The materials for this life of Leibnitz are chiefly taken from the Éloge of his contemporary Fontenelle.

Godfrey William Leibnitz was born at Leipzic, June 23, 1646. His father was Professor of Moral Philosophy in the University of that place: he died when his son was only six years old. Leibnitz’s education therefore was left to his mother; and the great variety of his studies is traced to his free access to a large collection of books which his father left. He thus became a poet, an orator, an historian, a lawyer, a metaphysician, a mathematician, and a theologian. In some of these capacities he would not have escaped oblivion; but every accession to such a mass of titles becomes interesting, when it is remembered how conspicuous he became in more than one of them.

At the age of twenty he applied to the University of Leipzic for the degree of doctor of laws. This was refused, on the plea that he was too young; and he then went to Altdorf, where he maintained a public disputation, and was admitted to the degree which he desired, with unusual distinction. From Altdorf he repaired to Nuremberg, where he heard of a secret society of chemists, or, which was then the same thing, of searchers after the philosopher’s stone. Desiring to obtain some insight into their pursuits, he procured some books on chemistry, a subject which he had never studied, and picking out the phrases which seemed hardest, he wrote a letter altogether unintelligible to himself, which he addressed to them as his certificate of qualification. He was admitted with great honour, and was even offered the post of secretary, with a salary; and though he continued his intercourse with them for some time, he kept up his character as an adept to the last.

His first work, which appeared when he was twenty-two years old, was a treatise written under the name of George Vlicorius, recommending the choice of the Elector Palatine to be King of Poland. In 1670 he published his first philosophical work, an edition of ‘Marius Nizolius contra Pseudophilosophos;’ and in the following year two treatises on abstract and concrete motion, severally dedicated to the French Academy and the Royal Society.

During his abode at Nuremberg, the Baron de Boinebourg, minister of the Elector of Mayence, procured a legal appointment for him in that state. While he held this post he travelled into France and England. After the death of the Elector, he accepted a similar appointment in the dominions of the Duke of Brunswick-Lunenberg. At the peace of Nimeguen in 1678 he wrote upon some disputed ceremonials, under the title of Cesarinus Furstnerius, and displayed a great extent of reading, and a little of that speculative spirit which afterwards produced the pre-established harmony. He is said, though a Lutheran, to have argued on the supposition that Europe was to be considered as a large federation, of which the Emperor was the temporal, and the Pope the spiritual, head. In 1679 he was engaged by the reigning Duke to write the history of the House of Brunswick. On this service he went through Germany and Italy in search of authorities. It is related that, on one occasion, having left Venice in a small boat, a storm arose, and the boatmen began to discuss in Italian, which they supposed their passenger did not understand, the propriety of throwing the heretic overboard. Leibnitz, with great presence of mind, drew out a rosary, which he had about him par prÉcaution, as Fontenelle supposes, who does not seem to guess that this anecdote, coupled with what has preceded, makes it at least an even chance that Leibnitz was really a Catholic. And this is negatively supported by the fact, that, Lutheran as he was considered, he very rarely attended the services of his church, in spite of the publicly-expressed disapprobation of the clergy. But on the other hand, he positively refused to profess Catholicism, when an advantageous settlement at Paris was offered on that condition. That he was both a religious man and a Christian is sufficiently attested by his writings.

He returned from his tour in 1690, and in 1693 published his ‘Codex Juris Gentium Diplomaticus.’ He had published almost at the same time with his first work a treatise on the study of jurisprudence. The first volume of the ‘History of Brunswick’ appeared in 1707, and two others in 1710 and 1711.

In 1700 he induced the Elector of Brandenburg to found the Academy of Berlin, of which he was appointed perpetual president. He contributed many valuable papers to its memoirs. His patron, the Duke of Brunswick-Lunenberg, died in 1678, and was succeeded by Ernest-Augustus, first Elector of Hanover, on whose issue by the Electress Sophia the crown of England was settled. Leibnitz continued in the Elector’s service till his death. This took place from gout, November 14, 1716, at Hanover. The real life of such a man is in his character and writings. With regard to the first, the account of Fontenelle is as follows. He had a strong constitution, ate a good deal, drank little, and never undiluted liquors. When alone, he always took his meals as his studies permitted. His chair was frequently his only bed, and in this way he is said to have sometimes passed whole months. He made notes of all he read, not to preserve them, but to fix the contents on his memory; for when once written, they were finally laid aside. He communicated freely with all classes of men, and could entirely divest himself of his character of a philosopher. His correspondence was immense; he answered every one who wrote, however small the pretext for addressing him. He was of a gay humour, easily excited to anger, and easily appeased. He lived at great expense, but had preserved and hid two years’ amount of his salary. The securing of this treasure gave him great uneasiness; and upon this slight ground he has been charged with avarice. He was never married: it is said that he contemplated such a connexion at the age of fifty, but that the lady desired time to consider. “This,” says his biographer, “gave M. Leibnitz the same opportunity, and he continued unmarried.”

The number and variety of characters in which Leibnitz is known will not permit us to say much upon each subject. His public life was that of a jurist. His ‘History of Brunswick’ was continued by M. Echard; who supplied Fontenelle with the necessary information for his Éloge. In youth he was a poet; and he is said in one day to have made three hundred Latin verses without a single elision. But the Leibnitz of our day is either the mathematician or the metaphysician.

In the first of these two characters he is coupled in the mind of the reader with Newton, as the co-inventor of what was called by himself the Differential Calculus, and by Newton the Method of Fluxions. Much might be instanced which was done by him for the pure sciences in other respects; but this one service, from its magnitude as a discovery, and its notoriety as the cause of a great controversy, has swallowed up all the rest.

Leibnitz was in London in 1673, and from that time began to pay particular attention to mathematics. He was in correspondence with Newton, Oldenburg, and others, on questions connected with infinite series, and continued so more or less till 1684, when he published his first ideas on the Differential Calculus in the Leipzic Acts. But it is certain that Newton had been in possession of the same powers under a different name, from about 1665. The English philosopher drops various hints of his being in possession of a new method, but without explaining what it was, except in one letter of 1672, of which it was afterwards asserted that a copy had been forwarded to Leibnitz in 1676. Leibnitz published both on the Differential and Integral Calculus before the appearance of Newton’s Principia in 1687; and indeed before 1711, the era of the dispute, this new calculus had been so far extended by Leibnitz and the Bernoullis, that it began to assume a shape something like that in which it exists at the present day. In the first edition of the Principia, Newton expressly avows that he had, ten years before (namely, about 1677), informed Leibnitz that he had a method of drawing tangents, finding maxima and minima, &c.; and that Leibnitz had, in reply, actually communicated his own method, and that he (Newton) found it only differed from his own in symbols. This passage was, not very fairly, suppressed in the third edition of the Principia, which appeared in 1726, alter the dispute; and the space was filled up by an account of other matters. It was obvious that, on the supposition of plagiarism, it only gave Leibnitz a year to infer, from a hint or two, his method, notation, and results.

Some discussion about priority of invention led Dr. Keill to maintain Newton’s title to be considered the sole inventor of the fluxional calculus. Leibnitz had asserted that he had been in possession of the method eight years before he communicated it to Newton. He appealed to the Royal Society, of which Newton was President, and that body gave judgment on the question in 1712. Their decision is now worth nothing; firstly, because it only determined that Newton was the first inventor, which was not the whole point, and left out the question whether Leibnitz had or had not stolen from Newton; secondly, because the charge of plagiarism is insinuated in the assertion that a copy of Newton’s letter, as above mentioned, had been sent to Leibnitz. Now they neither prove that he had received this letter in time sufficient to enable him to communicate with Newton as above described, or, if he had received it, that there was in it a sufficient hint of the method of fluxions. The decision of posterity is, that Leibnitz fairly invented his own method; and though English writers give no strong opinion as to the fairness with which the dispute was carried on, we imagine that there are few who would now defend the conduct of their predecessors. Whoever may have had priority of invention, it is clear that to Leibnitz and the Bernoullis belongs the principal part of the superstructure, by aid of which their immediate successors were enabled to extend the theory of Newton; and thus Leibnitz is placed in the highest rank of mathematical inventors.

The metaphysics of Leibnitz have now become a by-word. He is pre-eminent, among modern philosophers, for his extraordinary fancies. His monads, his pre-established harmony, and his best of all possible worlds, are hardly caricatured in the well-known philosophical novel of Voltaire. If any thinking monad should find that the pre-established harmony between his soul and body would make the former desire to see more of Leibnitz as a metaphysician, and the latter able to second him, we can inform him that it was necessary, for the best of all possible universes, that Michael Hansch should in 1728 publish the whole system at Frankfort and Leipzic, under the title, ‘Leibnitzii Principia philosophica more geometrico demonstrata;’ and also that M. Tenneman should give an account of this system, and M. Victor Cousin translate the same. It is not easy to give any short description of the contents, nor would it be useful. A school of metaphysicians of the sect of Leibnitz continued to exist for some time in Germany, but it has long been extinct.

The mathematical works of Leibnitz were collected and published at Geneva in 1768. His correspondence with John Bernoulli was also published in 1745, at Lausanne and Geneva. It is an interesting record, and exhibits him in an amiable light. He gives his friend a check for his manner of speaking of Newton, at the time when the partizans of the latter were attacking his own character, both as a man and a discoverer. He says (vol. ii. p. 234), “I thank you for the animadversions which you have sent me on Newton’s works; I wish you had time to examine the whole, which I know would not be unpleasant even to himself. But in so beautiful a structure, non ego paucis offendar maculis.” He also says that he has been informed by a friend in England, that hatred of the Hanoverian connexion had something to do with the bitterness with which he was assailed; “Non ab omni veri specie abest, eos qui parum Domui HanoveranÆ favent, etiam me lacerare voluisse; nam amicus Anglus ad me scribit, videri aliquibus non tam ut mathematicos et Societatis RegiÆ Socios in socium, sed ut Toryos in Whigium quosdam egisse.” (Vol. ii. p. 321.)