the connection to ''dū'lkarnayn'', a Persian term via Arabic, writing in his 1612 preface to

Michael Drayton Michael Drayton (1563 – 23 December 1631) was an English poet who came to prominence in the Elizabethan era. He died on 23 December 1631 in London. Early life Drayton was born at Hartshill, near Nuneaton, Warwickshire, England. Almost nothin ...

's ''Polyolbion''. He used it to point to Chaucer as a learned and a witty poet. Stephen Skinner in the later 17th century corrected a muddled annotation to Chaucer's line by

Thomas Speght Thomas Speght (died 1621) was an English schoolmaster and editor of Geoffrey Chaucer. Life He was from a Yorkshire family, and matriculated as a sizar of Peterhouse, Cambridge in 1566, graduating B.A. in 1570, and M.A. in 1573. At Cambridge he was ...

Walter William Skeat Walter William Skeat, (21 November 18356 October 1912) was a British philologist and Anglican deacon. The pre-eminent British philologist of his time, he was instrumental in developing the English language as a higher education subject in th ...

adopted the derivation of Dulcarnon from the Arabic: for which see ''

Dhul-Qarnayn , ( ar, ذُو ٱلْقَرْنَيْن, Ḏū l-Qarnayn, ; "He of the Two Horns") appears in the Quran, Surah Al-Kahf (18), Ayahs 83–101 as one who travels to east and west and sets up a barrier between a certain people and Gog and Magog ...

''. ''Dulcarnon: A Novel'' was published in 1926 by

Henry Milner Rideout Henry Milner Rideout (1877–1927) was a native of Calais, Maine. Author of sixteen novels, twenty-three short stories and novellas, and a biographical memoir, he also was editor of one college textbook, as well as co-editor of three others. Man ...

Notes

{{reflist English phrases English proverbs