Most people are sure to think that, at least in the matter of inventions, ours is the only time worth considering. The people of the Thirteenth Century, however, made many wonderful inventions and adaptations of mechanical principles, as well as many ingenious appliances. Their faculty of invention was mainly devoted to work in other departments besides that of mechanics. They were inventors of designs in architecture, in decoration, in furnishings, in textiles, and in the beautiful things of life generally. Their inventiveness in the arts and crafts was especially admirable and, indeed, has been fruitful in our time, since, with the reawakening in this matter, we have gone back to imitate their designs. Good authorities declare these to be endless in number and variety. Such mechanical inventions as were {457} needed for the building of their great cathedrals, their munic.i.p.al buildings, abbeys, castles, piers, bridges and the like were admirably worked out. Necessity is the mother of invention, and whenever needs a.s.serted themselves, these old generations responded to them, very successfully. There are, however, a number of inventions that would attract attention even, in the modern time for their practical usefulness and ingenuity. With the growth of the universities writing became much more common, textbooks were needed, and so paper was invented. With the increase of reading, to replace teaching by hearing, spectacles were invented. Time became more precious, clocks were greatly improved, and we hear of the invention of something like an alarm clock, an apparatus which, after a fixed number of hours, woke the monk of the abbey whose duty it was to arouse the others. Organs for churches were greatly improved, bells were perfected, and everything else in connection with the churches so well fashioned that we still use them in their Thirteenth Century forms. Gunpowder was not invented, but a great many new uses were found for it, and Roger Bacon even suggested, as I have said, that sometime explosives would enable boats to move by sea without sails or oars, or carriages to move on land without horses or men. Roger Bacon even suggested the possibility of airships, described how one might be made, the wings of which would be worked by a windla.s.s, and thought that he could make it. His friend and pupil, Peregrinus, invented the double pivoted compa.s.s, and, as the first perpetual-motion faddist, described how he would set about making a magnetic engine that he thought would run forever. When we recall how much they accomplished mechanically in the construction of buildings, it becomes evident that any mechanical problem that these generations wanted solved they succeeded in solving very well. What they have left us as inventions are among the most useful appliances that we have. Without paper and without spectacles, the intellectual world would be in a sad case, indeed. Many of the secrets of their inventions in the arts and crafts have been lost, and, in spite of all our study, we have not succeeded in rediscovering them.

XXIII. INDUSTRY AND TRADE.

We are rather inclined to think that large organizations of industry and trade were reserved for comparatively modern times. To think so, however, is to forget the place occupied by the monasteries and convents in the olden time. We have heard much of the lazy monks, but only from those who know nothing at all about them. Idleness in the monasteries was one of the accusations made by the commission set to furnish evidence to Henry VIII. on which he might suppress the monasteries, but every modern historian has rejected the findings of that commission as false. Many forms of manufacture were carried on in the monasteries and convents. They were {458} the princ.i.p.al bookmakers and bookbinders. To a great extent they were the manufacturers of art fabrics and arts-and-crafts work intended for church use, but also for the decoration of luxurious private apartments. Most of us have known something of all this finer work, but not that they had much to do with cruder industries also. They were millers, cloth-makers, brush- and broom-makers, shoemakers for themselves and their tenantry; knitting was done in the convents, and all the finer fancy work. A recent meeting of the Inst.i.tute of Mining Engineers in England brought out some discussion of coal mining in connection with the early history of the coal mines in England. The records of many of the English monasteries show that in early times the monks knew the value of coal, and used it rather freely. They also mined it for others. The monks at Tynemouth are known to have been mining coal on the Manor of Tynemouth in 1269, and shipping it to a distance. At Durham and at Finchale Abbey they were doing this also about the same time. It would require special study to bring out the interesting details, but there is abundant material not alone for a chapter, but for a volume on the industries of the Thirteenth Century, which, like the education and the literature and the culture of the time, we have thought undeveloped, because we knew nothing of them.

The relation of the monasteries to trade, domestic and foreign, is very well brought out in a paragraph of Mr. Ralph Adams Cram's book on "The Ruined Abbeys of Great Britain" (New York, The Churchman Co., 1905), in which he describes the remains at Beaulieu, which show the place of that monastery, not by any means one of the most important in England, in trade. For the benefit of their tenantry others had done even more.

"Some idea of the power of one of these great monasteries may be gained from traces still existing of the center of trade built up by the monks outside their gates. Here, at the head of tide water, in a most out-of-the-way spot, a great stone quay was constructed, to which came ships from foreign lands. Near by was a great marketplace, now, as then, called Cheapside, though commerce exists there no longer. At the height of monastic glory the religious houses were actually the chief centers of industry and civilization, and around them grew up the eager villages, many of which now exist, even though their impulse and original inspiration have long since departed. Of course, the possessions of the abbey reached far away from the walls in every direction, including many farms even at a great distance, for the abbeys were then the great landowners, and beneficent landlords they were as well, even in their last days, for we have many records of the cruelty and hardships that came to the tenants the moment the stolen lands came into the hands of laymen."

XXIV. FAIRS AND MARKETS.

A chapter might well have been devoted to showing the significance of those curious old inst.i.tutions, the fairs and market days of the {459} Middle Ages. The country folk flocked into town, bringing with them their produce, and found there gathered from many parts merchants come to exchange and barter. The expense of maintaining a store all the year around was done away with, and profits did not have to be large.

Exchanges were direct, and the profits of the middlemen were to a great extent eliminated. It was distinctly to the advantage of the poor, for the expenses of commerce were limited to the greatest possible extent, and every advantage accrued to the customer.

Besides, these market days became days of innocent merriment, amus.e.m.e.nt and diversion. Wandering purveyors of amus.e.m.e.nt followed the fairs, and obtained their living from the generosity of the people who were amused. These amus.e.m.e.nts were conducted out of doors, and with very few of the objectionable features as regards hygiene and morality that are likely to attach themselves to the same things in our day.

The amus.e.m.e.nt was what we would call now vaudeville, singing, dancing, the exhibition of trained animals, acrobatic feats of various kinds, so that we cannot very well say that our people are in advance of their medieval forbears in such matters, since their taste is about the same. Fairs and market days made country life less monotonous by their regular recurrence, and so prevented that emptying of the country into the city which we deprecate in our time. They had economic, social, even moral advantages, that are worth while studying.

XXV. INTENSIVE FARMING.

We hear much of intensive farming in the modern time, and it is supposed to be a distinctly modern invention mothered by the necessity due to great increase of population. One of the most striking features of the story of monasticism in the countries of Europe, however, during the Middle Ages, and especially during the Thirteenth Century, when so many of the greatest abbeys reached a climax of power and influence and beauty of construction, is their successful devotion paid to agriculture. In the modern time we are gradually learning the lesson of growing larger and larger crops on the same area of ground by proper selection of seed, and of developing cattle in such a way as to make them most valuable as a by-product of farming. This is exactly what the old monastic establishments did. At the beginning of the Thirteenth Century many of them were situated in rather barren regions, sometimes, indeed, surrounded by thick forests, but at the end of the century all the great monastic establishments had succeeded in making beautiful luxuriant gardens for themselves, and had taught their numerous tenantry the great lessons of agricultural improvement which made for plenty and happiness.

Many monasteries belonged to the same religious order, and the traditions of these were carried from one to the other by visiting {460} monks or sometimes by the transfer of members of one community to another. The monastic establishments were the great farmers of Europe, and it was their proud boast that their farming lands, instead of being exhausted from year to year, were rather increasing in value.

They doubtless had many secrets of farming that were lost and had to be rediscovered in the modern time, just as in the arts and crafts, for their success in farming was as noteworthy. Their knowledge of trees must have been excellent, since they surrounded themselves with fine forests, at times arranged so as to provide shady walks and charming avenues. Their knowledge of simple farming must have been thorough, for the farms of the monasteries were always the most prosperous, and the tenantry were always the happiest. With the traditions that we have especially in English history, this seems almost impossible to credit, but these traditions, manufactured for a purpose, have now been entirely discredited. We have learned in recent years what wonderful scholars, architects, painters, teachers, engineers these monks were, and so it is not surprising to find that they had magnificently developed agricultural knowledge as well as that of every other department in which they were particularly interested.

XXVI. CARTOGRAPHY AND THE TEACHING OF GEOGRAPHY.

In the chapter on Great Explorers and The Foundation of Geography, in the body of the book, much might have been said about maps and map-making, for the Thirteenth Century was a great period in this matter. Lecoy de la Marche among his studies of the Thirteenth Century has included a volume of a collection of the maps of the Thirteenth Century. If the purpose had been to make this a work of erudition rather than of popular information, much might have been said of the cartography of the time even from this work alone (_Receuil de Charles du XIII e Siecle_, Paris, 1878). One of the great maps of the Thirteenth Century, that on the Cathedral wall of Hereford, deserves a place here. It was made just at the end of the Thirteenth Century. The idea of its maker was to convey as much information as possible about the earth, and not merely indicate its political divisions and the relative size and position of the different parts. It is to a certain extent at least a resume of history, of physical geography, and even of geographical biology and anthropology, for it has indications as to the dwelling-place of animals and curious types of men. It contains, besides, references to interesting objects of other kinds. Because of its interest I have reproduced the map itself, and the key to it with explanations published at Hereford.

{461}

[Ill.u.s.tration]

_Key to the Photograph of the Ancient Map of the World_.

PRESERVED IN HEREFORD CATHEDRAL.

[Ill.u.s.tration]

MAP OF THE WORLD (HEREFORD CATHEDRAL)

The Map is executed on a single sheet of vellum, 54 in. in breadth, by 63 in. in extreme height, it is fixed on a strong framework of oak. At the top (Fig. 1) is a representation of the Last Judgment. Our Saviour is represented in glory, and below is the Virgin Mary interceding for mankind.

For convenience of reference the Key Map is divided into squares marked by Roman capitals, with the more prominent objects in figures.

I.--Commencing with sq. 1. the circle marked by Fig. 2 represents the Garden of Eden, with the four rivers, and Adam and Eve eating the forbidden fruit. The remainder of the square, as also in II. and III., is occupied by India. At Fig. 3 is shown the expulsion of Adam and Eve, to the right of which is shown a race of Giants, and to the left the City of Enoch, and still further the Golden Mountains guarded by Dragons. Below these mountains are shown a race of pigmies. In a s.p.a.ce bounded by two rivers is placed a crocodile, and immediately below a female warrior. To the left of the latter are a pair of birds called in the Map Alerions. The large {462} river to the left is the Ganges.

II.--Shows one of the inhabitants of this part of India, who are said to have but one foot, which is sufficiently large to serve as an umbrella to shelter themselves from the sun. The city in the center is Samarcand. III.--In which is seen an Elephant, to the left a Parrot. A part of the Red Sea is also shown with the Island of Taprobana (Ceylon), on which are shown two Dragons. It also bears an inscription denoting that dragons and elephants are found there. The small Islands shown are Crise, Argire, Ophir, and Frondisia (Aphrodisia).

IV.--Contains the Caspian Sea, below which is a figure holding its tail in his hand, and which the author calls the Minotaur. To the left is shown one of the Albani, who are said to see better at night than in the daytime. Below are two warriors in combat with a Griffin (Fig.

27). V.--In the upper part are Bokhara and Thrace, in the latter of which (Fig. 29) is shown the Pelican feeding its young, to the left a singular figure representing the Cicones, and to the right the Camel, in Bactria. Below to the left is the Tiger, and on the right an animal with a human head and the body of a lion, called the Mantichora. Still lower is seen Noah's ark (Fig. 28), in which are shown three human figures, with beasts, birds and serpents. In the lower corner, at Fig.

26, is the Golden Fleece. VI.--The upper parts contain Babylonia, with the City of Babylon (Fig. 4) on the river Euphrates, below which is the city of Damascus, which has on its right an unknown animal called the Marsok. To the right is Lot's wife turned into a pillar of salt (Fig. 8). Decapolis and the River Jordan are near the bottom of the square. Above the River Euphrates is a figure in a frame representing the Patriarch Abraham's residence at Ur of the Chaldees. VII.--The Red Sea (Figs. 5, 5) is the most conspicuous object here. In the fork formed by it is shown the giving of the Tables of The Law on Mount Sinai. Below, and touching the line (Fig. 6) showing the wanderings of the Israelites, is seen the worship of the Golden Calf. The Dead Sea and submerged Cities are shown lower down to the left, and between this and the Red Sea is the Phoenix. At the bottom is a mythical animal with long horns, called the Eale. VIII.--In the upper part is the Monastery of St. Anthony in Ethiopia. The river to the left is the Nile, between this and a great interior lake (Figs. 7, 7) is a figure of Satyr. Beyond the lake, and extending a distance down the Map (Figs. 12, 12, 12), are various singular figures, supposed to represent the races dwelling there. In a circular island to the left (Meroe) is a man riding a crocodile, and at the bottom left-hand corner is a centaur. IX.--The upper part is Scythia, and shows some cannibals, below which (Fig. 25) are two Scythians in combat. Under this again is a man leading a horse with a human skin thrown over it, and to the right of the latter is placed the ostrich. X.--Asia Minor with the Black Sea (Fig. 24). Many cities are shown prominent, among which is Troy (Fig. 21), described as "_Troja civitas bellicosissima_." Near the bottom to the left is Constantinople. The lynx is shown near the center. XI.--Is nearly filled by the Holy Land.

In the center is Jerusalem (Fig. 23), the supposed center of the world, surrounded by a high wall, and above is the Crucifixion. Below Jerusalem to the right is Bethlehem with the manger. Near a circular place to the right, called _"Puteus Juramenti"_ (well of the oath), is an unknown bird, called on the Map Avis Cirenus. XII.--Egypt with the Nile. At the upper part (Fig. 9) are Joseph's granaries, i.e., the Pyramids, immediately below which is the Salamander, and to the right of that the Mandrake. Fig. 10 denotes the Delta with its cities. {463} On the other side of the Nile, and partly in sq. XIII., is the Rhinoceros, and below it the Unicorn. XIII.--Ethiopia. In the upper left-hand corner is the Sphinx, and near the bottom the Temple of Jupiter Ammon, represented by a singular horse-shoe shaped figure. The camp of Alexander the Great is in the bottom left-hand corner, immediately above which is the boundary line between Asia and Africa, XIV.--At the top of the left is Norway, in which the author has placed the Monkey. The middle is filled by Russia. The small circular islands on the left are the Orkneys, immediately below which is an inscription relating to the Seven Sleepers, Scotland and part of England are shown in the lower part, but the British Isles will be described in sq. XIX.

The singular triangular figure in the center of this square cannot be identified. XV.--Germany, with part of Greece, in the upper part to the right. The Danube and its tributaries are seen in the upper part, in the lower is the Rhine. On the bank of the latter the scorpion is placed; Venice is shown on the right, XVI.--Contains Italy and a great part of the Mediterranean Sea (Fig. 14). About the center (Fig. 17) is Rome, which bears the inscription, "Roma caput mundi tenet orbis frena rotundi." In the upper part of the Mediterranean Sea is seen a Mermaid, below (Fig. 11) is the Island of Crete, with its famous labyrinth, to the left of which is the rock Scylla. Below Crete is Sicily (Fig. 15), on which Mount Etna is shown; close to Sicily is the whirlpool Charybdis, XVII.--Part of Africa; in the lower part to the left, on a promontory, is seen Carthage; on the right the Leopard is shown. XVIII.--Also part of Africa. The upper part is Fezzan, below is shown the basilisk, and still lower some Troglodytes or dwellers in caves. XIX.--On the left hand are the British Isles (Figs. 19, 20, 22), on the right France. Great Britain (Figs. 19, 22) is very fully laid down, but of Ireland the author seemed to know but little. In England twenty-six cities and towns are delineated, among which Hereford (H'ford) is conspicuous. Twenty rivers are also seen, but the only mountains shown are the Clee Hills. In Wales, Snowdon is seen, and the towns of Carnarvon, Conway and St. David's. In Ireland four towns, Armagh, Bangor, Dublin and Kildare, with two rivers, the Banne, which, as shown, divides the island in two, and the Shannon. In Scotland there are six towns. In France the City of Paris (Fig. 18) is conspicuous. XX.--The upper part is Provence, the lower Spain. In the Mediterranean Sea are laid down, among others, the Islands of Corsica, Sardinia, Majorca, and Minorca. At the bottom are (Fig. 16) the pillars of Hercules (Gibraltar), which were considered the extreme western limits of the world. XXI.--At the top to the left (Fig. 13) is St. Augustine of Hippo, in his pontifical habit. And at the opposite corner the Lion, below which are the Agriophagi, a one-eyed people who live on the flesh of lions and other beasts. The kingdoms on the sh.o.r.e of the Mediterranean are Algiers, Setif, and Tangier.

{464}

APPENDIX III.

CRITICISMS, COMMENTS, DOc.u.mENTS.

HUMAN PROGRESS.

For most people the impossible would apparently be accomplished if a century so far back as the Thirteenth were to be even seriously thought of as the greatest of centuries. Evolution has come to be accepted so unquestioningly, that of course "we are the heirs of all the ages of the foremost files of time," and must be far ahead of our forbears, especially of the distant past, in everything. When a man talks glibly about great progress in recent times, he usually knows only the history of his own time and not very much about that. Men who have studied other periods seriously hesitate about the claim of progress, and the more anyone knows about any other period, the less does he think of his own as surpa.s.sing. There are many exemplifications of this in recent literature. Because this was a cardinal point in many criticisms of the book, it has seemed well to ill.u.s.trate the position here taken as to the absence of progress in humanity by quotations from recognized authorities. Just as the first edition of this book came from the press, Amba.s.sador Bryce delivered his address at Harvard on "What is Progress?" It appeared in the _Atlantic Monthly_ for August, 1907. Mr. Bryce is evidently not at all persuaded that there is human progress in any real sense of the word.

Some striking quotations may be made from the address, but to get the full impression of Mr. Bryce's reasons for hesitation about accepting any progress, the whole article needs to be read. For instance, he said:

"It does not seem possible, if we go back to the earliest literature which survives to us from Western Asia and Southeastern Europe, to say that the creative powers of the human mind in such subjects as poetry, philosophy, and historical narrative or portraiture, have either improved or deteriorated. The poetry of the early Hebrews and of the early Greeks has never been surpa.s.sed and hardly ever equaled. Neither has the philosophy of Plato and Aristotle, nor the speeches of Demosthenes and Cicero. Geniuses like Dante, Chaucer, and Shakespeare appear without our being able to account for them, and for aught we know another may appear at any moment. It is just as difficult, if we look back five centuries, to a.s.sert either progress or decline in painting. Sculpture has never again risen to so high a level as it touched in the fifth century, B. C, nor within the last three centuries, to so high a level as it reached at the end of the fifteenth. But we can found no generalizations upon that fact. Music is the most inscrutable of the arts, and whether there is any progress to be expected other {465} than that which may come from a further improvement in instruments const.i.tuting an orchestra, I will not attempt to conjecture, any more than I should dare to raise controversy by inquiring whether Beethoven represents progress from Mozart, Wagner progress from Beethoven."

Perhaps the most startling evidence on this subject of the absence of evolution in humanity is the opinion of Prof. Flinders Petrie, the distinguished English authority on Egyptology, who has added nearly a millennium to the history of Egypt. His studies have brought him in intimate contact with Egypt from 2,000 to 5,000 B. C. He has found no reason at all for thinking that our generation is farther advanced in any important qualities than men were during this period. In an article on "The Romance of Early Civilization" (_The Independent_, Jan. 7, 1909), he said:

"We have now before us a view of the powers of man at the earliest point to which we can trace written history, and what strikes us most is how very little his nature or abilities have changed in seven thousand years; _what he admired we admire; what were his limits in fine handiwork also are ours_. We may have a wider outlook, a greater understanding of things; our interests may have extended in this interval; but so far as human nature and tastes go, man is essentially unchanged in this interval." ... "This is the practical outcome of extending our view of man three times as far back as we used to look, and it must teach us how little material civilization is likely in the future to change the nature, the weaknesses, or the abilities of our ancestors in ages yet to come."

Those who think that man has advanced in practical wisdom during the 6,000 years of history, forget entirely the lessons of literature.

Whenever a great genius has written, he has displayed a knowledge of human nature as great as any to be found at any other time in the world's history. The wisdom of Homer and of Solomon are typical examples. Probably the most striking evidence in this matter is to be found in what is considered to be the oldest book ever written. This is the Instructions of Ptah Hotep to his son. Ptah Hotep was the vizier of King Itosi, of the Fifth Dynasty of Egypt (about 3650 B.C.).

There is nothing that a father of the modern time would wish to tell his boy as the result of his own experience that is not to be found in this wise advice of a father, nearly 6,000 years ago. This was written longer before Solomon than Solomon is before us, yet no practical knowledge to be gained from intercourse with men has been added to what this careful father of the long ago has written out for his son.

THE CENTURY OF ORIGINS.

To many readers apparently, it has seemed that the main reason for writing of The Thirteenth as the Greatest of Centuries was the fact that the Church occupied so large a place in the life of that time, and that, therefore, most of what was accomplished must naturally revert {466} to her account. It is not only those who are interested in the old Church, however, who have written enthusiastically about the Thirteenth Century. Since writing this volume, I have found that Mr. Frederick Harrison is almost, if not quite, as ardent in his praise of it as I have been. There are many others, especially among the historians of art and of architecture, who apparently have not been able to say all that they would wish in admiration of this supreme century. Most of these have not been Catholics; and if we place beside Mr. Frederick Harrison, the great Positivist of our generation, Mr. John Morley, the great Rationalist, the chorus of agreement on the subject of the greatness of the Thirteenth Century ought to be considered about complete. Mr. Morley, in his address on Popular Culture, delivered as President of the Midland Inst.i.tute, England, October, 1876 (Great Essays. Putnam, New York), said:

"It is the present that really interests us; it is the present that we seek to understand and to explain. I do not in the least want to know what happened in the past, except as it enables me to see my way more clearly through what is happening to-day. I want to know what men thought and did in the Thirteenth Century, not out of any dilettante or idle antiquarian's curiosity, but because the Thirteenth Century is at the root of what men think and do in the nineteenth."

EDUCATION.

Many even of the most benevolent readers of the book have been quite sure that it exaggerated the significance of medieval education and, above all, claimed too much for the breadth of culture given by the early universities. Prof. Huxley is perhaps the last man of recent times who would be suspected for a moment of exaggerating the import of medieval education. In his Inaugural Address on Universities Actual and Ideal, delivered as Rector of Aberdeen University, after discussing the subject very thoroughly, he said:

"The scholars of the Medieval Universities seem to have studied grammar, logic and rhetoric; arithmetic and geometry; astronomy, theology and music. Thus their work, however imperfect and faulty, judged by modern lights, it may have been, brought them face to face with all the leading aspects of the many-sided mind of man. For these studies did really contain, at any rate in embryo, sometimes it may be in caricature, what we now call philosophy, mathematical and physical science, and art. _And I doubt if the curriculum of any modern university shows so clear and generous a comprehension of what is meant by culture, as this old Trivium and Quadrivium does_."

(Italics ours.)

The results of this system of education may be judged best perhaps from Dante as an example. In The Popes and Science (Fordham University Press, N. Y., 1908) a chapter is devoted to Dante as the typical university man of the time, above all in his knowledge of science as displayed in his great poem. No poet of the modern time has {467} turned with so much confidence to every phase of science for his figures as this product of medieval universities. Anyone who thinks that the study of science is recent, or that nature study was delayed till our day, need only read Dante to be completely undeceived.

The fact that the scholars and the professors at the universities were almost without exception believers in the possibility of the trans.m.u.tation of metals in the old days, used to be considered by many educated people as quite sufficient to stamp them as lacking in judgment and as p.r.o.ne to believe all sorts of incredible and even impossible things without justification. Such supercilious condemnation of the point of view of the medieval scholars in this matter, however, has recently received a very serious jolt. Sometime ago, Sir William Ramsey, the greatest of living English chemists, announced at the meeting of the British a.s.sociation for the Advancement of Science, that he had succeeded in changing copper into lithium. This created a sensation at the time, but represented, after all, a culmination of effort in this direction that had long been expected. More recently, Sir William has reported to the British Chemical Society that he has succeeded in obtaining carbon from four substances not containing this element--bis.m.u.th, hydro-fluo-silicic acid, thorium and zirconium. An American professor of chemistry has declared that he would like to remove all traces of silver from a quant.i.ty of lead ore, and then, after allowing it to stand for some years, have the opportunity to re-examine it, since he is confident that he would find further traces of silver in it that had developed in the meantime. He is sure that the reason why these two metals always occur together, as do copper and, gold, is that they are products of a developmental process, the precious metals being a step farther on in that process than the so-called base metals. It would seem, then, that the medieval scholars were not so silly as they used to appear before we knew enough about the subject to judge them properly. Only their supercilious critics were silly.

It is probably with regard to the exact sciences that most even educated people are quite sure that the Thirteenth Century does not deserve to be thought of as representing great human advance. For them the Middle Ages were drowsily speculative, but never exact in thinking. Of course, such people know nothing of the intense exactness of thought of St. Thomas or Albertus Magnus or Duns Scotus. It would be impossible, moreover, to make them realize, from the writings of these men, how exact human thought actually was in the Thirteenth Century, though the more that modern students devote themselves to scholastic philosophy, the more surely do they appreciate and admire this very quality in the medieval philosophy. For such people, very probably, the only evidence that would have made quite an adequate answer to their objection, would be a chapter on the mathematics of the Thirteenth Century. {468} That might very easily have been made, for Cantor, in his History of Mathematics (Vorlesungen uber Geschichte der Mathematik, Leipzig, 1892), devotes nearly 100 pages of his second volume to the mathematicians of the Thirteenth Century, two of whom, Leonardo of Pisa and Jorda.n.u.s Nemorarius, did so much in Arithmetic, the Theory of Numbers, Algebra and Geometry, as to make a revolution in mathematics. Cantor says that they accomplished so much, that their contemporaries and successors could scarcely follow them, much less go beyond them. They had great disciples, like John of Sacrobusco (probably John of Holywood, near Dublin), Joannes Campa.n.u.s and others.

Cantor calls attention particularly to the spread of arithmetical knowledge among the ma.s.ses, which is a well-deserved tribute to the century, for it was a characteristic of the time that the new thoughts and discoveries of scholars were soon made practical and penetrated very widely among the people. Brewer, in the Preface to Roger Bacon's works, quotes some of Bacon's expressions with regard to the value of mathematics. The English Franciscan said: "For without mathematics, nothing worth knowing in philosophy can be attained." And again: "For he who knows not mathematics cannot know any other science; what is more, he cannot discover his own ignorance or find its proper remedy."

The term mathematics, as used by Bacon, had a much wider application then than now, and Brewer notes that the Thirteenth Century scientist included therein Geometry, Arithmetic, Astronomy, and Music.