English

Noun

quae erant demonstranda

1. plural of quod erat demonstrandum
   • 1894: Benjamin Franklin Finkel, The American mathematical monthly: devoted to the interests of collegiate mathematics, volume 1, page 190 (Mathematical Association of America)

     Therefore it is established that the join CD will be equal, or less, or greater than this AB, according as the angles at the same CD are right, or obtuse, or acute. Quae erant demonstranda.

   • 1955: Maurice Leonard Jacks, The education of good men, page 47 (Gollancz)

     The proving of a geometrical theorem is, of course, an exercise in logical thinking, but the pupil needs to be made conscious of this, and also conscious of the fact that the same processes of thought are applicable in quite other fields and will lead to equally satisfactory results (quae erant demonstranda) there too.

Latin

Etymology

quae (nominative neuter plural of quī) + erant (third-person plural imperfect active indicative of sum) + dēmonstranda (nominative neuter plural of dēmonstrandus, future participle of dēmonstrō)

Phrase

quae erant dēmonstranda

1. plural of quod erat dēmonstrandum
   • 1986: Girolamo Saccheri, George Bruce Halsted (translator), Girolamo Saccheri’s Euclides vindicatus, page 24 (AMS Bookstore; ISBN 0‒8284‒0289‒2, 978‒0‒8284‒0289‒7)

     Itaque constat junctam CD aequalem fore, aut mino- ^[4] rem, aut majorem ipsa AB, prout anguli ad eandem CD fuerint aut recti, aut obtusi, aut acuti. Quae erant demonstranda.