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the greatest minds of the Middle Ages, Abbot for years at Fulda, and a mediaeval textbook writer of importance, has left us a good description of each of the Seven Liberal Arts studies as they were developed in his day, and their use in the Christian scheme of education (R. 74).

 

I. THE TRIVIUM

 

Of the three studies forming the Trivium, grammar always came first as the basal subject. No uniformity existed for the other two.

 

1. GRAMMAR. The foundation and source of all the Liberal Arts was grammar, it being, according to Maurus, “the science which teaches us to explain the poets and historians, and the art which qualifies us to speak and write correctly” (R. 74 a). In the introduction to an improved Latin grammar, [3] published about 1119, grammar is defined as “The doorkeeper of all the other sciences, the apt expurgatrix of the stammering tongue, the servant of logic, the mistress of rhetoric, the interpreter of theology, the relief of medicine, and the praiseworthy foundation of the whole quadrivium.” Figure 45, from one of the earliest books printed in English, also emphasizes the great importance of grammar with the words: “Wythout whiche science (s)ycherly alle other sciences in especial ben of lytyl recomme(d).” In addition to grammar in the sense we know the study to-day, grammar in the old Roman and mediaeval mind also included much of what we know as the analytical side of the study of literature, such as comparison, analysis, versification, prosody, word formations, figures of speech, and vocal expression (R. 76). These were considered necessary to enable one to read understandingly the Holy Scriptures, and hence, “though the art be secular,” says Maurus, “it has nothing unworthy about it.”

 

[Illustration: FIG. 45. A SCHOOL: A LESSON IN GRAMMAR

(After a woodcut printed by Caxton in The Mirror of the World, 1481 (?).

From Blades’ Life and Typography of William Caxton, ii, Plate LVI) This is a good example of early English printing. Can you read it? This “Old English,” like the German type (see Fig. 26), shows the change in Latin letters which came about with the copying of manuscripts during the Middle Ages. After the invention of printing the English soon returned to the Latin forms; the Germans are only now doing so.]

 

The leading textbook was that of Donatus, [4] written in the fourth century, and Donatus (_donat_) and grammar came to be synonymous terms.

The text by Priscian, [5] written in the sixth century, was also extensively used. The treatment in each was catechetical in form; that is, questions and answers, which were learned. The text was of course in Latin, and the teacher usually had the only copy, so that the pupils had to learn from memory or copy from dictation. The cost of writing-material usually precluded the latter method. After sufficient ability in grammar had been attained, simple reading exercises or colloquies (R. 75), usually of a religious or moralizing nature, were introduced, though where permitted the Latin authors, especially Vergil, [6] were read. At Saint Gall, in Switzerland, and at some other places, many Latin authors were read; at Tours, on the other hand, we find the learned Abbot Alcuin saying to the monks: “The sacred poets are sufficient for you; there is no reason why you should sully your mind with the rank luxuriance of Vergil’s verse.”

 

2. RHETORIC. Rhetoric, as defined by Maurus, was “the art of using secular discourse effectively in the circumstances of daily life,” and enabling the preacher or missionary to put the divine message in eloquent and impressive language (R. 74 b). Much of the old Roman rhetoric had been taken over by grammar, but in its place was added a certain amount of letter and legal documentary writing. The priest, it must be remembered, became the secretary and lawyer of the Middle Ages, as well as the priest, and upon him devolved the preparation of most of the legal papers of the time, such as wills, deeds, proclamations, and other formal documents.

Accordingly the art of letter-writing [7] and the preparation of legal documents were made a part of the study of rhetoric, and some study of both the civil (“worldly”) and canon (church) law was gradually introduced.

 

3. DIALECTIC. Dialectic, or logic, says Maurus, is the science of understanding, and hence the science of sciences (R. 74 c). By means of its aid one was enabled to unmask falsehood, expose error, formulate argument, and draw conclusions accurately. The study was one of preparation for ethics and theology later on. Extracts from the works of Aristotle, prepared by Boethius, and later his complete works, constituted the texts used. While grammar was the great subject of the seven during all the early Middle Ages, dialectic later came to take its place. After the rise of the universities and the organization of schools of theology, with theology more of a rational science and less a matter of dogma, dialectic came to hold first place in importance as a preparation for the disputations of the later Middle Ages. Theological questions formed the practical exercises, and the schools doing most in dialectic attracted many students because of this.

 

These three studies, constituting the Trivium, based as they were directly on the old Roman learning and schools, contained more that was within the teaching knowledge of the time than did the subjects of the Quadrivium, and also subject-matter which was much more in demand.

 

II. THE QUADRIVIUM

 

The trivial studies, in most cases before the thirteenth century, sufficed to prepare for the study of theology, though those few who desired to prepare thoroughly also studied the subjects of the quadrivium. In schools not offering instruction in this advanced group some of the elements of its four studies were often taught from the textbooks in use for the Trivium. Particularly was this the case during the early Middle Ages, when the knowledge of arithmetic, geometry, and astronomy possessed by western Europe was exceedingly small. No regular order in the study of the subjects of this group was followed.

 

4. ARITHMETIC. Naturally little could be done in this subject as long as the Roman system of notation was in use (see footnote, i, p. 64), and the Arabic notation was not known in western Christian Europe until the beginning of the thirteenth century, and was not much used for two or three centuries later. So far as arithmetic was taught before that time, it was but little in advance of that given to novitiates in the monasteries, except that much attention was devoted to an absurd study of the properties of numbers, [8] and to the uses of arithmetic in determining church days, calculating the date of Easter, and interpreting passages in the Scriptures involving measurements (R. 74 d). The textbook by Rhabanus Maurus On Reckoning, issued in 820, is largely in dialogue (catechetical) form, and is devoted to describing the properties of numbers, “odd, even, perfect, imperfect, composite, plane, solid, cardinal, ordinal, adverbial, distributive, multiple, denunciative, etc.”; to pointing out the scriptural significance of number; [9] and to an elaborate explanation of finger reckoning, after the old Roman plan (see p. 65). Near the end of the tenth century Gerbert, [10] afterwards Pope Sylvester II, devised a simple abacus-form for expressing numbers, simple enough in itself, but regarded as wonderful in its day. This greatly simplified calculation, and made work with large numbers possible. He also devised an easier form for large divisions.

 

Gerbert’s form for expressing numbers may be shown from the following simple sum in addition:

 

Arabic Form Roman Form Gerbert’s Form

M C X I

 

1204 MCCIV I II IV

538 DXXXVIII V III VIII 2455 MMCCCCLV II IV V V

619 DCXIX VI I IX

–— ––– ––––––-

4816 MMMMDCCCXVI IV VIII I VI No study of arithmetic of importance was possible, however, until the introduction of Arabic notation and the use of the zero.

 

5. GEOMETRY. This study consisted almost entirely of geography and reasoning as to geometrical forms until the tenth century, when Boethius’

work on Geometry, containing some extracts from Euclid, was discovered by Gerbert. The geography of Europe, Asia, and Africa also was studied, as treated in the textbooks of the time, and a little about plants and animals as well was introduced. The nature of the geographic instruction may be inferred from Figure 46, which reproduces one of the best world maps of the day. The main geographical features of the known world can be made out from this, but many of the mediaeval maps are utterly unintelligible.

 

To illustrate the reasoning as to geometrical forms which preceded the finding of Euclid we quote from Maurus, who says that the science of geometry “found realization also at the building of the tabernacle and the temple; and that the same measuring rod, circles, spheres, hemispheres, quadrangles, and other figures were employed. The knowledge of all this brings to him, who is occupied with it, no small gain for his spiritual culture.” (R. 74 e). After Gerbert’s time some geometry proper and the elements of land surveying were introduced. The real study of geometry in Europe, however, dates from the twelfth century, when Euclid was translated into Latin from the Arabic.

 

6. ASTRONOMY. In astronomy the chief purpose of the instruction was to explain the seasons and the motions of the planets, to set forth the wonders of the visible creation, and to enable the priests “to fix the time of Easter and all other festivals and holy days, and to announce to the congregation the proper celebration of them.” (R. 74 g).

 

[Illustration: FIG. 46. AN ANGLO-SAXON MAP OF THE WORLD

(From a tenth-century map in the British Museum) This is one of the better maps of the period. Note the mixture of Biblical and classical geography (Bethlehem, Jerusalem, Pillars of Hercules), and the animal life (lion) introduced in the upper corner. The Mediterranean Sea in the center, the Greek islands, the British isles, the Italian peninsula, the Nile, and the northern African coast are easily recognized.

Western Europe, the best-known part of the world at that time, is very poorly done.]

 

Even after Ptolemy’s Mechanism of the Heavens (p. 49) and Aristotle’s On the Heavens had filtered across the Pyrenees from the Saracens, in the eleventh century, the Ptolemaic theory of a flat earth located at the center of the heavenly bodies and around which they all revolved, while a very pleasing theological conception, was absolutely fatal to any instruction in astronomy worth while and to any astronomical advance. All mediaeval astronomy, too, was saturated with astrology, as the selection on the motion of the heavenly bodies reproduced from Bartholomew Anglicus shows (R. 77 b), and the supernatural was invoked to explain such phenomena as meteors, comets, and eclipses. The Copernican theory of the motion of the heavenly bodies was not published until 1543, and all our modern ideas date from that time.

 

Physics was often taught as a part of the instruction in astronomy, and consisted of lessons on the properties of matter (R. 77 a) and some of the simple principles of dynamics. Little else of what we to-day know as physics was then known.

 

7. MUSIC. Unlike the other studies of the Quadrivium, the instruction in music was quite extensive, and from early times a good course in musical theory was taught (R. 74 f). Boethius’ De Musica, written at the beginning of the sixth century, was the text used. Music entered into so many activities of the Church that much naturally was made of it. The organ, too, is an old instrument, going back to the second century B.C., and the organ with a keyboard to the close of the eleventh century. This

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