[In the following essay, West surveys Alcuin's didactic works.]

Alcuin's writings have been preserved to us in tolerable completeness, and may be classified under a fourfold division. First come his theological works, which embrace the greater part, perhaps two-thirds, of all that he wrote. This theological portion may in turn be divided into four parts, exegetical, dogmatic, liturgical and practical, and lives of the saints. Of the remaining third of his writings, the major parts is embraced in his epistles, and least in extent are the didactic treatises and poems which make up the rest.

It will thus be seen that the greater part of Alcuin's writings have little connection with the history of education, and yet, even his theological works have incidental interest in this respect. Besides a few scanty gleanings from his exegetical writings, there are two of his practical treatises, On the Virtues and Vices and On the Nature of the Soul, which have a general connection with education, but beyond this there is nothing to be found. The epistles are of high value for the general history of the times, and more particularly for the abundant light which they shed upon the activity of Alcuin in his relation to the restoration of school-learning. The poems have a lesser value, but contain important help for the history of the school at York, where Alcuin was bred, and for his later career in Frankland. But the chief interest centres in his specifically didactic writings, for they contain most fully his general views on education as well as separate treatises on some of the liberal arts.

Let it be remarked at the outset that Alcuin is rarely an original writer, but usually a compiler and adapter, and even at times a literal transcriber of other men's work. He adds nothing to the sum of learning, either by invention or by recovery of what has been lost. What he does is to reproduce or adapt from earlier authors such parts of their writings as could be appreciated by the age in which he lived. Accordingly, while he must be refused all the credit that belongs to a courageous mind which advances beyond what has been known, he must yet be highly esteemed for the invaluable service he rendered as a transmitter and conserver of the learning that was in danger of perishing, and as the restorer and propagator of this learning in a great empire, after it had been extinct for generations. A passage from the letter dedicating his commentary on the Gospel of John to Gisela and Rotrud, states so aptly the timorously conservative attitude which appears in all his literary efforts, educational or otherwise, that it is worth citing here. He writes: “I have reverently traversed the storehouses of the early fathers, and whatever I have been able to find there, I have sent of it for you to taste. First of all, I have sought help from St. Augustine, who has devoted the greatest study to expounding the most holy words of this holy gospel. Next, I have drawn somewhat from the lesser works of St. Ambrose, that most holy doctor, and likewise from the Homilies of the distinguished father, Gregory the Great. I have also taken much from the Homilies of the blessed presbyter Bede, and from other holy fathers, whose interpretations I have here set forth. For I have preferred to employ their thoughts and words rather than to venture anything of my own audacity, even if the curiosity of my readers were to approve of it, and by a most cautious manner of writing I have made it my care, with the help of God, not to set down anything contrary to the thoughts of the fathers.”

Fortunately for his theological works, he depends mainly on the really great fathers of the Latin Church. Most of what he writes comes from Augustine, Jerome, Ambrose and Gregory the Great, while Bede is the chief of his later authorities. Of the Greek fathers, however, he knows nothing, except through Latin versions, and of these he makes no considerable use beyond drawing on a translation of Chrysostom to help in composing his commentary on the Epistle to the Hebrews. His literary sources are all Latin, nor is there any Greek to be found in what he wrote, apart from some citations copied from Jerome and occasional Greek words from elsewhere. On the educational side he depends mainly on Isidore and Bede, but with subsidiary help from Cassiodorus and the treatise On the Categories falsely ascribed to Augustine. He knew of Boethius, but made only indirect use of him. Martianus Capella is not so much as mentioned.

The separate educational treatises of Alcuin of undoubtedly genuine character are the following: On Grammar, On Orthography, On Rhetoric and the Virtues, On Dialectics, a Disputation with Pepin, and a tedious astronomical treatise, entitled De Cursu et Saltu Lunæ ac Bissexto. Three others are ascribed to him with less certainty: On the Seven Arts, A Disputation for Boys, and the so-called Propositions of Alcuin.

First and most important of these is his Grammar, which falls into two parts, the one a dialogue between Alcuin and his pupils on philosophy and liberal studies in general, and the other a dialogue between a young Saxon and a Frank on grammar, also conducted in the presence of Alcuin. The former dialogue is an original composition and contains in brief compass Alcuin's views on the end and method of education, and on the duty of studying the liberal arts, to which the entire dialogue serves as a general introduction. “Most learned master,” says one of the disciples, opening the dialogue, “we have often heard you say that Philosophy was the mistress of all the virtues, and alone of all earthly riches never made its possessor miserable. We confess that you have incited us by such words to follow after this excellent felicity, and we desire to know what is the sum of its supremacy and by what steps we may make ascent thereunto. Our age is yet a tender one and too weak to rise unhelped by your hand. We know, indeed, that the strength of the mind is in the heart, as the strength of the eyes is in the head. Now our eyes, whenever they are flooded by the splendor of the sun, or by reason of the presence of any light, are able to discern most clearly whatever is presented to their gaze, but without this access of light they must remain in darkness. So also the mind is able to receive wisdom if there be any one who will enlighten it.” Alcuin benignantly replies, “My sons, ye have said well in comparing the eyes to the mind, and may the light that lighteneth every man that cometh into this world enlighten your minds, to the end that ye may be able to make progress in philosophy, which, as ye have well said, never deserts its possessor.” The disciples assent to this and then renew their entreaty in the same figurative and flowery manner. “Verily, Master,” they urge, “we know that we must ask of Him who giveth liberally and upbraideth not. Yet we likewise need to be instructed slowly, with many a pause and hesitation, and like the weak and feeble to be led by slow steps until our strength shall grow. The flint naturally contains in itself the fire that will come forth when the flint is struck. Even so there is in the human mind the light of knowledge that will remain hidden like the spark in the flint, unless it be brought forth by the repeated efforts of a teacher.” Alcuin answers: “It is easy indeed to point out to you the path of wisdom, if only ye love it for the sake of God, for knowledge, for purity of heart, for understanding the truth, yea, and for itself. Seek it not to gain the praise of men or the honors of this world, nor yet for the deceitful pleasures of riches, for the more these things are loved, so much the farther do they cause those who seek them to depart from the light of truth and knowledge.”

After this elaborately courteous opening the dialogue proceeds to show that true and eternal happiness, and not transitory pleasure, is the proper end for a rational being to set before him, and that this happiness consists in the things that are proper and peculiar to the soul itself, rather than in what is alien to it. “That,” says Alcuin, “which is sought from without is alien to the soul, as is the gathering together of riches, but that which is proper to the soul is what is within, namely, the graces of wisdom. Therefore, O man,” he calls out in fervid apostrophe, “if thou art master of thyself, thou shalt have what thou shalt never have to grieve at losing, and what no calamity shall be able to take away. Why then, O mortals, do ye seek without for that which ye have within? How much better is it to be adorned within than without!” “What, then, are the adornments of the soul?” the disciples naturally inquire, and Alcuin answers: “Wisdom is the chief adornment, and this I urge you to seek above all things.”

Alcuin then explains that wisdom is itself eternal because it is an inseparable property of the soul, which is immortal, and in this differs from everything else of a secular character. But its pursuit is laborious. The scholar will not gain his reward without study, any more than the soldier without fighting or the farmer without plowing. It is an old proverb that the root of learning is bitter but the fruit is sweet, and so St. Paul asserts that “every discipline at the present is not joyous but grievous, yet afterwards it yieldeth the peaceable fruit of righteousness to them that were exercised in it.” Progress in secular knowledge is to be made by slow ascents, step by step, and is to lead to “the better ways of wisdom, which conduct to life eternal.” “May the divine grace guide and lead us,” exclaims Alcuin, “into the treasures of spiritual wisdom, that ye may be intoxicated at the fountain of divine plenty; that there may be within you a well of water springing up unto everlasting life. But, inasmuch as the Apostle enjoins that everything be done decently and in order, I think that ye should be led by the steps of erudition from lower to higher things until your wings gradually grow stronger, so that ye may mount on them to view the loftier visions of the pure ether.” The disciples are overwhelmed and humbly answer: “Master, raise us from the earth by your hand and set our feet upon the ascents of wisdom.” Alcuin accordingly proceeds to set before his pupils the seven ascents of the liberal arts in the following manner: “We have read how Wisdom herself saith by the mouth of Solomon, ‘Wisdom hath builded her house, she hath hewn out her seven pillars.’ Now although this saying pertains to the Divine Wisdom which builded for Himself a house (that is, the body of Christ in the Virgin's womb), and endued it with the seven gifts of the Holy Ghost, or may mean the Church, which is the House of God that shines with these gifts, yet Wisdom is also built upon the seven pillars of liberal letters, and it can in no wise afford us access to any perfect knowledge, unless it be set upon these seven pillars, or ascents.” Here is a distinct advance on Alcuin's part beyond the earlier writers on the liberal arts. Augustine had regarded them with qualified approval because they were helpful towards understanding divine truth. Cassiodorus saw in addition a mystical hint of their excellence in the fact that they were seven, and fortified his position by the text, “Wisdom hath builded her house, she hath hewn out her seven columns.” Alcuin takes up the text from Proverbs quoted by Cassiodorus, and finds in it the liberal arts as a matter of direct interpretation. Sapientia, or Wisdom, who had builded her house and hewn out her seven pillars, he mystically explains first of Christ the Divine Wisdom and next of the Church, each endued with the seven gifts of the Spirit, and then proceeds to his third application, which is that Sapientia, or Wisdom, which in the speech of his time often meant learning, was built upon the seven liberal arts. Augustine found the arts outside of Scripture, but deemed them helpful towards understanding it. Cassiodorus found in Scripture a mystical hint as to their excellence, and Alcuin gets them out of Scripture itself. It needs not to be told how influential such an interpretation would be on the fortunes of secular learning; for if the arts were once found in the Scriptures, there was no way of getting them out of the Church. Henceforth the proscriptive utterances of Tertullian, though echoed once and again down the middle ages,¹ could never dominate the Church.

But let us return to the dialogue. The pupils renew their request: “Open to us, as you have often promised, the seven ascents of theoretical discipline.” Alcuin replies: “Here, then, are the ascents of which ye are in search, and O that ye may ever be as eager to ascend them as ye now are to see them. They are grammar, rhetoric, dialectics, arithmetic, geometry, music, and astrology. On these the philosophers bestowed their leisure and their study.” Then he adds with a boldness which might well have alarmed him: “By reason of these philosophers the catholic teachers and defenders of our faith have proved themselves superior to all the chief heretics in public controversy,” and closes with the exhortation: “Let your youthful steps, my dearest sons, run daily along these paths until a riper age and a stronger mind shall bring you to the heights of Holy Scripture.”

Plainly in Alcuin's mind the arts were seven and only seven. They are the necessary ascents to the higher wisdom of the Scriptures. Not the fact that they are simply useful to the Scriptures, but indispensable, is what gives them such value in Alcuin's eyes. Much of the rhetoric in which his ideas exfoliate is childish enough, but it is impossible not to see behind it all a pure and gentle spirit, who valued the scanty sum of learning he possessed for no lesser reasons than the love of God, purity of soul, knowledge of truth, and even for its own sake, as against any pursuit of learning for the vulgar ends of wealth, popularity or secular honor.

The second dialogue in the treatise is properly grammatical. Two of Alcuin's pupils, a Saxon and a Frank, are beginners in the study, or, to put it in Alcuin's flowery language, “They but lately rushed upon the thorny thickets of grammatical density.” The Frank is a boy of fourteen years and the Saxon of fifteen. The master presides over their interrogations and answers. It is decided that grammar must begin with the consideration of what a letter is, though Alcuin stops on the way to expound the nature of words. It is defined as “the least part of an articulate sound.” The letters are the “elements” of language because they are ultimate and indivisible, and are built up first into syllables, and thereafter successively into words, clauses, and sentences. Letters are of two sorts, vowels and consonants, and are defined as follows: “The vowels are uttered by themselves and of themselves make syllables. The consonants cannot be uttered by themselves, nor can they of themselves make syllables.” But this sapient definition by antithesis, though accepted by the pupils, does not contain all that is to be said. There is an occult reason why the alphabet is divided into vowels and consonants, as Alcuin at once informs them. “The vowels,” he says, “are, as it were, the souls, and the consonants, the bodies of words.” “Now the soul moves both itself and the body, but the body is immovable apart from the soul. Such, then, are the consonants without the vowels. They may indeed be written by themselves, but they can neither be uttered nor have any power apart from vowels.” This explanation seems to satisfy them, for they pursue the matter no further. The peculiarities of the consonants are then discussed very much in the same manner, and the syllable is next taken up. It is defined as “a sound expressed in letters (vox litteralis), which has been uttered with one accent and at one breath.” The discussion of syllables falls into four parts, accent (accentus), breathings (spiritus), quantity (tempus), and the number of constituent letters. After these are discussed, the pupils entreat that before proceeding further they may be furnished with a definition of grammar. Alcuin accordingly tells them that “Grammar is the science of written sounds (litteralis scientia), the guardian of correct speaking and writing. It is founded on nature, reason, authority, and custom.” It has been well observed that this shrunken notion of grammar on the part of Alcuin as contrasted with the wide conception of the study that prevailed among the grammarians of the later Roman Empire is thoroughly characteristic of the intellectual feebleness of the later time. Instead of being both the art of writing and speaking, and also the study of the great poets and orators, it has now become only the former of these, a childish, technical and barren study. This appears more plainly as we advance to Alcuin's alarming enumeration of the parts of grammar. They are “words, letters, syllables, clauses, sayings, speeches, definitions, feet, accents, punctuation marks, critical marks, orthographies, analogies, etymologies, glosses, distinctions, barbarisms, solecisms, faults, metaplasms, figurations, tropes, prose, metres, fables, and histories.”

Words, letters and syllables, the first three of Alcuin's twenty-six parts of grammar, have been discussed, and each of the others is next defined. Alcuin then proceeds to the consideration of the different parts of speech in the following order: the noun, its genders, numbers, “figures” and cases; the pronoun, its genders, “figures,” numbers and cases; then the verb with its modes, “figures,” inflections and numbers; and the adverb with its “figures.” Lastly he treats of the participle, the conjunction, the preposition and the interjection. By “figures” Alcuin means the facts relating to the simplicity, composition or derivation of words. Thus, under his “figures” of verbs, the word cupio is in simple figure, concupio is in composite figure, and concupisco is in derivative figure, because it comes from concupio. The whole treatment of the parts of speech is similarly feeble in spirit and almost entirely restricted to etymology, so that Alcuin's Grammar is really devoid of orthography, syntax and prosody. Whatever is excellent in any way in his Grammar ought to be credited to Donatus, whom Alcuin follows. Isidore also furnishes him many a definition, but wherever this happens the treatise is apt to be childish. An example or two may suffice. The derivation of littera is said to be from legitera, “because the littera prepares a path for readers (leg entibus iter).” Feet in poetry are so named “because the metres walk on them,” and so on. Yet his book had great fame, and Notker, writing a century later, praised it, saying, “Alcuin has made such a grammar that Donatus, Nicomachus, Dositheus and our own Priscian seem as nothing when compared with him.”

In the manuscript copies of the Grammar there appear to be some slight parts missing at the end, so that it may have been more extended than we suppose; but there is no ground for thinking it covered more than etymology. However, Alcuin's next work is on orthography, and is properly a pendant to his Grammar. It is a short manual containing a list of words, alphabetically arranged, with comments on their proper spelling, pronunciation and meanings, and with remarks on their correct use, drawn to some extent from a treatise by Bede on the same subject. It is a sort of Antibarbarus, a help towards securing accuracy of form and propriety of use in the employment of Latin words, and must have been serviceable in the instruction of youth, but more so in the copying of ancient manuscripts. We may reasonably believe that Alcuin's scribes in the monastery of Tours, busily engaged in recovering one and another patristic and classical writer, were guided by his book in the purification of the copies they made, and for which the monastery at Tours became so famous. “Let him who would publish the sayings of the ancients read me, for he who follows me not will speak without regard to law,”² is the translation of the couplet which stands at the head of the Orthography and indicates its purpose. It is Alcuin's attempt to purge contemporary Latin of its barbarisms. He puts his comments oddly enough. “Write vinea,” he says, “if you mean a vine, with i in the first syllable and e in the second. But if you mean pardon, write venia with e in the first syllable and i in the second. Write vacca with a v, if you mean a cow, but write it with a b if you mean a berry.” In the same way be careful to write vellus with a v to mean wool, and bellus, if you mean fair. Similarly, when writing, do not confuse vel with fel which means gall, or with Bel, the heathen god. By no means consider benificus, a man of good deeds, the same as venificus, a poisoner. So bibo and vivo are not to be mixed. Such examples indicate that Alcuin had to struggle against “rusticity” in pronunciation as well as in writing,—a rusticity which was due to the modifying influence of the barbarous Tudesque upon the pronouncing of Latin,—an influence which, even in Alcuin's time, was altering the forms of words in a manner which presaged the final demolition of Latin prior to the rise of French.

Some of the definitions are quite amusing. Coelebs, a bachelor, is defined as “one who is on his way ad cœlum,” evidently the true monk. “Write œquor with a diphthong,” for the reason that it is derived from aqua. Mālus, a mast, is to have a long a, but “a mălus homo ought to have a short a.”

It is on the Grammar and Orthography that Alcuin's didactic fame principally rests, and justly so, for in spite of their puerile character they did more good service than anything else he wrote. Let it be remembered that the tall, blue-eyed barbarians, whom Alcuin was aiming to civilize, were but little children when it came to school-learning. Let it also be remembered that Alcuin, divesting himself of all vanity and conceit, wisely and even humbly set before them what they could learn, and the only thing they could learn at the start. Even his master, Charles, had to toil painfully to bend his fingers, stiffened with long use of the sword, to the clerkly task of writing, and confessed that he acquired the art with great difficulty.

The dialogue On Rhetoric and the Virtues has for its two interlocutors Charles and Alcuin, and was composed in response to a request from the king. Alcuin instructs him in the elements of the rhetorical art with special reference to its applications in the conduct and settlement of disputes in civil affairs, and closes with a short description of the four cardinal virtues,—prudence, justice, fortitude and temperance. It is, therefore, not strictly a book on rhetoric, but rather on its applications. It is based on rhetorical writings of Cicero, which are rehandled by Alcuin, and always with loss and injury to his originals. The hand of Isidore is likewise visible in places, and contributes to the general deterioration. If the Grammar was rudimentary and ill-arranged, the Rhetoric suffers yet more from its miscellaneous presentation of ill-digested bits of rhetoric, and from its greater dulness of style. Moreover, it is less jocose in spirit than are parts of the Grammar, though Alcuin's specimen of sophistical reasoning, which he produces for the instruction of the king, is indeed comical. “What art thou?” asks Alcuin, and after Charles answers, “I am a man (homo),” the dialogue goes on as follows:—

ALCUIN.
See how thou hast shut me in.
CHARLES.
How so?
ALCUIN.
If thou sayest I am not the same as thou, and that I am a man, it follows that thou art not a man.
CHARLES.
It does.
ALCUIN.
But how many syllables has homo?
CHARLES.
Two.
ALCUIN.
Then art thou those two syllables?
CHARLES.
Surely not; but why dost thou reason thus?
ALCUIN.
That thou mayest understand sophistical craft and see how thou canst be forced to a conclusion.
CHARLES.
I see and understand from what was granted at the start, both that I am homo and that homo has two syllables, and that I can be shut up to the conclusion that I am these two syllables. But I wonder at the subtlety with which thou hast led me on, first to conclude that thou wert not a man, and afterward of myself, that I was two syllables.

After the Rhetoric comes the Dialectics, which is in part extracted or abridged from Isidore, who in his turn had taken from Boethius, and in part copied almost solidly from the supposed work of Augustine on the Categories of Aristotle. If possible, it is less original than the Rhetoric, but is at least what its title indicates,—an attempt to say something about dialectics. However, as the age of medieval logic had not yet begun in earnest, Alcuin's treatise was perhaps as much as the times would bear, especially in view of the existing indifference or antagonism in the Church to the subtleties of Aristotle. In conjunction with the Grammar and Rhetoric, it may be taken as constituting such instruction in the trivium as was given in the palace school.

Interesting in its way as a specimen of Alcuin's teaching is his dialogue written for Pepin, then a young prince of sixteen years, and entitled The Disputation of Pepin, the Most Noble and Royal Youth, with Albinus the Scholastic. It rambles without plan and allegorizes without restraint. Parts of it run as follows:—

PEPIN.
What is writing?
ALBINUS.
The guardian of history.
PEPIN.
What is language?
ALBINUS.
The betrayer of the soul.
PEPIN.
What generates language?
ALBINUS.
The tongue.
PEPIN.
What is the tongue?
ALBINUS.
The whip of the air.
PEPIN.
What is air?
ALBINUS.
The guardian of life.
PEPIN.
What is life?
ALBINUS.
The joy of the happy; the expectation of death.
PEPIN.
What is death?
ALBINUS.
An inevitable event; an uncertain journey; tears for the living; the probation of wills; the stealer of men.
PEPIN.
What is man?
ALBINUS.
The slave of death; a passing traveler; a stranger in his place.
PEPIN.
What is man like?
ALBINUS.
An apple.

Let us understand this short and sudden definition. Alcuin means that man hangs like an apple on a tree without being able to know when he is to fall.

The questions on natural phenomena are not less instructive:—

PEPIN.
What is water?
ALBINUS.
A supporter of life; a cleanser of filth.
PEPIN.
What is fire?
ALBINUS.
Excessive heat; the nurse of growing things; the ripener of crops.
PEPIN.
What is cold?
ALBINUS.
The febricity of our members.(3)
PEPIN.
What is frost?
ALBINUS.
The persecutor of plants; the destruction of leaves; the bond of the earth; the source of waters.
PEPIN.
What is snow?
ALBINUS.
Dry water.
PEPIN.
What is the winter?
ALBINUS.
The exile of summer.
PEPIN.
What is the spring?
ALBINUS.
The painter of the earth.
PEPIN.
What is the autumn?
ALBINUS.
The barn of the year.

After more of this same sort, the dialogue rapidly runs into puzzles and then closes.

The treatise De Cursu et Saltu Lunœ ac Bissexto needs no special notice. It deals with the method of calculating the changes of the moon with special reference to the determination of Easter, and is compiled for the instruction of the king. Bede is the principal authority.

There remain for consideration the three works somewhat doubtfully attributed to Alcuin. The first is entitled On the Seven Arts, and is a fragment derived from the work of Cassiodorus on the same subject. But only the first two parts, grammar and rhetoric, are described, and they are in part copied and in part abridged from their original. Alcuin may have taken them after his manner from Cassiodorus, without any thought of laying claim to the production as his own. But whether he did this or not, the fragment is useful in that it shows that the book of Cassiodorus On the Arts and Disciplines of Liberal Letters was consulted in the time of Alcuin. The so-called Disputation of the Boys is likewise doubtful. It is a set of questions and answers on Scriptural subjects and may at least serve as another example of the catechetical method of that time. Much more interesting is the set of puzzles entitled The Propositions of Alcuin, the Teacher of the Emperor Charles the Great, for Whetting the Wit of Youth. Unfortunately, the Venerable Bede had written just such a treatise, which is here closely copied. But this need not weigh against the probability of Alcuin's taking and using it. But whether he did really do so, or whether copyists attributed it to him, is a matter of little moment, for it well represents the character of the teaching of the time. It is, in fact, not unlikely that these are the propositions which Alcuin enclosed in a letter to Charles and styled “certain figures of arithmetical subtlety sent for the sake of amusement.” Charles himself refers to his excursions with Alcuin “through the plains of arithmetical art,” and Alcuin speaks in one of his poems of “studying the fair forms of numbers” with Charles. The propositiones consist in the main of very simple exercises, all solved by painfully rudimentary methods. Not one of them exhibits an apprehension on Alcuin's part of any mathematical idea or formula. Forty-five of the fifty-three propositions may, by courtesy, be styled exercises in reckoning. Each one is twofold in its structure, containing the propositio and its attached solutio. They are put in the style of a master towards his pupils, the proposition generally culminating in some such formula as “let him solve this who can” (solvat qui potest), or, “let him that understandeth say how we must divide,” or simply, “let him who is able answer.” The propositions themselves are various, but are confined to a few kinds of questions, all put in concrete form and sometimes jocosely. Occasionally there is no regard paid to the probability of the state of things pictured in the proposition. Thus a king is represented as gathering an army in geometrical progression, one man in the first town, two in the second, four in the third, eight in the fourth, and so on through thirty towns. The total is 1,073,741,823 soldiers, an army whose number might well amuse the imperial pupil. Of course Alcuin is entirely ignorant in this problem of any formula for the sum of a geometrical progression, and so he proceeds to count it all out. The solutions are alarmingly infantile in their methods. The numerals are Roman, and this adds enormously to the slowness of working the examples. The only processes employed are the simplest operations of addition, multiplication, and division, commonly neglecting all “remainders” in division, and there is rarely any use of subtraction. Common fractions of a very elementary sort are at times used, but no fractional symbols are employed. They are spoken of as “the half,” “the half of the half,” “the third part,” “the sixth part,” and “the eleventh part.” They are not treated as fractions, but as divisors. “Aliquot parts” frequently figure in constructing the puzzles, and there are some examples of finding areas of triangles, always isosceles, and of quadrangular and “round” figures. His forty-second proposition is unique, in being clever. There is a ladder with one hundred steps. One dove is on the first step, two on the second, three on the third, and so on. How many doves are on the ladder? On the first and ninety-ninth steps there are accordingly one hundred doves, and so on the second and ninety-eighth steps. Proceeding thus through the pairs of steps, we find forty-nine pairs of steps, each containing one hundred doves, with the fiftieth and hundredth steps omitted, which last contain jointly one hundred and fifty doves. The total is accordingly five thousand and fifty. In this example Alcuin unconsciously goes through the process which underlies arithmetical progression. Some of the propositions are properly algebraical, involving the simple equation in one unknown quantity, but of course he is not aware of this and works them out mechanically.

Not only are the methods of solution employed so crude, but no principle of arithmetic ever seems to dawn upon his mind. Cumbrous manipulation of particular problems is his only accomplishment. The character of most of the problems solved is depressing to think about. Of course they are concrete and meant to be witty. They are “ad acuendos juvenes.” They are “figures of arithmetical subtlety” meant to whet the wit of youth, but it is surely startling to read of a sty that holds 262,304 pigs, as one which some unknown quidam has constructed, starting with one sow and a litter of seven;—and all this invented to get an example in multiplication. Other examples are equally silly without being funny. Quadrangular houses are to be put into a triangular city so as to fill the triangle completely, or into a “round” city with a similar result, the answers being worked out in entire unconsciousness of the logical impossibility involved. Leaving the semi-arithmetical exercises, we have a variety of trivial puzzles remaining. After an ox has plowed all day, how many steps does he take in the last furrow? The answer is, “none, because the last furrow covers his tracks.” This would serve as well for the first or for any or for all furrows. When a farmer goes plowing, and has turned thrice at each end of his field, how many furrows has he drawn? Alcuin says six, but the Venerable Bede said seven, and the Venerable Bede was right, if only the farmer starts in his first furrow on a straight line from one end of the field and finishes his last furrow. In another proposition Alcuin requests that three hundred pigs be killed in three batches on successive days, an odd number to be killed each day. But as three odd numbers cannot add up an even sum, he has an impregnably insoluble proposition. “Ecce fabula!” he cries in glee, “here's a go! There is no solution. This fable is only to provoke boys.” He adds a scholium at the end to the effect that the proposition will work in the same way if only thirty pigs are taken.

Let not Alcuin's treatises be judged apart from the environment of his times. The age, whose intellect he addressed, thought as a child and spake as a child, and to have presented anything else was to present what it could not understand. It was to invite certain failure in any attempt made in behalf of learning. It was a necessary first stage in the evolution of modern European culture that some one should at some time teach the rudiments to barbarous western Europe, and that Alcuin did this and recognized the limitations under which learning would be received, is not so much a proof of mediocrity as of his sagacity. He was not a writer of genius, nor of originality, nor of vast learning, but he was a man of great practical sense.

Nor should his properly didactic writings furnish the basis for a judgment as to the educational attainments of their author, except as exhibiting the substance of his formal instruction. If this is all we have, then the best that can be said for his teaching is that he gave western Europe imperfectly understood fragments of the wisdom of the ancients, and is more significant from the fact that he makes plain the intellectual darkness of the time than that he is introducing a learning that relieves it. Happily, there is another side to his educational activity which appears in many of his letters. They give us many a glimpse of his utter unselfishness, his purity and gentleness, his fidelity to the spiritual welfare of his pupils, and his never-ceasing personal anxiety that their lives and minds should be moulded by the spirit of Christ. Here is the true Alcuin, not the reviver of a decayed and fragmentary school learning, but the inspirer of Christian ideals, both as to studies and conduct, in an age when both seemed to be disappearing from the face of Europe.

Alcuin's eye followed his pupils in their later life and his hand of support or restraint was outstretched to them again and again. When one of them, who was fond of high living and the company of actors, was going to Italy, he cautioned him soberly not only as to the care of his health in that climate, but as to his general conduct. “My dearest son,” he writes, “great is my longing for your health and prosperity. I therefore desire to send you a letter of exhortation in place of the spoken words of paternal affection, beseeching you to keep God before your eyes and in your remembrance with entire devotion of mind and virtuous intention. Let Christ be on your lips and in your heart. Act not childishly and follow not boyish whims, but be perfect in all uprightness and continence and moderation, that God may be glorified by your works, and that the father who bore you may not be made ashamed. Be temperate in food and drink, regarding rather your own welfare than any carnal delight or the vain praise of men, which profiteth not if your acts be displeasing to God. It is better to please God than to please actors, to look after the poor than to go after buffoons. Let your feastings be decorous, and those who feast with you be religious. Be old in morals, though young in years.” Another letter written from Tours in Alcuin's old age to the young princes still at the palace, when Charles, their father, was away in Italy, is both tender and playful in its affection. It reads in part: “To my dearest sons in Christ their father wisheth eternal welfare. I would write you a great deal if only I had a dove or a raven that would carry my letter on its faithful pinions. Nevertheless, I have given this little sheet to the winds, that it may come to you by some favoring breeze, unless, perchance, the gentle zephyr change to an eastern blast. But arise, O south or north or any wind! and bear away this little parchment to bid you greeting and to announce our prosperity, and our great desire to see you well and whole, even as the father desires his sons to be. Oh, how happy was that day when amid our labors we played at the sports of letters! But now all is changed. The old man has been left to beget other sons, and weeps for his former children that are gone.”

In his little book, On The Virtues and Vices, sent to Count Wido for his moral instruction, he commends to him the reading of the Scriptures in words of quiet serenity and deep spirituality. “In the reading of the Holy Scriptures,” he writes, “lies the knowledge of true blessedness, for therein, as in a mirror, man may consider himself, what he is and whither he goes. He who would be always with God ought frequently to pray and frequently to read, for when we pray we are speaking with God, and when we read God is speaking to us.” More than one letter of Alcuin's to wayward pupils has come to us. To one of them he writes in the following manner: “A mourning father sends greeting to his prodigal son. Why hast thou forgotten thy father who taught thee from infancy, imbued thee with the liberal disciplines, fashioned thy morals, and fortified them with the precepts of eternal life, to join thyself to the company of harlots, to the feastings of revellers, to the vanities of the proud? Art not thou that youth that was once a praise in the mouth of all, a delight to their eyes, and a pleasure to their ears? Alas! alas! now art thou a reproach in the mouth of all, the curse of their eyes and the detestation of their ears. What has so overturned thee but drunkenness and luxury? Who, O gracious boy, thou son and light of the Church, has persuaded thee to feed the swine and to eat of their husks? Arise, my son, arise, and return to thy father and say not once, but often, ‘Father, I have sinned against heaven and in thy sight.’”

Such are a few out of many instances where Alcuin has left on record the secret of his power over the character of his pupils. He had been their master in things scholastic, but he was also their father in things spiritual.

Notes

1. As late as the thirteenth century we read in a regulation of the Dominican order:

   “In libris gentilium philosophorum non studeat, et si ad horam suscipiat saeculares scientias, non addiscat, nec artes quas liberales vocant.”

2. Me legat antiquas vult qui proferre loquelas.
   Me qui non sequitur, vult sine lege loqui.

3. This “cold” is apparently a chill.