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by which man goes down into the fierce battle of this world, conquering and to conquer. That education I honestly believe is best which mingles books with business, action with meditation, theory with practice, interchanges solitude with society. I consider it, then, young men, propitious rather than unfavourable, in the condition of the most of those who hear me, that you are engaged in active employments. Milton, the greatest master in English literature, was a considerable part of his life a schoolmaster. Newton interchanged his sublime studies with the dry and monotonous duties of Master of the Mint. Our Bowditch, that miracle of self-education, pursued those mathematical studies which afterwards made him the translator of La Place, and the universal guide of navigation through the trackless seas, in the uncongenial employment of a supercargo and a sca captain. And Charles Lamb, that most accomplished of belles lettres scholars and sweetest of prose writers, passed his life at the desk of a common clerk. Roscoe, the historian of Leo the Tenth, was an active and successful merchant at the same time that he was delighting the world with his literary productions. Bacon was one of the most laborious men that ever lived, in the common drudgery of his profession ; he was at the same time the deepest of philosophers, and yet he found leisure so to cultivate elegant literature, as to become the most perfect master of mere English composition that the nation has ever produced.*
Look into our own National Legislature. Who are they who place themselves at its head and gain the greatest influence over its deliberations? It is not the mere scholar, nursed up in the effeminacy of literary leisure. It is not he whose knowledge, gained by mere reading, is most extensive. It is more often the man who has been trained up in the school of business; whose mind has been disciplined by action, as well as stored with knowledge; who has united to the common round of employment, habits of thought, study, and investigation. It is the lawyer, who has not confined his attention to the technicalities of forms, or the chicanery of petty disputes, but who has extended his investigations into all branches of collateral science, into history, political economy, statistics, commerce, agriculture, manufactures. It is the merchant who has risen above his class ; who has not consumed all his powers in the details of profit and loss; who has read and thought while he has been building himself up a fortune; who has taken pains to inform himself concerning the condition, physical, political, and moral, of the different nations whose products he buys and sells ; who has investigated and ascertained the causes of commercial changes and revulsions.
* Chaucer also turned from the drudgery of official life (he was Comptroller of the Customs) to the composition of his exquisite poems.-ED.
This leads me to speak of a point which is very necessary to to be mentioned here, for the encouragement of those who hear me. It is much easier to superinduce the ornament and aid of a cultivated mind upon business habits, than practical efficiency upon a merely scholastic education. The mind must be consolidated by close and vehement application of its powers to things which task its strength to the utmost. Action forms the intellectual constitution to robustness, energy, and strength. Mere scholastic education has no such power. It may give grace and dexterity to action, but cannot confer original and self-sustaining force.
The man who has been exclusively a student has necessarily lost much time in the pursuit of that which is without value, or in the investigation of that which either never can be known, or would be worthless if it were fully understood. The man of business is in no danger of thus misapplying his time and his powers. He acquires in the practical affairs of life a sagacity which teaches him to distinguish almost intuitively the useful from the vain. He learns to know his intellectual wants, and what books or studies best supply them. But I fancy that I hear some of you object—“How is it possible to unite a life of business with intellectual cultivation ? Not one moment can be added to the hours of the day, nor can weariness and exhaustion be warded off from the human faculties.” There is an answer to this, which is sufficiently satisfactory. Nothing is more true than that if you wish to have anything done promptly and well, you must go to one whose time is already, as it would appear, occupied to the full. He has been forced to learn the great secret of this world's welfare—the economy of time. He accomplishes much, from the very fact that he uses all the precious hours of life. The most idle are the very people who complain most of the want of time, and find it most difficult to bring anything to pass. Let an idle man have anything to do which will occupy but a few hours of the day, and he will inevitably put it off to the latest possible moment; and the surest way to accomplish it seasonably and well would be to fill up the rest of the day with some other employment. But is there any one who hears me, who can honestly say that want of time is the reason why he does not cultivate his mind? Is his time so accurately divided between labour and necessary recreation and repose, that no portion can be snatched for reading and thought? How agrees with this the daily and eternal complaint that business is dull, and there is nothing to do? No! That is not the cause. The true reasons are want of settled conviction of the importance of the thing, and still more, a want of the habit of so employing your faculties. There is the fatal difficulty. The natural and fatal propensity of man, is to do as little as he can ; to do less and less the less is imposed upon him; and if the necessity of labour is removed altogether, he sinks into a mere animal, who divides his time between eating and sleep. It is in vain, therefore, that you afford men more leisure for intellectual culture with the hope that they will improve it. It is in vain that you look to the heirs of hereditary wealth, who are exempted from the necessity of personal exertion, for high intellectual culture. The sons and daughters of opulence have seldom been the possessors of distinguished mental accomplishment. They have rarely been the inventors of art, or the cultivators of science, or the contributors to the amusement of mankind. Their minds are seldom trained by effort and struggle to the achievement of anything bold or original. It is the vigorous sons of toil and privation who have carried off the great prizes of intellectual distinction. The plea, then, of want of time and opportunity, of the multiplication of cares and avocations, is altogether invalid. Habits of indolence, not want of time, are the death of our intellectual being.– From Burnap's Lectures to Young Men.
EUCLID'S ELEMENTS OF GEOMETRY: A NEW EDITION, WITH GEOMETRICAL EXERCISES, AND AN OUTLINE OF THE HISTORY OF GEOMETRY. BY ROBERT POTTS,
TRIN. COLL., CAMBRIDGE.
“If a man's wit be wandering,” says Lord Bacon, “let him study the mathematics; for, in demonstrations, if his wit be called away never so little, he must begin again.” The noble and learned lord (to use a Parliamentary phrase) might have written at greater length respecting the effect of the mathematics upon the wit. Possibly few knew better than himself, how much a close attention to some abstruse reasoning promotes a cheerfulness, nay, a positive liveliness, of disposition. Whether it is that the mind, bent so strenuously in one direction, flies back as sharply in the first moment of relaxation; or whether it is, as old Chaucer says, that “ Each thing is declared” (that is, manifested, brought to light) “by its contrary," we do not know; but certain it is, that most of the great mathematicians, whose histories have come down to us, have exhibited to the world a demeanour uniformly thoughtful and composed, but characterised, in no small degree, by a lively cheerfulness, and a keen appreciation of the humorous, not to be expected from persons who had devoted themselves to such abstruse
pursuits. On the other hand, as if to confirm Chaucer's opinion, what can be more gloomy and uncertain than the temperament of professed wits, comic writers, comedians, and clowns; at least, so far as we can judge from the information which we possess respecting those personages? This much, also, we may add with respect to the effect of different books upon the student's mind, -that if we compel the mind to achieve, or to attempt only, the mastery of a difficult subject, we rouse it into vigorous action ; but that if we suffer it to dwell upon the pages of a novel, or some work of similar character, the easiness of its task lulls into useless inactivity.
After so proper a preface and recommendation to the study of a mathematical work, we shall briefly notice some few of the thousand and one mathematicians and geometricians, whose names have been recorded by the erudite Mr. Potts in the introduction to his work. We shall not follow him through his elaborate disquisitions upon the origin of the mathematical sciences; he himself cannot tell whether to attribute it to the Egyptians or to Pythagoras. But we are of opinion, that the Egyptians, as being the first agriculturists possessed of any wealth and consequence, must have been the inventors of practical geometry ; though they may not have entertained very clear theoretical notions upon the subject, nor have been able to demonstrate mathematically the correctness of their practice. Plato, on his return from Egypt, B.C. 390, established a school in Athens, over the door of which he caused to be inscribed, “Let no one ignorant of geometry enter here !" a formidable prohibition, which, if exercised in England, would have the effect of emptying all the schools and half the colleges to boot; so that we must conclude, either that Plato wished to preserve his establishment select, or that there was a vast amount of knowledge in the little Athenian republic. We have often wondered that schoolmasters do not insist more upon the dignity of their occupation—as one which was followed by so great a man as Plato; they seem, however, more willingly to consider Dionysius the Tyrant as their prototype, because he taught “the youth of nations" after his dethronement; and indeed, it used to be our opinion that they bad inherited their attributes from him rather than from the divine sage. Plato's remuneration, however, was somewhat greater than that of the modern pedagogues, as we may learn from the following circumstances, for which we are indebted to Adam Smith. Isocrates, the rhetorician, is said to have received 10 mina, or £33, for each scholar; and when he taught at Athens, he is said to have had a hundred scholars; so that he must have received 1,000 mine, or £3,300, which, according to Plutarch, was really his annual stipend for teaching. Gorgias, another eminent teacher, presented to the temple of Delphi a statue of himself, of pure gold, but not, we may suppose, of the size of life. His way of living, as well as that of Hippias and Protagoras, two other eminent teachers, is represented by Plato as splendid, even to ostentation ; and even Plato is said to have indulged in a good deal of magnificence. Aristotle, though he received from Philip and Alexander a few towns and villages (the ancient substitutes for the modern college livings), thought it worth his while to resume his school, and issued a circular, no doubt, soliciting “ the continued lavours of the nobility, gentry, and tradespeople, of Stagyra.” Nor
need we suppose that Plato, so superior to these in genius, was behind them in the recompense which his services obtained,
We are glad to learn from Mr. Potts, that Euclid was only the compiler, and not the inventor, of the terrible book which bears his name; it is some consolation to reflect that the tormentors of our childhood were Legion, and not one man; and, therefore, we hail with joy the statement of Proclus, who says, “ Euclid composed Elements of Geometry, and improved and arranged many things of Eudoxus, and perfected many things which had been discovered by Theatetus, and gave invincible demonstrations of many things which had been loosely or unsatisfactorily demonstrated before him.” It would have been more satisfactory to our feelings, however, if Proclus and Potts, between them, had discovered and chronicled the inventor of the Pons asinorum ; we would not that the imprecations which we and others have vented upon the author of that problem should fall on any innocent man. But alas! we fear that the real culprit is no more to be discovered. How truly did Shakspeare say,
“The evil that men do lives after them;" that is, after their miserable appellations have been discarded from the world's memory. By the bye, we never rightly knew by whom, or why, the term, Pons asinorum (bridge of asses), was applied to that particular problem. The origin of it has been lost somewhere in the backwoods of tradition, and it seems to have been handed down, along with the cane and birch, from one generation to another—the everlasting heirlooms of successive pedagogues. We met, some few days agone, with an anecdote which gives a new interest to the appellation. It relates to two Arabian philosophers, who disputed, after the manner of such men, upon predestination. We shall not trouble our readers with the burden of their discourse, but merely state, that one, having put rather a difficult problem, was asked by the other, “if the devil possessed him, to ask such questions?" "Nay," replied the first, " but the master's ass cannot pass the bridge;" namely, he is posed. We appeal, as a last resource, to those who are acquainted with the natural history of asses, for assistance in our difficulty. Have asses, as a body, a natural antipathy to passing over bridges, that they have been thus singled out, and converted into a proverb ? In the East, the ass is not regarded as a stupid animal ; on the contrary, if we could utter the wise sayings which the Eastern writers have put into his mouth, we would be contented, like Dogberry, "to be written down an ass,” for the rest of our lifetime.
Archimedes next attracts our attention ; an honest man, and shrewd, doubtless, though he was the inventor of the “ screw-principle.” The story of King Hiero's crown is somewhat of the oldest ; but as it illustrates his method of finding out the specific gravity of bodies, we shall relate it. King Hiero, who reigned in Syracuse, had delivered a certain quantity of gold to a workman, to be fashioned into a crown. The king, suspecting that the workman had not made use of the whole quantity of gold delivered to him, and yet finding the weight accurate, solicited Archimedes to discover some means of detecting the theft, without melting the crown. Archimedes,