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bound. Just as the Florentine school of painting was above all things a school of design, so the scientific men of Florence, not even excepting Galileo, shine by the rigour of their observation and the wisdom of their deductions. But such was the intellectual vitality of Italy, even when the seventeenth century was well on its way, that if for a moment activity died down in one province it was rekindled in another. Thus one sees, on an apparently exhausted soil, the Neapolitan school of philosophy spring up to seize the torch dropped in the north, and to give the world men like Telesio, Giordano Bruno, Campanella, and Vanini.

North Italy played the part of leaven in the case of Leonardo ; it was contact with the Milanese that drew out his scientific powers. His new fellow-citizens had neither the lofty culture of the Florentines nor their spiritual aspirations. They adhered, in fact, to doctrines diametrically opposed to those of the Tuscans. To the altar of Plato they opposed that of Aristotle, and of Avicenna and Averroes, his Arab interpreters. In the seventeenth century these leaders still counted numerous followers among the professors of Pavia, Padua, and Bologna.2 They were, if I am not mistaken, the true initiators of Leonardo. They taught him to observe as well as to reflect, and to alternate experiments with abstract thinking. Their disciple, independent as he is, constantly invokes their evidence, although he does not hesitate to expose any errors into which they seem to him to have fallen..

In the exact sciences, classical antiquity was by no means the only source of progress. A whole section of mathematics, and that not the least important, owed nothing to the Greeks, for numeration by means of ciphers came to us from the Hindoos through the Arabs. It was, moreover, by an Italian, Leonardo Pisano, called Fibonacci, the greatest mathematician of the Middle Ages, that these ciphers were made generally known.

On the other hand the Ptolemaic system of cosmography weighed

i Leonardo quotes Avicenna more than once (Richter, vol. ii. pp. 429, 431).
2 This Renan has abundantly proved in his book on Averroes and Averröism.

3 Liber Abaci, published in 1202. See Rudio, Ueber den Antheil der mathematischen Wissenschaften an der Kultur der Renaissance, Hamburg, 1892, p. 16.

heavily on Italian science and paralysed all progress. It was a foreign student in the Italian universities, Copernicus, who at last threw off the yoke.

Yet even if the Italians so easily put themselves at the head of civilisation, was it not owing to the rich legacies from the classic centuries which they had preserved, while the rest of the world was sunk in barbarism ? Besides, to place the commencement of the Renaissance in the fifteenth century, when the dreary school of the philologists arose, is to commit an anachronism. The Renaissance began a hundred years before that, with Petrarch.

If he had done nothing but enlarge the Florentine horizon by his migration to Upper Italy, Leonardo would have had no cause to regret his change of centre. But the Lombardo-Milanese character, heavy as it seemed, offered other advantages; it was energetic, coherent, and full of latent power. I am in a position to show how much, in one special direction, Leonardo owed to its inspiration or teaching. Until quite recently Leonardo has been credited with all the progress made in his time in hydraulics, and even with the invention canals! Now Signor Beltrami, the learned Milanese architect and engineer, has lately proved that as early as the twelfth century the Lombards had pressed the Ticino into the service both of irrigation and navigation. From that moment enterprises of the kind were rapidly multiplied, and a vast network of canals was spread over the fertile plains of Lombardy. In short, when Da Vinci appeared at Milan, that is, not before 1480, instead of being called upon to create hydraulics both in theory and practice, he had only to carry on the work of his predecessors, though a mind so gifted as his could not fail to renew it in details, and to enrich it in countless ways.

Here, as in so many other activities, we find the sceptical and initiative spirit, the realistic ferment, breaking into the classic tradition and becoming the chief factor in the Renaissance. Thanks to this tendency, as well as to the special aptitudes of Leonardo, the great renewal of human thought was extended to science as well as to art and poetry.)

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There is no doubt that Leonardo had already carried his own personal studies and experiments very far before he set to work to appropriate the labours of his predecessors, and to constitute what we should call the bibliography of the subject.

The detractors of the Renaissance—and they are not wanting in these days—affirm that the study of the classic writers and the idolatry of which they were once the object, long paralysed the progress of science. At first sight the example of Leonardo seems to justify their theory, but let us look a little deeper. Retrospective inquiry—a duty with all who really wish to understand what the past has left us--can only destroy initiative in those who possess but little of that faculty.1 Of this Leonardo himself affords a striking proof. He consults the ancients, but in the right sceptical spirit, accepting their discoveries when they seem to him well founded (what scientist could do

(Christ Church Library, Oxford.) otherwise ?) but never hesitating to set them aside when experience shows them to be mistaken. Thus he refutes Pliny's theory about the saltness of the

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ALLEGORICAL COMPOSITION. PLEASURE AND PAIN.

1 Take Polydorus Virgilius's Treatise on Inventions, for instance. Through this rigmarole of quotations we discern a faith in progress. The author examines the inventions of language, science, art, legislation, agriculture, in fact all the factors of civilisation. If he insists on the part played in these by the ancients, he does not forget to give the moderns credit for the invention of printing, explosives, and musical instruments,

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sea, and exhausts his powers of sarcasm over the notions of Epicurus as to the dimensions of the sun. “Let us suppose,” he says, “with Epicurus, that the sun's apparent size is its real one ; its diameter seeming to be the length of a foot, and the sun going one thousand times its own diameter in the course of the twenty-four hours, it would make a total journey of one thousand feet, say a sixth of a mile. It results that in its whole course, through one day and night, that old slug of a sun would go the sixth of a mile, or at the break-neck speed of twenty-five braccia' per hour!” Twenty more examples of Leonardo's independence of antique tradition will be found in the volume of M. Séailles.

It must be allowed that this spirit of revolt and initiative was not exactly a novelty in Christian Europe. As early as the thirteenth century Albertus Magnus, Roger Bacon, Arnauld de Villeneuve, and Ramon Lully had submitted the assertions of the ancients to a destructive criticism, and had done their best to throw off the scholastic yoke. But what were these attempts compared to those of their Italian rival ? No one had pushed freedom of thought and sincerity of observation so far as he; no one had combined rectitude of judgment and subtlety of analysis so completely. Leonardo is sagacity personified ; he seems to be preserved from mistakes of method or of conclusion alike by an instinct which never errs.

Theoretically, such independence and sincerity should do nothing but favour the progress of science; from the point of view of the propagation of ideas, they could only act as a drag. If the savant and philosopher in Leonardo had made the most of the ground won by his predecessors, he would, instead of exhausting himself in the creation of philosophy and science all over again, have been enabled to go on to that work of concentration, co-ordination, and synthesis which the analytical spirit too often led him to neglect. It is evident that we must, to some extent, blame his methods of formulating his opinions for the small effect they had upon his contemporaries. In his want of familiarity with the expository precision to which long

1 Léonard de Vinci, L'Artiste et le Savant, pp. 187 et seq.

practice had accustomed the humanists and their allies, Leonardo was content to embody the results of his studies in what seemed to him their most natural form. Is it surprising, then, that his isolation equalled his originality ? “Væ soli.” His style was neither striking nor concise ; his ideas lacked the system and order which would H have imposed them upon the learned bodies of his time. Rather than formulate his axioms and marshal his ideas into a “corpus” of doctrine, he chose, in his excess of sincerity, to group his discoveries into modest paragraphs, without pedantry, but also without any philosophical organisation. He was not one of those who think that when they have written a chapter, or a book, they have finished the question. He returned to it again and again, thinking only of science, which continually renews itself from its own bosom. His insatiable curiosity was his only guide. He called continually upon his own sagacity for the solution of problems, or at least for their statement, which, too, is a step towards truth. He made good his way rather by the light of genius than by methodical processes of investigation. Only now and then does he hit upon an argument which is really strict and close, such, for instance, as we find in his discussion of the connection between the Deluge and the shells found on the summits of mountains, or his refutation of the system of Epicurus.

Leonardo was quite alive to these defects of his, and more than once he feels it necessary to justify his studies by some more or less transcendental consideration. Listen to this : “In order to safeguard the greatest gift of nature, which is liberty” (thus speaks the future engineer-in-chief to Cæsar Borgia !), “ I know methods of attack and defence against the attempts of ambitious tyrants. And in the first place I shall speak of the situation of ramparts, and shall show how peoples may keep their rulers good and just."

His modesty equalled his ardour—what inventor has ever talked of his discoveries with more humility ? “Seeing that I could not choose any subject of great utility or of great pleasantness, for those who have come before me have taken for themselves all useful and necessary themes, I shall act like those who, being poor, arrive last at the fair.

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