Previously Unpublished Works, Fascicles VI-VII

to 1063, which was extended in after years to 1596 A.D., probably by Abbo Likely Abbo of Fleury, an influential 10th-century monk and mathematician..

After Bede, the next authority on the Computus The mathematical science used to calculate the date of Easter and other movable feasts. was Alcuin (735–804 A.D.), who was consulted by Charlemagne in his attempt at a revival of learning in Western Europe. In his letters to Charlemagne, Alcuin deals with subjects like the leap of the moon original: "saltus lune." A one-day adjustment made to the lunar calendar every 19 years to keep it in sync with the solar year., which he succeeds in muddling up by assuming the truth of the Metonic cycle A 19-year period after which the phases of the moon recur on the same days of the year; Alcuin's error lay in how he applied this lunar logic.; a treatise on this subject under his name is found (Migne, ci. 981) Referring to Jacques Paul Migne's "Patrologia Latina," a standard collection of medieval texts., dealing with the subject in a different way on the same assumption, probably of later date. A knowledge of the Computus was enforced on the clergy among other subjects in a number of Capitularies original: "Capitularia." Legislative or administrative decrees issued by the Frankish kings. of this period. The General Admonition original: "Admonitio Generalis" of 789 A.D. ordered all priests to have a good text of it (original: "M. H. G. Cap. Reg. Franc. i. 60"; referring to the "Historical Monuments of Germany: Capitularies of the Kings of the Franks."), an order repeated in 805 A.D. (ibid., pp. 121, 235), by Bishop Haiton about 813 A.D. (ibid., p. 363), and in the Collection of Laws original: "Legiloquum" of 827 A.D. (ibid., p. 403). As a consequence, a number of elementary treatises were compiled either by Alcuin or his school, some of which seem to have been preserved in the very early manuscript used by Pamelius Jacobus Pamelius, a 16th-century theologian and editor of early Christian texts.. The habit of medieval scribes of using the current year as an example instead of that given by the original author makes it difficult to date these precisely. Thus, for example, the Canons and Tables of Bede (Migne, xc. 857) have passages pointing to 703 A.D.—the authorship of Bede—and 764 A.D.—probably Alcuin. Other tables pointing to the years 811–12 A.D.—and probably from his school—are printed in the Cassinese Anthology original: "Florilegium Cassinense", vol. i. Rabanus Maurus (820 A.D.) also writes on the subject (Migne, cvii. 670). The first important work on the Computus after Bede is, however, that of Helpericus or Heiric of Auxerre, printed by Pez in 1721 (Migne, cxxxvii. 15) in a poor text. The preface is printed by Mabillon, Ancient Fragments original: "Veter. Analect." (Veterum Analectorum), i. 113. The date of the texts of Helpericus was studied by Traube in 1893 (Lectures and Essays original: "Vorlesungen u. Abhandlungen", iii. 128), who puts it at before 900 A.D. The earliest manuscript in the British Museum, Sloane 263, uses the date of 903 A.D. as an example.

Helpericus is said to have been a pupil of Rabanus Maurus, and to have written for the school at Auxerre: a notice of his other works is found in the Literary History original: "Histoire littéraire", vi. 379. The On the Ecclesiastical Computation original: "De Computo Ecclesiastico" is founded directly on Bede and contains 38 chapters. He is the first to point out (c. 36) that the epacts The age of the moon in days on January 1st, essential for calculating Easter. fail in three years of the 19-year cycle, the 8th, 11th, and 19th, a failure remedied by