In the autumn of 1661, at the age of fifteen, he entered the university of Leipsic as a student of law. His first two years were devoted to philosophy under Scherzer, a follower of the scholastics, and Jacob Thomasius, a Neo-Aristotelian, who is looked upon as having founded the scientific study of the history of philosophy in Germany. It was at this time probably that he first made acquaintance with the modern thinkers who had already revolutionized science and philosophy, Francis Bacon, Cardan, and Campanella, Kepler, Galileo, and Descartes; and he began to discuss with himself the difference between the old and new ways of regarding nature. “I remember,” he says, “walking alone, at the age of fifteen, in a wood near Leipsic called the Rosenthal, to deliberate whether I should retain the doctrineof substantial forms. At last mechanism triumphed and induced me to apply myself to mathematics.” It was not, however, till the summer of 1663, which he spent at Jena under Weigel, that he obtained the instructions of a mathematician of repute; nor was the deeper study of mathematics entered upon till his visit to Paris and acquaintance with Huygens many years later.

The three years following his return from Jena were devoted to legal studies, and in 1666 Leibnitz became a candidate for the degree of doctor of law. The doctorate was a pathway to the post of assessor which he coveted, but through the opposition of older candidates for the same office his youth was made an excuse for refusing him the degree. Upon this he left his native town for ever. The doctor’s degree refused him there was at once (November 5, 1666) conferred on him at Altdorf,—the university town of the free city of Nuremberg,—where his brilliant dissertation procured him the immediate offer of a professor’s chair. This, however, he declined, having, as he said, “very different things in view.”

Leibnitz, not yet twenty-one years of age, was already the author of several remarkable essays. In his bachelor’s dissertation De principio individui (1663), he defended the nominalistic doctrine that individuality is constituted by the whole entity or essence of a thing; his arithmetical tract De complexionibus, published in an extended form under the title De arte combinatoria (1666), is an essay towards his life long project of a reformed symbolism and method of thought; and besides these there are four juridical essays, including the Nova methodus docendi discendiqιιe juris, written in the intervals of his journey from Leipsic to Altdorf. This last essay is remarkable, not only for the reconstruction it attempted of the Corpus Juris, but as containing the first clear recognition of the importance of the historical method in law.

Rejecting the professorial career, but without any definite plan for the future, Leibnitz turned his steps to Nuremberg. That city was a centre of the Rosicrucians, and Leibnitz, busying himself with writings of the alchemists, soon gained such a knowledge of their tenets that he was supposed to be one of the secret brotherhood, and was even elected their secretary. A more important result of his visit to Nuremberg was his acquaintance with Johann Christian von Boineburg, formerly first minister to the elector of Mainz, and one of the most distinguished statesmen of the day. By his advice Leibnitz printed his Nova methodus in 1667, dedicated it to the elector, and, going to Mainz, presented it to him in person. It was thus that Leibnitz entered the service of the elector of Mainz, at first as an assistant in the revision of the statute-book, afterwards on more important work.

The policy of the elector, which the pen of Leibnitz was now called upon to promote, was to maintain the security of the German empire, threatened on the west by the aggressive power of France, on the east by Turkey, and Russia. Thus when in 1669 the crown of Poland became vacant, it fell to Leibnitz to support the claims of the German candidate, which he did in his first political writing, Specimen demonstrationum politicarum, attempting, under the guise of a Catholic Polish nobleman, to show by mathematical demonstration that it was necessary in the interest of Poland that it should have the count palatine of Neuburg as its king. But neither the diplomatic skill of Boineburg, who had been sent as plenipotentiary to the election at Warsaw, nor the arguments of Leibnitz were successful, and a Polish prince was elected to fill the vacant throne.

A greater danger threatened Germany in the aggressions of Louis XIV. and the wars of conquest on which he was entering. Though Holland was in most immediate danger from his arms, the seizure of Lorraine in 1670 showed that Germany too was threatened. It was in this year that Leibnitz wrote his Thoughts on Public Safety, in which he urged the formation of a new “Rheinbund” for the protection of Germany, and contended that the states of Europe should employ their power, not against one another, but in the conquest of the non-Christian world, in which Egypt, “one of the best situated lands in the world,” would fall to the share of France. The plan thus proposed of averting the threatened attack on Germany by a French expedition to Egypt was discussed with Boineburg, and obtained the approval of the elector. French relations with Turkey were at the time so strained as to make a breach imminent, and at the close of 1671, about the . time when the war with Holland broke out, Louis himself was approached by a letter from Boineburg and a short memorial from the pen of Leibnitz, who attempted to show that Holland itself, as a mercantile power trading with the East, might be best attacked through Egypt, while nothing would be easier for France or would more largely increase her power than the conquest of Egypt. On February 12, 1672, a request came from the French secretary of state, Pomponne, that the author of the memorial should further explain himself, and on the 18th of next month Leibnitz started for Paris. Louis seems still to have kept the matter in view, but never granted Leibnitz the personal interview he desired, while Pomponne wrote from the camp before Doesburg, “I have nothing against the plan of a holy war, but such plans, you know, since the days of St Louis, have ceased to be the fashion.” Not yet discouraged, Leibnitz wrote a full account of his project for the king, and a summary of the same evidently intended for Boineburg. But Boineburg died in December 1672, before the latter could be sent to him. Nor did the former ever reach its destination. The French quarrel with the Porte was made up, and the plan of a French expedition to Egypt disappeared from practical politics till Napoleon menaced, the power of England by the same means as those by which Louis had been invited to cripple Holland. The history of this scheme, and the reason of Leibnitz’s journey to Paris, long remained hidden in the archives of the Hanoverian library. It was on his taking possession of Hanover in 1803 that Napoleon learned, through the Consilium Aegyptiacum, that the idea of a French conquest of Egypt had been first put forward by a German philosopher. In the same year there was published in London an account of the Justa dissertatio , London, 1803. ] i of which the British Government had procured a copy in 1799.

But it is only since the appearance of the edition of Leibnitz’s works begun by Onno Klopp in 1864 that the full history of the scheme has been made known.

Leibnitz had other than political ends in view in his visit to France. It was as the centre of literature and science that Paris chiefly attracted him. Political duties never made him lose sight of his philosophical and scientific interests. At Mainz he was still busied with the question of the relation between the old and new methods in philosophy. In a letter to Jacob Thomasius (1669) he contends that the mechanical explanation of nature by magnitude, figure, and motion alone is not inconsistent with the doctrines of Aristotle’s Physics, in which he finds more truth than in the Meditations of Descartes. Yet these qualities of bodies, he argues in 1668 (in an essay published without his knowledge under the title Confessio naturae contra atheistas'), require an incorporeal principle, or God, for their ultimate explanation. He also wrote at this time a defence of the doctrine of the Trinity against Wissowatius (1669), and an essay on philosophic style, introductory to an edition of the Antibarbams of Nizolius (1670). Clearness and distinctness alone, he says, are what makes a philosophic style, and no language is better suited for this popular exposition than the German. In 1671 he issued a Hypothesis physica nova, in which, agreeing with Descartes that corporeal phenomena should be explained from motion, he carried out the mechanical explanation of nature by contending that the original of this motion is a fine aether, similar to light, or rather constituting it, which, penetrating all bodies in the direction of the earth’s axis, produces the phenomena of gravity, elasticity, &c. The first part of the essay, on concrete motion, was dedicated to the Royal Society of London, the second, on abstract motion, to the French Academy.

Leibnitz thus came to Paris, not merely as a young diplomatist on an important if not very hopeful mission, but also as an author who had already made his début in the world of science and philosophy. At Paris he met with Arnauld, Malebranche, and, more important still, with Christian Huygens. This was pre-eminently the period of his mathematical and physical activity. Before leaving Mainz he was able to announce an imposing list of discoveries, and plans for discoveries, arrived at by means of his new logical art, in natural philosophy, mathematics, mechanics, optics, hydrostatics, pneumatics, and nautical science, not to speak of new ideas in law, theology, and politics. Chief among these discoveries was that of a calculating machine for performing more complicated operations than that of Pascal—multiplying, dividing, and extracting roots, as well as adding and subtracting. This machine was exhibited to the Academy of Paris and to the Royal Society of London, and Leibnitz was elected a fellow of the latter society in April 1673. In January of this year he had gone to London as an attaché on a political mission from the elector of Mainz, returning in March to Paris, and while in London had become personally acquainted with Oldenburg, the secretary of the Royal Society, with whom he had already corresponded, with Boyle the chemist, and Pell the mathematician. It is from this period that we must date the impulse that directed him anew to mathematics. By Pell he had been referred to Mercator’s Logamthmotechnica as already containing some numerical observations which Leibnitz had thought original on his own part; and, on his return to Paris, he devoted himself to the study of higher geometry under Huygens, entering almost at once upon the series of investigations which culminated in his discovery of the differential and integral calculus. For the history of this discovery and of the controversies to which it gave rise, see vol. xiii. p. 8 sq.

Shortly after his return to Paris in 1673, Leibnitz ceased to be in the Mainz service any more than in name, but in the same year entered the employment of Duke John Frederick of Brunswick-Lüneburg, with whom he had corresponded for some time. In 1676 he removed at the duke’s request to Hanover, travelling thither by way of London and Amsterdam. At the latter place he saw and conversed with Spinoza, now in the last year of his life.

For the next forty years, and under three successive princes, Leibnitz was in the service of the Brunswick family, and his headquarters were at Hanover, where he had charge of the ducal library. In leaving the electorate of Mainz for the dukedom of Brunswick, Leibnitz passed into a political atmosphere formed by the dynastic aims of the typical German state. The recognition of the rights of the dukedom amongst the states of Europe, the consolidation and permanence of the reigning house, the union of the two branches of the Brunswick family, and lastly, —the aim to which all the others led up—the attainment of the electoral hat, were the ends of its political action. Leibnitz had thus to support by his pen the claim of Hanover to appoint an ambassador at the congress of Nimeguen (1676) to defend the establishment of primogeniture in the Lüneburg branch of the Brunswick family; and, when the proposal was made to raise the duke of Hanover to the electorate, with the charge of the imperial banner, he had to show that this did not interfere with the rights of the duke of Würtemberg, who was the hereditary custodian of the imperial colours. It was in 1692 that the duke of Hanover was made elector. Before, and with a view to this, Leibnitz had been employed by him to write the history of the Brunswick-Lüneburg family, and, to collect material for his history, had undertaken a journey through Germany and Italy in 1687-90, visiting and examining the records in Marburg, Frankfort-on-theMain, Munich, Vienna (where he remained nine months), Venice, Modena, and Rome. At Rome he was offered the custodianship of t∣ιe Vatican library on condition of his joining the Catholic Church.

About this time too his thoughts and energies were partly taken up with the scheme for the reunion of the Catholic and Protestant Churches. While at Mainz he had joined in an attempt made by the elector and Boineburg to bring about a reconciliation, and now, chiefly through the energy and skill of the Catholic Royas de Spinola, and from the spirit of moderation which prevailed among the theologians he met with at Hanover in 1683 it almost seemed as if some agreement might be arrived at. It was in these circumstances that, in 1686, Leibnitz wrote his Systema theologicum, in which he strove to find common standing-ground for Protestants and Catholics in the details of their creeds. But the English Revolution of 1688, and the establishment of the Protestant succession, became a political obstacle to the prosecution of the scheme in Hanover, while it was soon found that the religious difficulties were greater than had at one time appeared. Spinola’s practical and conciliatory tone did not make full allowance for the ecclesiastical and dogmatical claims of Rome, and the moderation of the Hanover theologians was not fairly representative of the spirit of the Protestant Churches. In the letters to Leibnitz from Boβsuet, the landgrave of Hessen-Rhe inf els, and Madame de Brinon, the aim is obviously to make converts to Catholicism, not to arrive at a compromise with Protestantism, and when it was found that Leibnitz refused to be converted the correspondence ceased. A further scheme of church union in which Leibnitz was engaged, that between the Reformed and Lutheran Churches, met with no better success.

Returning from Italy in 1690, Leibnitz was appointed librarian at Wolfenbüttel by Duke Anton of Brunswick-Wolfenbüttel. Some years afterwards began his connexion with Berlin through his friendship with the electress Sophie Charlotte of Brandenburg and her mother the princess Sophie of Hanover. He was invited to Berlin in 1700, and on the 11th July of that year the academy he had planned was founded, with himself as its president for life. In the same year he was made a privy councillor of justice by the elector of Brandenburg. Four years before he had received a like honour from the elector of Hanover, and twelve years afterwards the same distinction was conferred upon him by Peter the Great, to whom he gave a plan for an academy at St Petersburg, carried out after the czar’s death. At Berlin, in the pleasant suburb of Charlottenburg, Leibnitz read and philosophized with his royal pupil, whose death in 1705 was the greatest loss he ever suffered. After this event his visits to Berlin became less frequent and less welcome, and in 1711 he was there for the last time. In the following year he undertook his fifth and last journey to Vienna, where he stayed till 1714. An attempt to found an academy of science there was defeated by the opposition of the Jesuits, but he now attained the honour he had coveted of an imperial, privy councillorship (1712), and either at this time or on a previous occasion, was made a baron of the empire {Reichsfreiherr). Leibnitz returned to Hanover in September 1714, but found the elector George Louis had already gone to assume the crown of England. Leibnitz would gladly have followed him to London, but was bidden remain at Hanover and finish his history of Brunswick.

During the last thirty years Leibnitz’s pen had been busy with many matters. Mathematics, natural science, philosophy, theology, history, jurisprudence, politics (particularly the French wars with Germany, and the question of the Spanish succession), economics, and philology, all gained a share of his attention; almost all of them he enriched with original observations.

His genealogical researches in Italy—through which he established the common origin of the families of Brunswick and Este—were not only preceded by an immense collection of historical sources, but enabled him to publish materials for a code of international law. The history of Brunswick itself was the last work of his life, and had covered the period from 768 to 1005 when death ended his labours. But the Government, in whose service and at whose order the work had been carried out, left it to lie unheeded in the archives of the Hanover library, till it was published by Pertz in 1813.

It was in the years between 1690 and 1716 that Leibnitz’s chief philosophical works were composed, and during the first ten of these years the accounts of his system were, for the most part, preliminary sketches. Indeed, he never gave a full and systematic account of his doctrines. His views have to be gathered from letters to friends, from occasional articles in the Acta Eruditorum, the Journal des Savants, and other journals, and from one or two more extensive works It is evident, however, that philosophy had not been entirely neglected in the years in which his pen was almost solely occupied with other matters. A letter to the duke of Brunswick, and another to Arnauld, in 1671, show that he had already reached his new notion of substance; and it seems to have been the want of leisure and opportunity alone that prevented the systematic expression of his views. In a letter to Arnauld, of date March 23, 1690, the leading peculiarities of his system are clearly stated. The appearance of Locke’s Essay in 1690 induced him (1696) to note down his objections to it, and his own ideas on the same subjects. In 1703-4 these were worked out in detail and ready for publication, when the death of...