Previously Unpublished Works, Fascicles VI-VII

...common calculation) original: "garis computus". This is likely the end of the phrase "vulgaris computus," referring to the standard, though flawed, method of time-reckoning used by the public and the Church. because of the Paschal limits The specific window of dates during which Easter is permitted to fall., namely the fourteenth moon, confirmed by the Council of Nicaea, we dare to change.’ As a matter of fact the only reference I have found in the Canon Law is in the Decretum The Decretum Gratiani, a collection of Canon Law compiled in the 12th century., part 3, distinction 3, on consecration, chapter 22: ‘from the fourteenth moon of the first month until the twenty-first day of the same month, let the same festival be celebrated’ original: "a xiv vero luna primi mensis usque ad xxi diem ejusdem mensis eadem celebretur festivitas", attributed to Pope Victor in the Isidorian decretals. The first canon of the Council of Antioch (346 A.D.) condemns all who celebrate Easter otherwise than as defined by the Council of Nicaea. Other decrees to the same effect are found in the Decretum, part 3, distinction 3, on consecration, chapters 23 and 26. Roger Referring to Roger Bacon, the 13th-century philosopher and scientist. devotes much space to the elucidation of the table of epacts epacts The age of the moon in days on January 1st, used to synchronize solar and lunar calendars., giving the exact lengths of the lunations in the old notation of atoms, moments, etc. In medieval timekeeping, an "atom" was the smallest unit of time (1/22,560 of an hour) and a "moment" was 1/40 of an hour. He shows that the error of the computists computists Scholars who specialized in the science of calculating calendar dates. amounts sometimes to five or six days, and proposes to change the golden numbers golden numbers A number from 1 to 19 used to indicate the position of a year in the 19-year lunar cycle. as a means of correcting the calendar.

Another important tract written the year before (1175 A.D.) is the anonymous treatise on the Computus (British Museum, Vitellius A. xii, folio 81). It is the year of the translation of the Almagest The influential 2nd-century mathematical and astronomical treatise by Ptolemy., which the author could hardly have known, but he is familiar with the names of Arab astronomers and some of the results of their work, as well as that of his predecessors. He uses the notation of atoms, etc.—a proof of pre-Arabic use, and probably learned his science from Jewish sources. His table of the 532-year cycle runs from 1064 A.D. to 1596 A.D., and on it are marked the dates of the Incarnation and Passion according to Dionysius, Gerland, and Marianus Dionysius Exiguus, Gerlandus Compotista, and Marianus Scotus were all significant medieval chronologists.. He is aware of the error not only in the length of the mean lunar month, but also of that caused by the movement of the equinox, and predicts that in 1392 A.D. the equinox will fall on the 3rd of the Ides of March (13 March). He discusses the theories of Gerland and of Marianus, pointing out errors in their assumptions—for example, showing that the Passover could not fall on a Friday. He quotes Ptolemy, Abrachis The medieval name for the Greek astronomer Hipparchus., Alpharaganus, Azarchel, Thebit, Albathani, and Rabbi Samuel. He knows algorism algorism The system of Arabic numerals and the decimal system., pointing out that ‘a minute in algorism, however, is taken as the 60th part of a unit’ original: "minutum in alchoarizmo tamen accipitur pro 60ᵃ parte rei", and is thus at the turning-point of the introduction of Arabic science: the last important work which shows no trace of it being the Massa Computi of Alexander de Villa Dei (1200 A.D.).

The first treatise on the Computus to make direct use of the new sources is that of John of Hollywood (Sacrobosco), written in 1235 A.D., several times printed (the date 1232 A.D. in the printed texts, folio 34, is an error). Sacrobosco was an indefatigable textbook writer, and had great gifts of exposition. He quotes Lucan, Ovid, Virgil, and Claudian.