William of Auberive (french: Guillaume d'Auberive) was a

Cistercian The Cistercians, () officially the Order of Cistercians ( la, (Sacer) Ordo Cisterciensis, abbreviated as OCist or SOCist), are a Catholic religious order of monks and nuns that branched off from the Benedictines and follow the Rule of Saint ...

monk and

numerologist Numerology (also known as arithmancy) is the belief in an occult, divine or mystical relationship between a number and one or more coinciding events. It is also the study of the numerical value, via an alphanumeric system, of the letters in ...

who served as the abbot of from 1165 until 1186.Uta-Renate Blumenthal, "Cardinal Albinus of Albano and the ''Digesta pauperis scolaris Albini'': Ms. Ottob. lat. 3057", ''Archivum Historiae Pontificiae'' 20 (1982): 7–49 (at p. 37, n. 124). Two of William's treatises—''De sacramentis numerorum a ternario usque ad duodenarium'' and ''Regule arithmetice''—and three of his letters have been published. Robert Earl Kaske,

Arthur Groos Arthur B. Groos (born 5 February 1943 in Fullerton, California) is an American philologist, musicologist, medievalist and Germanist. Groos began teaching at Cornell University in 1973, held the Avalon Foundation Professorship in Humanities, and w ...

and Michael W. Twomey, ''Medieval Christian Literary Imagery: A Guide to Interpretation'' (University of Toronto Press, 1988), p. 171. He belonged to a group of Cistercians whose work was an expansion on the work of

Hugh of Saint-Victor Hugh of Saint Victor ( 1096 – 11 February 1141), was a Saxon canon regular and a leading theologian and writer on mystical theology. Life As with many medieval figures, little is known about Hugh's early life. He was probably born in the 1090s. ...

allegorizing numbers in the

Bible The Bible (from Koine Greek , , 'the books') is a collection of religious texts or scriptures that are held to be sacred in Christianity, Judaism, Samaritanism, and many other religions. The Bible is an anthologya compilation of texts of a ...

. His ''De sacramentis'' on the numbers three (3) through twelve (12) is a direct continuation of the ''Analytica numerorum'' of Odo of Morimond on the first three natural numbers. It was itself followed by the work of

Geoffrey of Auxerre Geoffrey of Clairvaux, or Geoffrey of Auxerre, was the secretary and biographer of Bernard of Clairvaux and later abbot of a number of monasteries in the Cistercian tradition. Life He was born between the years 1115 and 1120, at Auxerre. At an ea ...

, beginning with thirteen (13).Guy Beaujouan, "The Transformation of the Quadrivium", in Robert L. Benson, Giles Constable and Carol Dana Lanham (eds.), ''Renaissance and Renewal in the Twelfth Century'' (University of Toronto Press, 1991), pp. 463–487 (at 483). He was an influence on Theobald of Langres. William probably wrote around 1164, before he became abbot. He knew the ''De arithmetica'' of

Boethius Anicius Manlius Severinus Boethius, commonly known as Boethius (; Latin: ''Boetius''; 480 – 524 AD), was a Roman senator, consul, ''magister officiorum'', historian, and philosopher of the Early Middle Ages. He was a central figure in the tr ...

and was especially interested in

perfect numbers In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. T ...

. He invented some terms of his own. If the

aliquot sum In number theory, the aliquot sum ''s''(''n'') of a positive integer ''n'' is the sum of all proper divisors of ''n'', that is, all divisors of ''n'' other than ''n'' itself. That is, :s(n)=\sum\nolimits_d. It can be used to characterize the prim ...

of a number was greater than the number, the difference between them he called ''fructus'' (fruit). If two numbers had identical aliquot sums, the sum was said be the "number of love".

Editions

*Leclercq, Jean. "L'arithmétique de Guillaume d'Auberive". ''Analecta Monastica'', 1st ser. Studia Anselmiana, 20. Vatican City, 1948. pp. 181–204. ''De sacramentis'' and the letter ''De sacramento quadragenarii'' are at pp. 197–202. *Lange, Hanne. "Les données mathématiques des traités du XII^e siècle sur la symbolique des nombres". ''Cahiers de l'Institut du Moyen-Âge Grec et Latin'', 32 (1979):1–128. ''Regule arithmetice'' and two other letters are at pp. 86–117.

References

{{reflist 12th-century Latin writers Cistercian abbots Numerologists