Algebra was apparently unknown to the Irish monks during the period under investigation and was probably not introduced into Europe until the twelfth century.[466]
GEOMETRY:
Up to the tenth century, the age of Gerbert, a knowledge of Geometry in our sense of the term hardly existed in Western Europe. In fact the term seems to have been used in its etymological meaning and not in the sense the Greeks understood it. We have found no evidence to warrant the assumption that Euclidean Geometry was taught in those early Irish monastic schools. But on the other hand an examination of the characteristic Irish style of ornament suggests that the Irish artist had at least a good working knowledge of practical Geometry. Possibly the amount of knowledge of theoretical Geometry did not extend beyond the narrow[467] limits of the works of Capella,[468] Cassiodorus,[469] and Isadore of Seville[470]—writers well known to Irish scholars as we have seen.
GEOGRAPHY:
If the mathematical science of Geometry was still undeveloped in the West geography, topography and cosmography made up the deficiency. It was but natural that the Irish monks, the greatest voyagers of their time, should be interested in the study of foreign lands. We have an instance of this in the case of Adamnan who wrote his De Locis Sanctis from the dictation of Arculfus, a Frankish bishop who had visited Palestine.[471] Bede based his work bearing a similar name on Adamnan’s volume. This work of Adamnan with that of Bede continued to be the only source of information of the geography, Christian antiquities, and customs of Palestine until the Crusades gave Western Europe a more acute and active interest in that distant, inhospitable region.[472] We have referred to a curious geographical poem[473] which was evidently used as a text in the monastic schools of Ireland. It contained probably all the geography that was taught prior to the tenth century. The tenth century map of the world[474] drawn in England for an Anglo-Saxon is supposed to have been the work of an Irish artist and further illustrates the state of geographical knowledge of the times. The more ambitious treatise of Dungal, De Mensura Orbis Terrarum, which will be described in the next chapter, marks a new departure in geographical texts—hitherto mere compendiums—inasmuch as it introduces new matter, is more critical, “up-to-date” and altogether a commendable attempt for a ninth century scholar.
Astronomy had a double interest for the Irish monks. Being great travellers in an age when they had no compass to direct their way the “study of the stars” was a matter of practical interest and possibly they were more observant of the courses of the heavenly bodies than the majority of us are to-day. Again, the ability to compute the date of Easter was a matter of great importance in ecclesiastical circles in those days. The controversies which centred around the Easter question caused many Irish monks to give special attention to practical methods of computing the date of Easter. They were also led to examine the history of the different cycles in use and finally they were led to inquire into the theoretical aspect of the science of Astronomy. In the present chapter we referred to the famous Paschal Epistle of Cummian Fada which showed that he was at one and the same time an accomplished classical scholar and an astronomer of no mean ability versed in all astronomical literature of his time. Other great astronomers were Virgilius, Dicuil and Dungal, of whom we shall have something to say in our next chapter when dealing with the scope of Irish monastic scholarship. Of all the secular sciences Astronomy was perhaps the most popular with Irish monastic scholars the superiority of whose scholarship in this regard is acknowledged by all writers of the early Middle Ages.[475]
We see, then, that though the actual amount of mathematical and scientific knowledge possessed by the Irish monks was small they freely taught all that was known at the time in Western Europe and, limited as was their educational equipment, we may safely conclude that it represented the maximum attainments in western scientific knowledge prior to the tenth century.
While we have no means of determining the precise way in which the curriculum was organised, we may safely conclude that it embraced the following groups of studies:
1. Vernacular Studies: The Irish language, its grammar, metrics, literature both secular and religious, prose and poetry, history, antiquities, etc.[476]
2. Christian Studies: Theology, especially the study of the Scriptures with the commentaries of the Fathers thereon, and in the ninth century at least the study of Dialectics and Philosophy was pursued with success.