Pythagoras and Archimedes

LADIES’ REPOSITORY. 594 PYTHAGORAS AND ARCHIMEDES. DY J, D, DELL. FIND two of all the sncionts whose lives to me seem thranged with the finest facideuts of intellectual experience. I take these men to bo instances of the most exquisite and intense happiness possible to be enjoyed on earth. They were is men of more brain than any thing else; which to say, that thoy lived less in the outer world than in tho inner. They were discoverers of now ideas and new forces. Moro than that, thoy, often and often, were discoverers overjoyed. I scarcely need hint to you, my reader, that from the study of these two oxamples, yon may derive many inspiring ideas and elevating lessons, I Let Pythagoras take your attention first. It may please yon, as it does mo, to go back through the conturies, and trace something special in the character and life of this great anciont. Thus to do is to soe a man who had come to be moro than a mero user of his hands, and more than a mere glestier with his mind, longing and toiling ever, aftor tho beautiful and grand of the yet unexplored parts of creation. All the noble things in the world have taken their origin in just such men as was Pythagoras of Samos. ‘That is to say, he was an uncommon map, and uncommon works wero among his Y>.BEL , San -SA$ History tells ns not all of the discoveries mada by Pythagoras. We know that to his disciples he opeuly taught doctrines sided by images and symbols, which seemed to them divine oracles. We know that he inculeated lessons in secret, dispensing with those aids which elevated the chosen ones who heard them into Pythagoreans, What these Istter teachings were, you can not know, and I can not. Did they contein the germs of great theories, which our times sce in application? Did they embrace sublime truths in regard to God and immortality, which none of that far-off mythic age, but such as had purged their souîs of all dross, by a long-continued course of mental and moral discipline, were capable of understanding? There is no voice to auswer these questious. We do but know that in the secret placo of his private and higher instructions, Pythagoras communicated discoveries, which only he and those who, by having passed the trials prescribed by him, had gained the privilege of hearing the femiliar words of his wise lips, could feel the wonderful magic of. Such a man as this man must have gone in thought mauy centuries ahead of his own, Ho was all right for thinking astonishingly—all right for thinking on into future civilizations. What he saw in the heauty of reality, all living cotemporaries but thoso ho had made in a good degres works, like himself, doubtless wonld have heard de- Ho wes the founder of a school of philosophy—the Italian school so called. He was more than that. Being asked by King Leon, of Phitius, what was his profession, he sublimely scribed, only to sneer at it. It pleases me to imagine that lofly thinker, lingering in the onchanting silence of his own deep meditations and feeling thrills of rapture, now and then, which could not but have still remained secrets of his own, even if he had tried to communicate them to answered, that ho was a lover of wisdom—a philosophos, and not a sophos; for the Deity only, he declared, is worthy the title of sage. Pause, reader, upon this profession of Pythagoras, the best Na‘ 1635 VY AS that was ever made by man. You shall, then, soon he prepared to hear the greatest of things about that majestio ancient, without thinking at all to ask, “How could this be so ?” What if at Crotona ho built up a great unique society, composed of six hundred seckers with him, after what Socrates in a later age called “the interior beauty of the soul?* What if his opinion on any subject of thought was, while _ he lived, taken by all who learned of him, as authority weighty enough to supersede the necessity of proof? What if after his death his scholars ‚paid him divino honors? And what if some modern German has called him “ Tho Tabothers. I love to imagine him in his elevation of life, his quiet dignity, his impressive gravity, his temperance, his virtue, his self-control. I love to conceive of his face, showiug in its paleness, not the want of bodily health, but the superiority of his restless mind. I love to think of him as abstaining habitually from animal food, and welcoming with a right relist all vegetables, excepting— beans! What pleasure to conceive of him as ono among his pupils living in perfect concord ; rising with them in the morning early enough to worship the outbursting sun; then determining how the day was to be spent; joining with them afterward in reciting Homeric verses, or in vocal siuging, in order to fit his own and their mental powers for the sovero activities soon to be entered upon; passing with them, then, into tho intense These things all are but tranquillity of serious study; after several hours, natural corollaries of the life of an ancient lover pausing awhile, for a solitary walk in which the of wisdom, wind might indulge itself in happy contemplaulous Wonder-Man fr

PYTHAGORAS AND ARCHIMEDES. tions; then mingling in cheerful conversation and in tho porformance of various gymnastic exoreises; then going to dine on the common meal of bread, honey, aud water; afterward attending to public and domestic affairs, to bathing, and to the duties of religion; and then, as the last business before sleep, reviewing what had been dove during the day. All this it pleases me to muse upon, in connection with the genius and works of that deep and mysterious man of history—Pythagoras. For thus I am taught that the most of his life was serenely and mightily intellectual. He was devoted to discovery. I will caution you, reader, right here, lest you forget that Pythagoras lived in an age when thinking was not so much of a practical and utilitarian process, as it is in there days, So if you find, in the systems which he built up, out of his own discoveries, too many wild and subtila conceptions, going to indicate something of a habit of fanciful idealization, you will still have the 595 thickly cluster in it, and for believing that Lucifer and Hesperus were but the same beautiful Venus, bearing, in the one case, her morning, and in the other her evening name. astronomer, who And that same early so rightly read the “heavens of the Lord,” without a telescope, could not fail oven to see that the other worlds must, like ours, be inhabited by living and inteliigent beings. Stop, just now, reader, and think within yourself, how the discoverer, Pythagoras, must hare reveled in the glorious light that filled his studious and contemplative soul! Did he not realize something of that Inxuty of joy which may be supposed to constitute the never-failing fruition of unfallen intelligences? What a splondid stand-point, in the universe of God, he must have regarded this world of oura! Do you wonder why it was that, amid a people given to senAual pleasures, he scorned to devote himself to other pursuits than such as tend to conquer appetite and passion? Do you wonder why it was uimost reverence for the great philosopher who that he so loved the still cloister of scholastic professed himself to be a “lover of wisdom.” severities? Think of the mental freedom and Although his ideal masterpieces are more or less | vigor, think of the rapturous peace which were tinged with the mysticism of his mystic Limes, gained at the expense of that subordination of to the spirit, of that rigid application to yet Pythagoras was the most practical explorer tho flesh of nature of all that lived when he lived. What tasks of solitary research, and at the habits of though he carried his reasonings about numbers Pythagoras you shall no longer wonder. “Thou beyond reason? You shall own that he discov- knowest best how to live, great man of the olden ered the five regular geomotrical bodies—tho cube, times?” I shall hear you say. Aud, without surtetradron, octædren, tcosceedron, and dodecelron—- prise, as if you wero a humble learner, now, toand that he originated the multiplication-table wo day, taking noble lessons from his lips, your mernuse to-day. What though he extended his nb- ory shall fasten to those sayings of his, the truth stractions in regard to music into hopeless matheof which matical subtilities? You shall not deny that he developed musical proportions and laws, known, even in our times, to ba as true us they are beantiful. What thoagh he taught the absurd doctrino of the transmigration of souls? You shall concede that he unfolded new and noble views in regard to the origin and destiny af man. What thoagh he held certain theories of astronomy "Strength of mind rests on sobriety, for this keeps the reason unclouded by passion.” “No one is to be decmod free who has not perfect selfwhich, in our age, appear strangely unreasonable? You shall grant that he was thie first of the ancients to anticipate tha system of Copernicus, Tor, wonderful as it may seem, he believed that the sun is the contor of tho planetary worlds, and that every star is a sun, He knew the causes of eclipses, and how to predict them. He knew that the earth is round, and that its surface is naturally divided into five zones, and that the ecliptic is inclined to its equator, and that this same earth daily revolves on its axis, and yearly wheels around the sun. He had found good reasons for believing that the Milky Way gets its whiteness from the innumerable little stars which control.” his own life so woll illustrated: “Intoxication is a temporary madness.” “The desire of the superfinous is folly, for it has no bounds.” There may be much, and there may be but little of reality in that fine theory in regard to the heavenly spheres, which has given a magical luster to the name of Pythagoras—+bat theory, which, as you will remember, contemplates the solar systern as arranged with such a reference to number, distance, and time, as ta malo it one great harmonivas whole, giving forth, in the varied movements of its parts through the ether, musical tones of most exquisite melody, Little of reality or much of reality, I say, there may be in this gorgeous conception of a grend organ, made up of rextless planets, spinning and glittering around a central sun, the mysterious intonations of which have heen singing, in space, through all the ages. But let that beautiful theory be true or false, cer-

LADIES’ REPOSITORY. tain it is that it points to a sublime thoughtfulness, as the habitual peculiarity of the genius of genius, to a generation of men moro than two could so look away from tho earth into the heavthousand yoars distant from his own. It was for none but him to take up the cirele, and by developing the relation of its diameter to its circumference, to make it a charming celebrator of individens, and see the creation of God in such a light of ual greatness, through all eras of subsequent hisits originator, Ho who, in an age when tho human race was but in the twilight of civilization, almost entrancing beauty and glory—tell me, was ; tory. he not wortby, simply in the view one must take of the joy of his experience, to have it said of him, as those who loved to learn of Pythagoras used to say of him, that “he was the only mortal whom the gods had permitted to hear the harmony of the spheres ?” You and I can but imperfectly conceive how rich the intellectual felicities of Pythagoras must have been to him, and how satisfied he must have felt with them, as rewards of his patient labors of thought, It shall, however, help us not a little, perhaps, toward forming more truly and more vividly that conception, lo recall the manner in which he Is said to have expressed his intense delight, when he had made the brilliant discovery in geometry, that the squares described on the hypothenuse of a righi-angle triangle, is equal to the sum of the squares described on the two other sides. It is recorded by Plutarch, that he offered an ox, and by other authorities, that he sacrificed even a whole hecatomb to the gods, a3 an indication of his great gratitude to thom, for permitting him to enjoy such an experience of noble pleasure. Not longer will 1 dwell upon Pythagoras, IL Archimedes, No man of science can hear with indifference the name of Archimedes; for that name is inseparable from scienco itself From this mun, this citizen of ancient Syracuse, thero camo forth into the world now seiontifie truths fo change the aspects of civilization. He was a discoverer in more than one department of science, He was a mathematical discoverer. By methods depending on developments made by Archimedes, men to-day measure their curvilinear surfaces and solids. What a penetrating mind was his, that he should bave caught sight of unique relations and laws, where a thousand other minds saw nothing! What an intellectual Midas was he, that whatever he put his thoughts upon should have shone with ‘a dazzling gold! It was for none but him to take up the sphere and the cylinder, and by the discovery of a surprising proportion existing between the solid contents of these two magnitudes, when such has a base and altitude equal to those of the other, to make them tell of the power of oue ancient man’s But, then, this said Archimedes, of whom I am speaking, was also a discoverer, and a groat one too, in practical mechanics. He it was who developed the principle of the first compound pulley, and the frst endless screw. His mind was full of mechanic theorics, which he himself had constructed and proved true. Ho daily fessted his thoughts on discoveries mado in solitude, by his evor-devolving genius The historians of the past, Polybius, Livy, Plutarch, each indulges himself in admiration of the Archimedean ingenuity, as displayed in the military machines which tho great discoverer projected and set in operation, to repel the attacks of the Romans, during the siege of Syracuse. Tt is not known, and never will be known, how much of mechanics Archimedes carried in his mind, which he never found time or means to bring into light—how mauy wonderful arts he knew something of, which the circumstances of the times, or his own circumstances, would not permit him to see brought into useful play—how many vast machines lived in his brain, the wheels of which were silent t the world’s eam, forever, Like most, if not all of the ancient discoverers, he himself had to bo the one who realized the practical applications of his own great developments of natural law. In other words, he was both a discoverer and an inventor. Aud hence it was that when he had got hold of the theory of the compound pulley, he set himself to making a compound pulley; and when he had discovered the principle of the screw, ho wont and made a screw; and when he had found out the Jaw, or laws, according to which some great war machine could be constructed, ha looked about for the material and means by which to make it, and if ho succeeded in finding them, really did make it, Not any living man can teli how many discoveries the wonderful Syracusan had made by which it came to be suggested to bis mind, that if he only had a place to stand in without it, he could stir the solid globe from its orbit; but it is known that he was a practical men, for all the world has learned the Archimedean cry, “Give me where to stand, and 1 will move the world!” If Archimedes died with good volumes of unrevealed mechanics rolled up in his head, it must have beon either from a want of patronage,

PYTHAGORAS AND ARCHIMEDES. or because he had no point of available action to operate in. But, then, Archimedes was also a discoverer in still another field of science. You have many times read of his beautiful discovery in hydrostatics, and of the great holiday 597 him. History says, that, in order to immortalize this discovery, on which ho himself set particular value, men placed on his tombstone a cylinder, with a sphere inscribed in it Perhaps they did not imagine the real reason why he set such & special value on it; and, perhaps, again, they which taok place in the soul over it, You need did concsive of that reason, well and truly. At not to be told about King Hiero's order for a crown all ovente, it shall give me delight to dream that to be made of pure gold, and about the decettful they thus ornamented his monument, chiefly to artist who added an alloy to it by fraud, and perpetuate their own interest in that jubilee which about him who, while teking a bath, seized hold he must have enjoyed in his soul, when he came of the splendid principle, then for the first time to realize what a splendid triumph he had gajued. discovered, that a body immersed in a fluid loses And I can easily fancy that when Cicero, while just as much in weight as the weight of an equal acting as questor over Sicily, found this monuvolume of the fluid, and about the application ment away back in a thicket, by which it was this man immediately made of the principle he had thus caught sight of, by which application he concealed, ho fixed his philosophic eyes upon the cylinder and sphere which appeared upon jt, and was able to determine to what an extent the King's crown of gold had been adulterated. You need not be told the fact, that when this maz, Archimedes, had come to soe, with certainty, what a fine discovery he had made, he was so filled with exulistion, that, yiclding to an impulse of wild, and almost insane delight, he leaped at once from his bathing-tub, and ran naked into the streets of Syracuse, shouting, * Eureka! Eureka la really exclaimed, "What a rapture these symbols I have found it! I havo found it!” Do you ask me to delay hore, and attempt to describe the joyous ecstesy which must have more than filled the soul of that “glorious old heathen” then? Who can describe the Archimedean felicity? Not even Archimedes himself could have described it. The manner of its oxpression is all that can ever be portrayed. It would, indeed, seem that, in the bour of that mental triumph, tho very faculties of the philosopher's mind hed shaken off their usual restraints, and, with a beautiful manliness, like so many victors, were clapping their bright hands, and laughing their sublime mpture right out! And it is not at all unreasonable to think of him as so unspeakably happy, that even if the glory of the “third heaven” had burst through the skies upon him, bis soul could not have been made happier. Bat then it would be doing injustice to Archimodes, to suppose that this instance of intense ploasure was any other than a single one among many of a like kind, which were experienced during his lifetime. I will not believe, and you will not beare carrying through history ?* Why did Archimedes love, like Pythagoras, the seclusion of thought? ‘Why, when the city of Syracuse had been taken possession of by tho Romans, under Marcellus, was ho found sitting in tho market-place, deeply sbsorhed in sereno study, over some geometrical figures he had drawn in the sand? Those superior pleasures, going to reward the labors of a mind devoted to discovery—these furnish the only satisfactory auswer to all interrogatories of this kind ! “Disturb not my circle!" said he to the rough Roman soldier who came into his gentle presence to pierce him, and make his bright blood gush out over the ground, “Disturb not my circle !” Beautiful, and yet melancholy saying! What a fino comment on that lovely tranquillity of soul, which is the inheritance of the philosopher! What an endless perpetuator in human memories of the meauness of a mean saldier ! In recent American history, you and I, reader, bave marked a tragical incident, which bears somethiug of a resemblance to this one. Need I refresh your memory of that polished scholar and gifted orator of Massachusetts, who, not long since, on the floor of our national senate-chamber, was made to see, by an experience almost 2 martyr's, what it fa that gives Lo the bully his strong. ost power to influence the human rain? It may better help our hearts to mourn for Archimedes, as he should be mourned for, now even in these times, so far from the age, and the hour, in which he was struck down, to call to mind some of the relation existing between the sphere and cylinder, sharper incidents of this modern crime, and in Think, his eyes grew not radiant with the light of an in- grief and tears live them over again, describable joy, and his heart throhbed not with then, of the act of brutal cruolty done to that the wild motion of a great transport, and his lips man, whose education, whose refinement, whose told not of the tumult of bliss going on within | virtue, whose genius, whose deeds of manly self. lieve, that when be had discovered the mutual

LADIES’ REPOSITORY. sacrifice, entitlo him, if such can justly entitle any man Lo live forever in his country's annals, as one of the noblest of patriots! Think of the apology offered for that act by him who perpotrated it! Think of the oxtraordinary triumph of intellectual and moral force, for which that application of brute force was designed as a pen- A LEGEND OF THE YBURG. i ig numerous demolished and ruined citadels and castles, which adorn the dark hights of the Black Forest, overlooking with their gray, moss-covered watch-towers and battlements the green valleys, bestow upon this beautiful conutry a still greater charm. ‘Thahistory of a time gone by, rich in eventful deeds, speaks to us out of altr! Think of the spot, crimioned as was the wooden cross, along whose fibers ran the blood of the world's Jesus—that spot in which Amer- many of these ruins, while of others hardly any ican eloquence seemed to reach a loftier strain, thing is known than their nsme. Numerous were oven imitating the high pitch of melody, and the the races which have grown up to great power mighty intensity of sublime heroism, which were but have died long since, for the most part, before common in the days of Patrick Honry! But this the decay and ruin of their ancestral castles. Of is not enough. You mast go in thought still several, history can relate many noble deeds; further, You must go and stand by the bed, others passed through life without leaving any where lies a great and wise senator, whose head traces bohind, or ang remembrance save that of is throbbing forever, with “a feeling as if quick their own, or their aticestors names; was it that and crushing blows were continually falling upon they lived an inglorious or obscure existence, or it” You mustses a countenance, which once that historians have failed to note down what glowed with the expression of inner splendors of they did worthy of praise? This was the case thought, cast down and made to present only one with tho former possessors of the castle of Yburg; “rigid record of protracted suffering.” Long, and they were little known, though the castle standing long must you bend, with pitying and prayerful upon the steep, abrupt hight of a mountain covsorrow, over that prostrated victim of lawless ered with dark fir-trees, unquestionably offers a vengeance. But, thank God! although Archi- moro magnificent view than all the other ruins; it is besides seventy feet high, and its strong medes perished, the smitten orator still lives. Tho brutal warrior saw no sublime moaning in tower immeasurable. When the oye first glances the las¢ words of Archimedes, and, as he pierced over the splendid landscape, it wanders about for tho peaceful man of science, had not soul enough along time from one object to anothor, and reto pce that he was only opening a way for him quires some moments before it gets accustomed to the perfection of that bliss of which he had to this extreme richness, and cau contemplate, in quiet and Icisure, the details of this charming picalready enjoyed so many happy foretastes. ture. Fifty years ago two of these immense stone towers were standing, but about that time one was PERYERSIONS OF SOCIAL LIFE. struck by lightning, and now only a few remains HE loss of that, the possession of which en- of it exist, The ruins which are still standing, particularly riches not, is a bonefit rather than an injury. med —— We do not lose faith in society, but in its perverthe surrounding walls, are of considerable circumsions and its emptinesses. They who look to it for instruction, entertainment, or affection, are equally disappointed; and yet it contains all those, but so rately realized, that faith falters, and we harden into doubt, or falter in dospair. Stern and solid mon exact the useful and substantial, but all the rest aro for show only, with persons. splendidly attired, but intellects mis. ference, and prove that Yburg must baye been once upon a timo the residence of a very mighty erably furnished. ‘The former have no soul, and the latter no heart; and between the two, although surrounded by myriads, we are left without a friend, a confident, or a companion, and are “Fiomelezs umidst a thousand bomes,” “<Q, we are querulous creatures! Little less Than all things can suffice to make us happy, And little more than nothing is enough To make us wretched.” race. Nothing is known of its other buildings, how they came to be destroyed, or of the possessor of the castle, It is seldom spoken of in history, or in records, and then only when the ancient race had been long extinct, and the estate had fallen into the hands of the Margraves of Baden. But though history has nothing to relate of these fortified ruins, tradition bus supplied what was wantivg, and many are the legends which the people narrate of them ; the following may be considered as one of the most interest ing: The last descendant and inheritar of the lords of Yburg, Knight Erkebrecht, bad wasted and spent his rich estates in a riotous, wild kind of