In one of the sections of his projectedTreatise on Painting, Leonardo has detailed at length, and obviously from his own observation, the pictorial aspects of a battle. His choice of subject in this instance was certainly not made from any love of warfare or indifference to its horrors. In his MSS. there occur almost as many trenchant sayings on life and human affairs as on art and natural law; and of war he has disposed in two words as a “bestial frenzy” (pazzia bestialissima). In his design for the Hall of Council he set himself to depict this frenzy at its fiercest. He chose the moment of a terrific struggle for the colours between the opposing sides; hence the work became commonly known as the “Battle of the Standard.” Judging by the accounts of those who saw it, and the fragmentary evidences which remain, the tumultuous medley of men and horses, and the expressions of martial fury and despair, must have been conceived and rendered with a mastery not less commanding than had been the looks and gestures of bodeful sorrow and soul’s perplexity among the quiet company on the convent wall at Milan. The place assigned to Leonardo for the preparation of his cartoon was the Sala del Papa at Santa Maria Novella. He for once worked steadily and unremittingly at his task. His accounts with the signory enable us to follow its progress step by step. He had finished the cartoon in less than two years (1504-1505), and when it was exhibited along with that of Michelangelo, the two rival works seemed to all men a new revelation of the powers of art, and served as a model and example of the students of that generation, as the frescoes of Masaccio in the Carmine had served to those of two generations earlier. The young Raphael, whose incomparable instinct for rhythmical design had been trained hitherto on subjects of holy quietude and rapt contemplation according to the traditions of Umbrian art, learnt from Leonardo’s example to apply the same instinct to themes of violent action and strife. From the same example Fra Bartolommeo and a crowd of other Florentine painters of the rising or risen generation took in like manner a new impulse. The master lost no time in proceeding to the execution of his design upon the mural surface; this time he had devised a technical method of which, after a preliminary trial in the Sala del Papa, he regarded the success as certain; the colours, whether tempera or other remains in doubt, were to be laid on a specially prepared ground, and then both colours and ground made secure upon the wall by the application of heat. When the central group was done the heat was applied, but it was found to take effect unequally; the colours in the upper part ran or scaled from the wall, and the result was a failure more or less complete. The unfinished and decayed painting remained for some fifty years on the wall, but after 1560 was covered over with new frescoes by Vasari. The cartoon did not last so long. After doing its work as the most inspiring of all examples for students it seems to have been cut up. When Leonardo left Italy for good in 1516 he is recorded to have left “the greater part of it” in deposit at the hospital of S. Maria Nuova, where he was accustomed also to deposit hismoneys, and whence it seems before long to have disappeared. Our only existing memorials of the great work are a number of small pen-studies of fighting men and horses, three splendid studies in red chalk at Budapest for heads in the principal group, one head at Oxford copied by a contemporary of the size of the original cartoon (above life); a tiny sketch, also at Oxford, by Raphael after the principal group; an engraving done by Zacchia of Lucca in 1558 not after the original but after a copy; a 16th-century Flemish drawing of the principal group, and another, splendidly spirited, by Rubens, both copies of copies; with Edelinck’s fine engraving after the Rubens drawing.
During these years, 1503-1506, Leonardo also resumed (if it is true that he had already begun it before his travels with Cesare Borgia) the portrait of Madonna Lisa, the Neapolitan wife of Zanobi del Giocondo, and finished it to the last pitch of his powers. In this lady he had found a sitter whose face and smile possessed in a singular degree the haunting, enigmatic charm in which he delighted. He worked, it is said, at her portrait during some portion of four successive years, causing music to be played during the sittings that the rapt expression might not fade from off her countenance. The picture was bought afterwards by Francis I. for four thousand gold florins, and is now one of the glories of the Louvre. The richness of colouring on which Vasari expatiates has indeed flown, partly from injury, partly because in striving for effects of light and shade the painter was accustomed to model his figures on a dark ground, and in this as in his other oil-pictures the ground has to a large extent come through. Nevertheless, in its dimmed and blackened state, the portrait casts an irresistible spell alike by subtlety of expression, by refinement and precision of drawing, and by the romantic invention of its background. It has been the theme of endless critical rhapsodies, among which that of Pater is perhaps the most imaginative as it is the best known.
In the spring of 1506 Leonardo, moved perhaps by chagrin at the failure of his work in the Hall of Council, accepted a pressing invitation to Milan, from Charles d’Amboise, Maréchal de Chaumont, the lieutenant of the French king in Lombardy. The leave of absence granted to him by the signory on the request of the French viceroy was for three months only. The period was several times extended, at first grudgingly, Soderini complaining that Leonardo had treated the republic ill in the matter of the battle picture; whereupon the painter honourably offered to refund the money paid, an offer which the signory as honourably refused. Louis XII. sent messages urgently desiring that Leonardo should await his own arrival in Milan, having seen a small Madonna by him in France (probably that painted for Robertet) and hoping to obtain from him works of the same class and perhaps a portrait. The king arrived in May 1507, and soon afterwards Leonardo’s services were formally and amicably transferred from the signory of Florence to Louis, who gave him the title of painter and engineer in ordinary. In September of the same year troublesome private affairs called him to Florence. His father had died in 1504, apparently intestate. After his death Leonardo experienced unkindness from his seven half-brothers, Ser Piero’s legitimate sons. They were all much younger than himself. One of them, who followed his father’s profession, made himself the champion of the others in disputing Leonardo’s claim to his share, first in the paternal inheritance, and then in that which had been left to be divided between the brothers and sisters by an uncle. The litigation that ensued dragged on for several years, and forced upon Leonardo frequent visits to Florence and interruptions of his work at Milan, in spite of pressing letters to the authorities of the republic from Charles d’Amboise, from the French king himself, and from others of his powerful friends and patrons, begging that the proceedings might be accelerated. There are traces of work done during these intervals of compulsory residence at Florence. A sheet of sketches drawn there in 1508 shows the beginning of a Madonna now lost except in the form of copies, one of which (known as the “Madonna Litta”) is at St Petersburg, another in the Poldi-Pezzoli Museum at Milan. A letter from Leonardo to Charles d’Amboise in 1511, announcing the end of his law troubles, speaks of two Madonnas of different sizes that he means to bring with him to Milan. One was no doubt that just mentioned; can the other have been the Louvre “Virgin with St Anne and St John,” now at last completed from the cartoon exhibited in 1501? Meantime the master’s main home and business were at Milan. Few works of painting and none of sculpture (unless the unfulfilled commission for the Trivulzio monument belongs to this time) are recorded as occupying him during the seven years of his second residence in that city (1506-1513). He had attached to himself a new and devoted young friend and pupil of noble birth, Francesco Melzi. At the villa of the Melzi family at Vaprio, where Leonardo was a frequent visitor, a colossal Madonna on one of the walls is traditionally ascribed to him, but is rather the work of Sodoma or of Melzi himself working under the master’s eye. Another painter in the service of the French king, Jehan Perréal or Jehan de Paris, visited Milan, and consultations on technical points were held between him and Leonardo. But Leonardo’s chief practical employments were evidently on the continuation of his great hydraulic and irrigation works in Lombardy. His old trivial office of pageant-master and inventor of scientific toys was revived on the occasion of Louis XII.’s triumphal entry after the victory of Agnadello in 1509, and gave intense delight to the French retinue of the king. He was consulted on the construction of new choir-stalls for the cathedral. He laboured in the natural sciences as ardently as ever, especially at anatomy in company with the famous professor of Pavia, Marcantonio della Torre. To about this time, when he was approaching his sixtieth year, may belong the noble portrait-drawing of himself in red chalk at Turin. He looks too old for his years, but quite unbroken; the character of a veteran sage has fully imprinted itself on his countenance; the features are grand, clear and deeply lined, the mouth firmly set and almost stern, the eyes strong and intent beneath their bushy eyebrows, the hair flows untrimmed over his shoulders and commingles with a majestic beard.
Returning to Milan with his law-suits ended in 1511, Leonardo might have looked forward to an old age of contented labour, the chief task of which, had he had his will, would undoubtedly have been to put in order the vast mass of observations and speculations accumulated in his note-books, and to prepare some of them for publication. But as his star seemed rising that of his royal protector declined. The hold of the French on Lombardy was rudely shaken by hostile political powers, then confirmed again for a while by the victories of Gaston de Foix, and finally destroyed by the battle in which that hero fell under the walls of Ravenna. In June 1512 a coalition between Spain, Venice and the pope re-established the Sforza dynasty in power at Milan in the person of Ludovico’s son Massimiliano. This prince must have been familiar with Leonardo as a child, but perhaps resented the ready transfer of his allegiance to the French, and at any rate gave him no employment. Within a few months the ageing master uprooted himself from Milan, and moved with his chattels and retinue of pupils to Rome, into the service of the house that first befriended him, the Medici. The vast enterprises of Pope Julius II. had already made Rome the chief seat and centre of Italian art. The accession of Giulio de’ Medici in 1513 under the title of Leo X. raised on all hands hopes of still ampler and more sympathetic patronage. Leonardo’s special friend at the papal court was the pope’s youngest brother, Giuliano de’ Medici, a youth who combined dissipated habits with thoughtful culture and a genuine interest in arts and sciences. By his influence Leonardo and his train were accommodated with apartments in the Belvedere of the Vatican. But the conditions of the time and place proved adverse. The young generation held the field. Michelangelo and Raphael, who had both, as we have seen, risen to greatness partly on Leonardo’s shoulders, were fresh from the glory of their great achievements in the Sistine Chapel and the Stanze. Their rival factions hated each other, but both, especially the faction of Michelangelo, turned bitterly against the veterannewcomer. The pope, indeed, is said to have been delighted with Leonardo’s minor experiments and ingenuities in science, and especially by a kind of zoological toys which he had invented by way of pastime, as well as mechanical tricks played upon living animals. But for the master’s graver researches and projects he cared little, and was far more interested in the dreams of astrologers and alchemists. When Leonardo, having received a commission for a picture, was found distilling for himself a new medium of oils and herbs before he had begun the design, the pope was convinced, not quite unreasonably, that nothing serious would come of it. The only paintings positively recorded as done by him at Rome are two small panels for an official of the papal court, one of a child, the other of a Madonna, both now lost or unrecognized. To this time may also belong a lost Leda, standing upright with the god in swan’s guise at her side and the four children near their feet. This picture was at Fontainebleau in the 16th century and is known from several copies, the finest of them at the Borghese gallery, as well as from one or two preliminary sketches by the master himself and a small sketch copy by Raphael. A portrait of a Florentine lady, said to have been painted for Giuliano de’ Medici and seen afterwards in France, may also have been done at Rome; or may what we learn of this be only a confused account of the Monna Lisa? Tradition ascribes to Leonardo an attractive fresco of a Madonna with a donor in the convent of St Onofrio, but this seems to be clearly the work of Boltraffio. The only engineering works we hear of at this time are some on the harbour and defences of Cività Vecchia. On the whole the master in these Roman days found himself slighted for the first and only time in his life. He was, moreover, plagued by insubordination and malignity on the part of two German assistant craftsmen lodged in his apartments. Charges of impiety and body-snatching laid by these men in connexion with his anatomical studies caused the favour of the pope to be for a time withdrawn. After a stay of less than two years, Leonardo left Rome under the following circumstances. Louis XII. of France had died in the last days of 1514. His young and brilliant successor, Francis I., surprised Europe by making a sudden dash at the head of an army across the Alps to vindicate his rights in Italy. After much hesitation Leo X. in the summer of 1515 ordered Giuliano de’ Medici, as gonfalonier of the Church, to lead a papal force into the Emilia and watch the movements of the invader. Leonardo accompanied his protector on the march, and remained with the headquarters of the papal army at Piacenza when Giuliano fell ill and retired to Florence. After the battle of Marignano it was arranged that Francis and the pope should meet in December at Bologna. The pope, travelling by way of Florence and discussing there the great new scheme of the Laurentian library, entertained the idea of giving the commission to Leonardo; but Michelangelo came in hot haste from Rome and succeeded in securing it for himself. As the time for the meeting of the potentates at Bologna drew near, Leonardo proceeded thither from Piacenza, and in due course was presented to the king. Between the brilliant young sovereign and the grand old sage an immediate and strong sympathy sprang up; Leonardo accompanied Francis on his homeward march as far as Milan, and there determined to accept the royal invitation to France, where a new home was offered him with every assurance of honour and regard.
The remaining two and a half years of Leonardo’s life were spent at the Castle of Cloux near Amboise, which was assigned, with a handsome pension, to his use. The court came often to Amboise, and the king delighted in his company, declaring his knowledge both of the fine arts and of philosophy to be beyond those of all mortal men. In the spring of 1518 Leonardo had occasion to exercise his old talents as a festival-master when the dauphin was christened and a Medici-Bourbon marriage celebrated. He drew the designs for a new palace at Amboise, and was much engaged with the project of a great canal to connect the Loire and Saône. An ingenious attempt has been made to prove, in the absence of records, that the famous spiral staircase at Blois was also of his designing.
Among his visitors was a fellow-countryman, Cardinal Louis of Aragon, whose secretary has left an account of the day. Leonardo, it seems, was suffering from some form of slight paralysis which impaired his power of hand. But he showed the cardinal three pictures, the portrait of a Florentine lady done for Giuliano de’ Medici (the Gioconda?), the Virgin in the lap of St Anne (the Louvre picture; finished at Florence or Milan 1507-1513?), and a youthful John the Baptist. The last, which may have been done since he settled in France, is the darkened and partly repainted, but still powerful and haunting half-length figure in the Louvre, with the smile of inward ravishment and the prophetic finger beckoning skyward like that of St Anne in the Academy cartoon. Of the “Pomona” mentioned by Lomazzo as a work of the Amboise time his visitor says nothing, nor yet of the Louvre “Bacchus,” which tradition ascribes to Leonardo but which is clearly pupil’s work. Besides pictures, the master seems also to have shown and explained to his visitors some of his vast store of notes and observations on anatomy and physics. He kept hoping to get some order among his papers, the accumulation of more than forty years, and perhaps to give the world some portion of the studies they contained. But his strength was nearly exhausted. On Easter Eve 1519, feeling that the end was near, he made his will. It made provision, as became a great servant of the most Christian king, for masses to be said and candles to be offered in three different churches of Amboise, first among them that of St Florentin, where he desired to be buried, as well as for sixty poor men to serve as torch-bearers at his funeral. Vasari babbles of a death-bed conversion and repentance. But Leonardo had never been either a friend or an enemy of the Church. Sometimes, indeed, he denounces fiercely enough the arts and pretensions of priests; but no one has embodied with such profound spiritual insight some of the most vital moments of the Christian story. His insatiable researches into natural fact brought upon him among the vulgar some suspicion of practising those magic arts which of all things he scouted and despised. The bent of his mind was all towards the teachings of experience and against those of authority, and laws of nature certainly occupied far more of his thoughts than dogmas of religion; but when he mentions these it is with respect as throwing light on the truth of things from a side which was not his own. His conformity at the end had in it nothing contradictory of his past. He received the sacraments of the Church and died on the 2nd of May 1519. King Francis, then at his court of St Germain-en-Laye, is said to have wept for the loss of such a servant; that he was present beside the death-bed and held the dying painter in his arms is a familiar but an untrue tale. After a temporary sepulture elsewhere his remains were transported on the 12th of August to the cloister of St Florentin according to his wish. He left all his MSS. and apparently all the contents of his studio, with other gifts, to the devoted Melzi, whom he named executor; to Salai and to his servant Battista Villanis a half each of his vineyard outside Milan; gifts of money and clothes to his maid Maturina; one of money to the poor of the hospital in Amboise; and to his unbrotherly half-brothers a sum of four hundred ducats lying to his credit at Florence.
History tells of no man gifted in the same degree as Leonardo was at once for art and science. In art he was an inheritor and perfecter, born in a day of great and many-sided endeavours on which he put the crown, surpassing both predecessors and contemporaries. In science, on the other hand, he was a pioneer, working wholly for the future, and in great part alone. That the two stupendous gifts should in some degree neutralize each other was inevitable. No imaginable strength of any single man would have sufficed to carry out a hundredth part of what Leonardo essayed. The mere attempt to conquer the kingdom of light and shade for the art of painting was destined to tax the skill of generations, and is perhaps not wholly and finally accomplished yet. Leonardo sought to achieve that conquest and at the same time to carry the old Florentine excellences of linear drawing and psychological expression to a perfection of which other menhad not dreamed. The result, though marvellous in quality, is in quantity lamentably meagre. Knowing and doing allured him equally, and in art, which consists in doing, his efforts were often paralysed by his strained desire to know. The thirst for knowledge had first been aroused in him by the desire of perfecting the images of beauty and power which it was his business to create.
Thence there grew upon him the passion of knowledge for its own sake. In the splendid balance of his nature the Virgilian longing,rerum cognoscere causas, could never indeed wholly silence the call to exercise his active powers. But the powers he cared most to exercise ceased by degree to be those of imaginative creation, and came to be those of turning to practical human use the mastery which his studies had taught him over the forces of nature. In science he was the first among modern men to set himself most of those problems which unnumbered searchers of later generations have laboured severally or in concert to solve. Florence had had other sons of comprehensive genius, artistic and mechanical, Leon Battista Alberti perhaps the chief. But the more the range and character of Leonardo’s studies becomes ascertained the more his greatness dwarfs them all. A hundred years before Bacon, say those who can judge best, he showed a firmer grasp of the principles of experimental science than Bacon showed, fortified by a far wider range of actual experiment and observation. Not in his actual conclusions, though many of these point with surprising accuracy in the direction of truths established by later generations, but in the soundness, the wisdom, the tenacity of his methods lies his great title to glory. Had the Catholic reaction not fatally discouraged the pursuit of the natural sciences in Italy, had Leonardo even left behind him any one with zeal and knowledge enough to extract from the mass of his MSS. some portion of his labours in those sciences and give them to the world, an incalculable impulse would have been given to all those enquiries by which mankind has since been striving to understand the laws of its being and control the conditions of its environment,—to mathematics and astronomy, to mechanics, hydraulics, and physics generally, to geology, geography, and cosmology, to anatomy and the sciences of life. As it was, these studies of Leonardo—“studies intense of strong and stern delight”—seemed to his trivial followers and biographers merely his whims and fancies,ghiribizzi, things to be spoken of slightingly and with apology. The MSS., with the single exception of some of those relating to painting, lay unheeded and undivulged until the present generation; and it is only now that the true range of Leonardo’s powers is beginning to be fully discerned.
So much for the intellectual side of Leonardo’s character and career. As a moral being we are less able to discern what he was like. The man who carried in his brain so many images of subtle beauty, as well as so much of the hidden science of the future, must have lived spiritually, in the main, alone. Of things communicable he was at the same time, as we have said, communicative—a genial companion, a generous and loyal friend, ready and eloquent of discourse, impressing all with whom he was brought in contact by the power and the charm of genius, and inspiring fervent devotion and attachment in friends and pupils. We see him living on terms of constant affection with his father, and in disputes with his brothers not the aggressor but the sufferer from aggression. We see him full of tenderness to animals, a virtue not common in Italy in spite of the example of St Francis; open-handed in giving, not eager in getting—“poor,” he says, “is the man of many wants”; not prone to resentment—“the best shield against injustice is to double the cloak of long-suffering”; zealous in labour above all men—“as a day well spent gives joyful sleep, so does a life well spent give joyful death.” With these instincts and maxims, and with his strength, granting it almost more than human, spent ever tunnelling in abstruse mines of knowledge, his moral experience is not likely to have been deeply troubled. In religion, he regarded the faith of his age and country at least with imaginative sympathy and intellectual acquiescence, if no more. On the political storms which shook his country and drove him from one employment to another, he seems to have looked not with the passionate participation of a Dante or a Michelangelo but rather with the serene detachment of a Goethe. In matters of the heart, if any consoling or any disturbing passion played a great part in his life, we do not know it; we know only (apart from a few passing shadows cast by calumny and envy) of affectionate and dignified relations with friends, patrons and pupils, of public and private regard mixed in the days of his youth with dazzled admiration, and in those of his age with something of reverential awe.
The Drawings of Leonardo.—These are among the greatest treasures ever given to the world by the human spirit expressing itself in pen and pencil. Apart from the many hundreds of illustrative pen-sketches scattered through his autobiographic and scientific MSS., the principal collection is at Windsor Castle (partly derived from the Arundel collection); others of importance are in the British Museum; at Christ Church, Oxford; in the Louvre, at Chantilly, in the Uffizi, the Venice Academy, the Royal Library at Turin, the Museum of Budapest, and in the collections of M. Bonnat, Mrs Mond, and Captain Holford. Leonardo’s chief implements were pen, silver-point, and red and black chalk (red chalk especially). In silver-point there are many beautiful drawings of his earlier time, and some of his later; but of the charming heads of women and young men in this material attributed to him in various collections, comparatively few are his own work, the majority being drawings in his spirit by his pupils Ambrogio Preda or Boltraffio. Leonardo appears to have been left-handed. There is some doubt on the point; but a contemporary and intimate friend, Luca Pacioli, speaks of his “ineffable left hand”; all the best of his drawings are shaded downward from left to right, which would be the readiest way for a left-handed man; and his habitual eccentric practice of writing from right to left is much more likely to have been due to natural left-handedness than to any desire of mystery or concealment. A full critical discussion and catalogue of the extant drawings of Leonardo are to be found in Berenson’sDrawings of the Florentine Painters.The Writings of Leonardo.—The only printed book bearing Leonardo’s name until the recent issues of transcripts from his MSS. was the celebratedTreatise on Painting(Trattato della pittura, Traité de la peinture). This consists of brief didactic chapters, or more properly paragraphs, of practical direction or critical remark on all the branches and conditions of a painter’s practice. The original MS. draft of Leonardo has been lost, though a great number of notes for it are scattered through the various extant volumes of his MSS. The work has been printed in two different forms; one of these is an abridged version consisting of 365 sections; the first edition of it was published in Paris in 1551, by Raphael Dufresne, from a MS. which he found in the Barberini library; the last, translated into English by J. F. Rigaud, in London, 1877. The other is a more extended version, in 912 sections, divided into eight books; this was printed in 1817 by Guglielmo Manzi at Rome, from two MSS. which he had discovered in the Vatican library; a German translation from the same MS. has been edited by G. H. Ludwig in Eitelberger’s series ofQuellenschriften für Kunstgeschichte(Vienna, 1882; Stuttgart, 1885). On the history of the book in general see Max Jordan,Das Malerbuch des Leonardo da Vinci(Leipzig, 1873). The unknown compilers of the Vatican MSS. must have had before them much more of Leonardo’s original text than is now extant. Only about a quarter of the total number of paragraphs are identical with passages to be found in the master’s existing autograph note-books. It is indeed doubtful whether Leonardo himself ever completed the MS. treatise (or treatises) on painting and kindred subjects mentioned by Fra Luca Pacioli and by Vasari, and probable that the form and order, and perhaps some of the substance, of theTrattatoas we have it was due to compilers and not to the master himself.In recent years a whole body of scholars and editors have been engaged in giving to the world the texts of Leonardo’s existing MSS. The history of these is too complicated to be told here in any detail. Francesco Melzi (d. 1570) kept the greater part of his master’s bequest together as a sacred trust as long as he lived, though even in his time some MSS. on the art of painting seem to have passed into other hands. But his descendants suffered the treasure to be recklessly dispersed. The chief agents in their dispersal were the Doctor Orazio Melzi who possessed them in the last quarter of the 16th century; the members of a Milanese family called Mazzenta, into whose hands they passed in Orazio Melzi’s lifetime; and the sculptor Pompeo Leoni, who at one time entertained the design of procuring their presentation to Philip II. of Spain, and who cut up a number of the note-books to form the great miscellaneous single volume called theCodice Atlantico, now at Milan. This volume, with a large proportion of the total number of other Leonardo MSS. then existing, passed into the hands of a Count Arconati, who presented them to the Ambrosian library at Milan in 1636. In the meantime the earl of Arundel had made a vain attempt to purchase one of these volumes (theCodice Atlantico?) at a great price for the king of England. Some stray parts of the collection, including the MSS. now at Windsor, did evidently come into Lord Arundel’s possession, and the history of some other parts can befollowed; while much, it is evident, was lost for good. In 1796 Napoleon swept away to Paris, along with the other art treasures of Italy, the whole of the Leonardo MSS. at the Ambrosiana: only theCodice Atlanticowas afterwards restored, the other volumes remaining the property of the Institut de France. These also have had their adventures, two of them having been stolen by Count Libri and passed temporarily into the collection of Lord Ashburnham, whence they were in recent years made over again to the Institute. The first important step towards a better knowledge of the MSS. was made by the beginning, in 1880, of the great series of publications from the MSS. of the Institut de France undertaken by C. Ravaisson-Mollien; the next by the publication in 1883 of Dr J. P. Richter’sLiterary Works of Leonardo da Vinci(see Bibliography): this work included, besides a history and analytical index of the MSS., facsimiles of a number of selected pages containing matter of autobiographical, artistic, or literary interest, with transcripts and translations of their MS. contexts. Since then much progress has been made in the publication of the complete MSS., scientific and other, whether with adequate critical apparatus or in the form of mere facsimile without transliteration or comment.A brief statement follows of the present distribution of the several MSS. and of the form in which they are severally published:—England.—Windsor: Nine MSS., chiefly on anatomy, published entire in simple facsimile by Rouveyre (Paris, 1901); partially, with transliterations and introduction by Piumati and Sabachnikoff (Paris, 1898, foll.);British Museum: one MS., miscellaneous, unpublished;Victoria and Albert Museum: ten note-books bound in 3 vols.; facsimile by Rouveyre,Holkham(collection of Lord Leicester), 1 vol., on hydraulics and the action of water; published in facsimile with transliteration and notes by Gerolamo Calvi.France.—Institut de France: seventeen MSS., all published with transliteration and notes by C. Ravaisson-Mollien (6 vols., Paris, 1880-1891).Italy.—Milan,Ambrosiana: theCodice Atlantico, the huge miscellany, of vital importance for the study of the master, put together by Pompeo Leoni; published in facsimile, with transliteration, by the Accademia dei Lincei (1894, foll.);Milan: collection of Count Trivulzio; 1 vol., miscellaneous; published and edited by L. Beltrami (1892);Rome: collection of Count Marszolini;Treatise on the Flight of Birds, published and edited by Piumati and Sabachnikoff (Paris, 1492).Bibliography.—The principal authorities are:—“Il libro di Antonio Billi,” edited from MS. by G. de Fabriazy inArchivio Storico Ital.ser. v. vol. 7; “Breve vita di Leonardo da Vinci, scritto da un adnonimo del 1500” (known as the Anonimo Gaddiano), printed by G. Milanesi inArchivio Storico Ital.t. xvi. (1872), translated with notes by H. P. Horne in series published by the Unicorn Library (1903); Paolo Giovio, “Leonardi Vincii vita,” in hisElogia, printed in Tiraboschi,Storia della Lett. Ital.t. vii. pt. 4, and inClassici Italiani, vol. 314; Vasari, in his celebratedLives of the Painters(1st ed., Florence, 1550; 2nd ed.ibid.1568; ed. Milanesi, with notes and supplements, 1878-1885); Sabba da Castiglione,Ricordi(Venice, 1565); G. P. Lomazzo,Trattato dell’ arte della pittura, &c. (Milan, 1584-1585);Id., Idea del tempio della pittura(Milan, 1591); Le Père Dan,Le Trésor ... de Fontainebleau(1642); J. B. Venturi,Essai sur les ouvrages physico-mathématiques de L. da V.(Paris, 1797); C. Amoretti,Memorie storiche sulla vita, &c. di L. da V.(Milan, 1804), a work which laid the foundation of all future researches; Giuseppe Bossi,Del Cenacolo di L. da V.(Milan, 1810); C. Fumagalli,Scuola di Leonardo da Vinci(1811); Gaye,Carteggia d’artisti(1839-1841); G. Uzielli,Ricerche intorno a L. da V., series 1, 2 (Florence, 1872; Rome, 1884; series 1 revised, Turin, 1896), documentary researches of the first importance for the study; C. L. Calvi,Notizie dei principali professori di belle arti(Milan, 1869); Arsène Houssaye,Histoire de L. de V.(Paris, 1869 and 1876, an agreeable literary biography of the pre-critical kind); Mrs Heaton,Life of L. da V.(London, 1872), a work also made obsolete by recent research; Hermann Grothe,L. da V. als Ingenieur und Philosoph(Berlin, 1874); A. Marks, theS. Anne of L. da V.(London, 1882); J. P. Richter,The Literary Works of L. da V.(2 vols., London, 1883), this is the very important and valuable history of and selection from the texts mentioned above under MSS.; Ch. Ravaisson-Mollien,Les Écrits de L. da V.(Paris, 1881); Paul Müller Walde,L. da V., Lebensskizze und Forschungen(Munich, 1889-1890);Id., “Beiträge zur Kenntniss des L. da V.,”in Jahrbuch der k. Preussischen Kunstsammlungen(1897-1899), the first immature and incomplete, the second of high value: the whole life of this writer has been devoted to the study of L. da V., but it is uncertain whether the vast mass of material collected by him will ever take shape or see the light; G. Gronau,L. da V.(London, 1902); Bernhard Berenson,The Drawings of the Florentine Painters(London, 1903); Edmondo Solmi,Studi sulla filosofia naturale di L. da V.(Modena, 1898);Id., Leonardo(Florence, 1st ed. 1900, 2nd ed. 1907; this last edition of Solmi’s work is by far the most complete and satisfactory critical biography of the master which yet exists); A. Rosenberg,L. da V., in Knackfuss’s series of art biographies (Leipzig, 1898); Gabriel Séailles,L. da V. l’artiste et le savant(1st ed. 1892, 2nd ed. 1906), a lucid and careful general estimate of great value, especially in reference to Leonardo’s relations to modern science; Edward McCurdy,L. da V., in Bell’s “Great Masters” series (1904 and 1907), a very sound and trustworthy summary of the master’s career as an artist;Id., L. da V.’s Note-Books(1908), a selection from the passages of chief general interest in the master’s MSS., very well chosen, arranged, and translated, with a useful history of the MSS. prefixed,Le Vicende del Cenacolo di L. da V. nel secolo XIX.(Milan, 1906), an official account of the later history and vicissitudes of the “Last Supper” previous to its final repair; Luca Beltrami,Il Castello di Milano(1894);Id., L. da V. et la Sala dell’ Asse(1902); Id., “Il Cenacolo di Leonardo,” inRaccolta Vinciana(Milan, 1908), the official account of the successful work of repair carried out by Signor Cavenaghi in the preceding years; Woldemar von Seidlitz,Leonardo da Vinci, der Wendepunkt der Renaissance(2 vols., 1909), a comprehensive and careful work by an accomplished and veteran critic, inclined to give perhaps an excessive share in the reputed works of Leonardo to a single pupil, Ambrogio Preda. It seems needless to give references to the voluminous discussion in newspapers and periodicals concerning the authenticity of a wax bust of Flora acquired in 1909 for the Berlin Museum and unfortunately ascribed to Leonardo da Vinci, its real author having been proved by external and internal evidence to be the Englishman Richard Cockle Lucas, and its date 1846.
The Drawings of Leonardo.—These are among the greatest treasures ever given to the world by the human spirit expressing itself in pen and pencil. Apart from the many hundreds of illustrative pen-sketches scattered through his autobiographic and scientific MSS., the principal collection is at Windsor Castle (partly derived from the Arundel collection); others of importance are in the British Museum; at Christ Church, Oxford; in the Louvre, at Chantilly, in the Uffizi, the Venice Academy, the Royal Library at Turin, the Museum of Budapest, and in the collections of M. Bonnat, Mrs Mond, and Captain Holford. Leonardo’s chief implements were pen, silver-point, and red and black chalk (red chalk especially). In silver-point there are many beautiful drawings of his earlier time, and some of his later; but of the charming heads of women and young men in this material attributed to him in various collections, comparatively few are his own work, the majority being drawings in his spirit by his pupils Ambrogio Preda or Boltraffio. Leonardo appears to have been left-handed. There is some doubt on the point; but a contemporary and intimate friend, Luca Pacioli, speaks of his “ineffable left hand”; all the best of his drawings are shaded downward from left to right, which would be the readiest way for a left-handed man; and his habitual eccentric practice of writing from right to left is much more likely to have been due to natural left-handedness than to any desire of mystery or concealment. A full critical discussion and catalogue of the extant drawings of Leonardo are to be found in Berenson’sDrawings of the Florentine Painters.
The Writings of Leonardo.—The only printed book bearing Leonardo’s name until the recent issues of transcripts from his MSS. was the celebratedTreatise on Painting(Trattato della pittura, Traité de la peinture). This consists of brief didactic chapters, or more properly paragraphs, of practical direction or critical remark on all the branches and conditions of a painter’s practice. The original MS. draft of Leonardo has been lost, though a great number of notes for it are scattered through the various extant volumes of his MSS. The work has been printed in two different forms; one of these is an abridged version consisting of 365 sections; the first edition of it was published in Paris in 1551, by Raphael Dufresne, from a MS. which he found in the Barberini library; the last, translated into English by J. F. Rigaud, in London, 1877. The other is a more extended version, in 912 sections, divided into eight books; this was printed in 1817 by Guglielmo Manzi at Rome, from two MSS. which he had discovered in the Vatican library; a German translation from the same MS. has been edited by G. H. Ludwig in Eitelberger’s series ofQuellenschriften für Kunstgeschichte(Vienna, 1882; Stuttgart, 1885). On the history of the book in general see Max Jordan,Das Malerbuch des Leonardo da Vinci(Leipzig, 1873). The unknown compilers of the Vatican MSS. must have had before them much more of Leonardo’s original text than is now extant. Only about a quarter of the total number of paragraphs are identical with passages to be found in the master’s existing autograph note-books. It is indeed doubtful whether Leonardo himself ever completed the MS. treatise (or treatises) on painting and kindred subjects mentioned by Fra Luca Pacioli and by Vasari, and probable that the form and order, and perhaps some of the substance, of theTrattatoas we have it was due to compilers and not to the master himself.
In recent years a whole body of scholars and editors have been engaged in giving to the world the texts of Leonardo’s existing MSS. The history of these is too complicated to be told here in any detail. Francesco Melzi (d. 1570) kept the greater part of his master’s bequest together as a sacred trust as long as he lived, though even in his time some MSS. on the art of painting seem to have passed into other hands. But his descendants suffered the treasure to be recklessly dispersed. The chief agents in their dispersal were the Doctor Orazio Melzi who possessed them in the last quarter of the 16th century; the members of a Milanese family called Mazzenta, into whose hands they passed in Orazio Melzi’s lifetime; and the sculptor Pompeo Leoni, who at one time entertained the design of procuring their presentation to Philip II. of Spain, and who cut up a number of the note-books to form the great miscellaneous single volume called theCodice Atlantico, now at Milan. This volume, with a large proportion of the total number of other Leonardo MSS. then existing, passed into the hands of a Count Arconati, who presented them to the Ambrosian library at Milan in 1636. In the meantime the earl of Arundel had made a vain attempt to purchase one of these volumes (theCodice Atlantico?) at a great price for the king of England. Some stray parts of the collection, including the MSS. now at Windsor, did evidently come into Lord Arundel’s possession, and the history of some other parts can befollowed; while much, it is evident, was lost for good. In 1796 Napoleon swept away to Paris, along with the other art treasures of Italy, the whole of the Leonardo MSS. at the Ambrosiana: only theCodice Atlanticowas afterwards restored, the other volumes remaining the property of the Institut de France. These also have had their adventures, two of them having been stolen by Count Libri and passed temporarily into the collection of Lord Ashburnham, whence they were in recent years made over again to the Institute. The first important step towards a better knowledge of the MSS. was made by the beginning, in 1880, of the great series of publications from the MSS. of the Institut de France undertaken by C. Ravaisson-Mollien; the next by the publication in 1883 of Dr J. P. Richter’sLiterary Works of Leonardo da Vinci(see Bibliography): this work included, besides a history and analytical index of the MSS., facsimiles of a number of selected pages containing matter of autobiographical, artistic, or literary interest, with transcripts and translations of their MS. contexts. Since then much progress has been made in the publication of the complete MSS., scientific and other, whether with adequate critical apparatus or in the form of mere facsimile without transliteration or comment.
A brief statement follows of the present distribution of the several MSS. and of the form in which they are severally published:—
England.—Windsor: Nine MSS., chiefly on anatomy, published entire in simple facsimile by Rouveyre (Paris, 1901); partially, with transliterations and introduction by Piumati and Sabachnikoff (Paris, 1898, foll.);British Museum: one MS., miscellaneous, unpublished;Victoria and Albert Museum: ten note-books bound in 3 vols.; facsimile by Rouveyre,Holkham(collection of Lord Leicester), 1 vol., on hydraulics and the action of water; published in facsimile with transliteration and notes by Gerolamo Calvi.France.—Institut de France: seventeen MSS., all published with transliteration and notes by C. Ravaisson-Mollien (6 vols., Paris, 1880-1891).Italy.—Milan,Ambrosiana: theCodice Atlantico, the huge miscellany, of vital importance for the study of the master, put together by Pompeo Leoni; published in facsimile, with transliteration, by the Accademia dei Lincei (1894, foll.);Milan: collection of Count Trivulzio; 1 vol., miscellaneous; published and edited by L. Beltrami (1892);Rome: collection of Count Marszolini;Treatise on the Flight of Birds, published and edited by Piumati and Sabachnikoff (Paris, 1492).
Bibliography.—The principal authorities are:—“Il libro di Antonio Billi,” edited from MS. by G. de Fabriazy inArchivio Storico Ital.ser. v. vol. 7; “Breve vita di Leonardo da Vinci, scritto da un adnonimo del 1500” (known as the Anonimo Gaddiano), printed by G. Milanesi inArchivio Storico Ital.t. xvi. (1872), translated with notes by H. P. Horne in series published by the Unicorn Library (1903); Paolo Giovio, “Leonardi Vincii vita,” in hisElogia, printed in Tiraboschi,Storia della Lett. Ital.t. vii. pt. 4, and inClassici Italiani, vol. 314; Vasari, in his celebratedLives of the Painters(1st ed., Florence, 1550; 2nd ed.ibid.1568; ed. Milanesi, with notes and supplements, 1878-1885); Sabba da Castiglione,Ricordi(Venice, 1565); G. P. Lomazzo,Trattato dell’ arte della pittura, &c. (Milan, 1584-1585);Id., Idea del tempio della pittura(Milan, 1591); Le Père Dan,Le Trésor ... de Fontainebleau(1642); J. B. Venturi,Essai sur les ouvrages physico-mathématiques de L. da V.(Paris, 1797); C. Amoretti,Memorie storiche sulla vita, &c. di L. da V.(Milan, 1804), a work which laid the foundation of all future researches; Giuseppe Bossi,Del Cenacolo di L. da V.(Milan, 1810); C. Fumagalli,Scuola di Leonardo da Vinci(1811); Gaye,Carteggia d’artisti(1839-1841); G. Uzielli,Ricerche intorno a L. da V., series 1, 2 (Florence, 1872; Rome, 1884; series 1 revised, Turin, 1896), documentary researches of the first importance for the study; C. L. Calvi,Notizie dei principali professori di belle arti(Milan, 1869); Arsène Houssaye,Histoire de L. de V.(Paris, 1869 and 1876, an agreeable literary biography of the pre-critical kind); Mrs Heaton,Life of L. da V.(London, 1872), a work also made obsolete by recent research; Hermann Grothe,L. da V. als Ingenieur und Philosoph(Berlin, 1874); A. Marks, theS. Anne of L. da V.(London, 1882); J. P. Richter,The Literary Works of L. da V.(2 vols., London, 1883), this is the very important and valuable history of and selection from the texts mentioned above under MSS.; Ch. Ravaisson-Mollien,Les Écrits de L. da V.(Paris, 1881); Paul Müller Walde,L. da V., Lebensskizze und Forschungen(Munich, 1889-1890);Id., “Beiträge zur Kenntniss des L. da V.,”in Jahrbuch der k. Preussischen Kunstsammlungen(1897-1899), the first immature and incomplete, the second of high value: the whole life of this writer has been devoted to the study of L. da V., but it is uncertain whether the vast mass of material collected by him will ever take shape or see the light; G. Gronau,L. da V.(London, 1902); Bernhard Berenson,The Drawings of the Florentine Painters(London, 1903); Edmondo Solmi,Studi sulla filosofia naturale di L. da V.(Modena, 1898);Id., Leonardo(Florence, 1st ed. 1900, 2nd ed. 1907; this last edition of Solmi’s work is by far the most complete and satisfactory critical biography of the master which yet exists); A. Rosenberg,L. da V., in Knackfuss’s series of art biographies (Leipzig, 1898); Gabriel Séailles,L. da V. l’artiste et le savant(1st ed. 1892, 2nd ed. 1906), a lucid and careful general estimate of great value, especially in reference to Leonardo’s relations to modern science; Edward McCurdy,L. da V., in Bell’s “Great Masters” series (1904 and 1907), a very sound and trustworthy summary of the master’s career as an artist;Id., L. da V.’s Note-Books(1908), a selection from the passages of chief general interest in the master’s MSS., very well chosen, arranged, and translated, with a useful history of the MSS. prefixed,Le Vicende del Cenacolo di L. da V. nel secolo XIX.(Milan, 1906), an official account of the later history and vicissitudes of the “Last Supper” previous to its final repair; Luca Beltrami,Il Castello di Milano(1894);Id., L. da V. et la Sala dell’ Asse(1902); Id., “Il Cenacolo di Leonardo,” inRaccolta Vinciana(Milan, 1908), the official account of the successful work of repair carried out by Signor Cavenaghi in the preceding years; Woldemar von Seidlitz,Leonardo da Vinci, der Wendepunkt der Renaissance(2 vols., 1909), a comprehensive and careful work by an accomplished and veteran critic, inclined to give perhaps an excessive share in the reputed works of Leonardo to a single pupil, Ambrogio Preda. It seems needless to give references to the voluminous discussion in newspapers and periodicals concerning the authenticity of a wax bust of Flora acquired in 1909 for the Berlin Museum and unfortunately ascribed to Leonardo da Vinci, its real author having been proved by external and internal evidence to be the Englishman Richard Cockle Lucas, and its date 1846.
(S. C.)
LEONARDO OF PISA(Leonardus PisanusorFibonacci), Italian mathematician of the 13th century. Of his personal history few particulars are known. His father was called Bonaccio, most probably a nickname with the ironical meaning of “a good, stupid fellow,” while to Leonardo himself another nickname, Bigollone (dunce, blockhead), seems to have been given. The father was secretary in one of the numerous factories erected on the southern and eastern coasts of the Mediterranean by the warlike and enterprising merchants of Pisa. Leonardo was educated at Bugia, and afterwards toured the Mediterranean. In 1202 he was again in Italy and published his great work,Liber abaci, which probably procured him access to the learned and refined court of the emperor Frederick II. Leonardo certainly was in relation with some persons belonging to that circle when he published in 1220 another more extensive work,De practica geometriae, which he dedicated to the imperial astronomer Dominicus Hispanus. Some years afterwards (perhaps in 1228) Leonardo dedicated to the well-known astrologer Michael Scott the second edition of hisLiber abaci, which was printed with Leonardo’s other works by Prince Bald. Boncompagni (Rome, 1857-1862, 2 vols.). The other works consist of thePractica geometriaeand some most striking papers of the greatest scientific importance, amongst which theLiber quadratorummay be specially signalized. It bears the notice that the author wrote it in 1225, and in the introduction Leonardo tells us the occasion of its being written. Dominicus had presented Leonardo to Frederick II. The presentation was accompanied by a kind of mathematical performance, in which Leonardo solved several hard problems proposed to him by John of Palermo, an imperial notary, whose name is met with in several documents dated between 1221 and 1240. The methods which Leonardo made use of in solving those problems fill theLiber quadratorum, theFlos, and aLetter to Magister Theodore. All these treatises seem to have been written nearly at the same period, and certainly before the publication of the second edition of theLiber abaci, in which theLiber quadratorumis expressly mentioned. We know nothing of Leonardo’s fate after he issued that second edition.
Leonardo’s works are mainly developments of the results obtained by his predecessors; the influences of Greek, Arabian, and Indian mathematicians may be clearly discerned in his methods. In hisPractica geometriaeplain traces of the use of the Romanagrimensoresare met with; in hisLiber abaciold Egyptian problems reveal their origin by the reappearance of the very numbers in which the problem is given, though one cannot guess through what channel they came to Leonardo’s knowledge. Leonardo cannot be regarded as the inventor of that very great variety of truths for which he mentions no earlier source.TheLiber abaci, which fills 459 printed pages, contains the most perfect methods of calculating with whole numbers and with fractions, practice, extraction of the square and cube roots, proportion, chain rule, finding of proportional parts, averages, progressions, even compound interest, just as in the completest mercantile arithmetics of our days. They teach further the solution of problems leading to equations of the first and second degree, to determinate and indeterminate equations, not by single and double position only, but by real algebra, proved by means of geometric constructions, and including the use of letters as symbols for known numbers, the unknown quantity being calledresand its squarecensus.The second work of Leonardo, hisPractica geometriae(1220) requires readers already acquainted with Euclid’s planimetry, who are able to follow rigorous demonstrations and feel the necessity for them. Among the contents of this book we simply mention a trigonometrical chapter, in which the wordssinus versus arcusoccur, the approximate extraction of cube roots shown more at large than in theLiber abaci, and a very curious problem, which nobody would search for in a geometrical work, viz.—To find a square number remaining so after the addition of 5. This problem evidently suggested the first question, viz.—To find a square number which remains a square after the addition and subtraction of 5, put to our mathematician in presence of the emperor by John of Palermo, who, perhaps, was quite enough Leonardo’s friend to set him such problems only as he had himself asked for. Leonardo gave as solution the numbers 1197⁄144, 1697⁄144, and 697⁄144,—the squares of 35⁄12, 41⁄12and 27⁄12; and the method of finding them is given in theLiber quadratorum. We observe, however, that this kind of problem was not new. Arabian authors already had found three square numbers of equal difference, but the difference itself had not been assigned in proposing the question. Leonardo’s method, therefore, when the difference was a fixed condition of the problem, was necessarily very different from the Arabian, and, in all probability, was his own discovery. TheFlosof Leonardo turns on the second question set by John of Palermo, which required the solution of the cubic equation x3+ 2x2+ 10x = 20. Leonardo, making use of fractions of the sexagesimal scale, gives x = 1022i7ii42iii33iv4v40vi, after having demonstrated, by a discussion founded on the 10th book of Euclid, that a solution by square roots is impossible. It is much to be deplored that Leonardo does not give the least intimation how he found his approximative value, outrunning by this result more than three centuries. Genocchi believes Leonardo to have been in possession of a certain method calledregula aureaby H. Cardan in the 16th century, but this is a mere hypothesis without solid foundation. In theFlosequations with negative values of the unknown quantity are also to be met with, and Leonardo perfectly understands the meaning of these negative solutions. In theLetter to Magister Theodoreindeterminate problems are chiefly worked, and Leonardo hints at his being able to solve by a general method any problem of this kind not exceeding the first degree.As for the influence he exercised on posterity, it is enough to say that Luca Pacioli, about 1500, in his celebratedSumma, leans so exclusively to Leonardo’s works (at that time known in manuscript only) that he frankly acknowledges his dependence on them, and states that wherever no other author is quoted all belongs to Leonardus Pisanus.Fibonacci’s seriesis a sequence of numbers such that any term is the sum of the two preceding terms; also known asLamé’s series.
Leonardo’s works are mainly developments of the results obtained by his predecessors; the influences of Greek, Arabian, and Indian mathematicians may be clearly discerned in his methods. In hisPractica geometriaeplain traces of the use of the Romanagrimensoresare met with; in hisLiber abaciold Egyptian problems reveal their origin by the reappearance of the very numbers in which the problem is given, though one cannot guess through what channel they came to Leonardo’s knowledge. Leonardo cannot be regarded as the inventor of that very great variety of truths for which he mentions no earlier source.
TheLiber abaci, which fills 459 printed pages, contains the most perfect methods of calculating with whole numbers and with fractions, practice, extraction of the square and cube roots, proportion, chain rule, finding of proportional parts, averages, progressions, even compound interest, just as in the completest mercantile arithmetics of our days. They teach further the solution of problems leading to equations of the first and second degree, to determinate and indeterminate equations, not by single and double position only, but by real algebra, proved by means of geometric constructions, and including the use of letters as symbols for known numbers, the unknown quantity being calledresand its squarecensus.
The second work of Leonardo, hisPractica geometriae(1220) requires readers already acquainted with Euclid’s planimetry, who are able to follow rigorous demonstrations and feel the necessity for them. Among the contents of this book we simply mention a trigonometrical chapter, in which the wordssinus versus arcusoccur, the approximate extraction of cube roots shown more at large than in theLiber abaci, and a very curious problem, which nobody would search for in a geometrical work, viz.—To find a square number remaining so after the addition of 5. This problem evidently suggested the first question, viz.—To find a square number which remains a square after the addition and subtraction of 5, put to our mathematician in presence of the emperor by John of Palermo, who, perhaps, was quite enough Leonardo’s friend to set him such problems only as he had himself asked for. Leonardo gave as solution the numbers 1197⁄144, 1697⁄144, and 697⁄144,—the squares of 35⁄12, 41⁄12and 27⁄12; and the method of finding them is given in theLiber quadratorum. We observe, however, that this kind of problem was not new. Arabian authors already had found three square numbers of equal difference, but the difference itself had not been assigned in proposing the question. Leonardo’s method, therefore, when the difference was a fixed condition of the problem, was necessarily very different from the Arabian, and, in all probability, was his own discovery. TheFlosof Leonardo turns on the second question set by John of Palermo, which required the solution of the cubic equation x3+ 2x2+ 10x = 20. Leonardo, making use of fractions of the sexagesimal scale, gives x = 1022i7ii42iii33iv4v40vi, after having demonstrated, by a discussion founded on the 10th book of Euclid, that a solution by square roots is impossible. It is much to be deplored that Leonardo does not give the least intimation how he found his approximative value, outrunning by this result more than three centuries. Genocchi believes Leonardo to have been in possession of a certain method calledregula aureaby H. Cardan in the 16th century, but this is a mere hypothesis without solid foundation. In theFlosequations with negative values of the unknown quantity are also to be met with, and Leonardo perfectly understands the meaning of these negative solutions. In theLetter to Magister Theodoreindeterminate problems are chiefly worked, and Leonardo hints at his being able to solve by a general method any problem of this kind not exceeding the first degree.
As for the influence he exercised on posterity, it is enough to say that Luca Pacioli, about 1500, in his celebratedSumma, leans so exclusively to Leonardo’s works (at that time known in manuscript only) that he frankly acknowledges his dependence on them, and states that wherever no other author is quoted all belongs to Leonardus Pisanus.
Fibonacci’s seriesis a sequence of numbers such that any term is the sum of the two preceding terms; also known asLamé’s series.
(M. Ca.)
LEONCAVALLO, RUGGIERO(1858- ), Italian operatic composer, was born at Naples and educated for music at the conservatoire. After some years spent in teaching and in ineffectual attempts to obtain the production of more than one opera, hisPagliacciwas performed at Milan in 1892 with immediate success; and next year hisMediciwas also produced there. But neither the latter norChatterton(1896)—both early works—obtained any favour; and it was not tillLa Bohèmewas performed in 1897 at Venice that his talent obtained public confirmation. Subsequent operas by Leoncavallo wereZaza(1900), andDer Roland(1904). In all these operas he was his own librettist.
LEONIDAS,king of Sparta, the seventeenth of the Agiad line. He succeeded, probably in 489 or 488B.C., his half-brother Cleomenes, whose daughter Gorgo he married. In 480 he was sent with about 7000 men to hold the pass of Thermopylae against the army of Xerxes. The smallness of the force was, according to a current story, due to the fact that he was deliberately going to his doom, an oracle having foretold that Sparta could be saved only by the death of one of its kings: in reality it seems rather that the ephors supported the scheme half-heartedly, their policy being to concentrate the Greek forces at the Isthmus. Leonidas repulsed the frontal attacks of the Persians, but when the Malian Ephialtes led the Persian general Hydarnes by a mountain track to the rear of the Greeks he divided his army, himself remaining in the pass with 300 Spartiates, 700 Thespians and 400 Thebans. Perhaps he hoped to surround Hydarnes’ force: if so, the movement failed, and the little Greek army, attacked from both sides, was cut down to a man save the Thebans, who are said to have surrendered. Leonidas fell in the thickest of the fight; his head was afterwards cut off by Xerxes’ order and his body crucified. Our knowledge of the circumstancesistoo slight to enable us to judge of Leonidas’s strategy, but his heroism and devotion secured him an almost unique place in the imagination not only of his own but also of succeeding times.
See Herodotus v. 39-41, vii. 202-225, 238, ix. 10; Diodorus xi. 4-11; Plutarch,Apophthegm. Lacon.; de malignitate Herodoti, 28-33; Pausanias i. 13, iii. 3, 4; Isocrates,Paneg.92; Lycurgus,c.Leocr.110, 111; Strabo i. 10, ix. 429; Aelian,Var. hist.iii. 25; Cicero,Tusc. disput.i. 42, 49;de Finibus, ii. 30; Cornelius Nepos,Themistocles, 3; Valerius Maximus iii. 2; Justin ii. 11. For modern criticism on the battle of Thermopylae see G. B. Grundy,The Great Persian War(1901); G. Grote,History of Greece, part ii., c. 40; E. Meyer,Geschichte des Altertums, iii., §§ 219, 220; G. Busolt,Griechische Geschichte, 2nd ed., ii. 666-688; J. B. Bury, “The Campaign of Artemisium and Thermopylae,” inBritish School Annual, ii. 83 seq.; J. A. R. Munro, “Some Observations on the Persian Wars, II.,” inJournal of Hellenic Studies, xxii. 294-332.
See Herodotus v. 39-41, vii. 202-225, 238, ix. 10; Diodorus xi. 4-11; Plutarch,Apophthegm. Lacon.; de malignitate Herodoti, 28-33; Pausanias i. 13, iii. 3, 4; Isocrates,Paneg.92; Lycurgus,c.Leocr.110, 111; Strabo i. 10, ix. 429; Aelian,Var. hist.iii. 25; Cicero,Tusc. disput.i. 42, 49;de Finibus, ii. 30; Cornelius Nepos,Themistocles, 3; Valerius Maximus iii. 2; Justin ii. 11. For modern criticism on the battle of Thermopylae see G. B. Grundy,The Great Persian War(1901); G. Grote,History of Greece, part ii., c. 40; E. Meyer,Geschichte des Altertums, iii., §§ 219, 220; G. Busolt,Griechische Geschichte, 2nd ed., ii. 666-688; J. B. Bury, “The Campaign of Artemisium and Thermopylae,” inBritish School Annual, ii. 83 seq.; J. A. R. Munro, “Some Observations on the Persian Wars, II.,” inJournal of Hellenic Studies, xxii. 294-332.