(Dionysius) of the academy of Berlin, the son of a cutler, was born at Langres in 1713. The Jesuits, with whom he went through a course of study, were desirous of having him in their order; and one of his uncles, desiring him for a canonry which he had in his gift, prevailed upon him to take the tonsure.

His father seems to have known him better; for perceiving that he was not inclined to be a Jesuit, nor fit to be a canon, he sent him to Paris to prosecute the study of the law. To the law, however, he paid very little attention, but devoted his time to science and general literature; which so offended his father, that he stopped the remittance of his pecuniary allowance, and seemed for some time to have abandoned him.

The talents of young Diderot supplied him with a maintenance, and drew him from obscurity. According to his friends, his capacious mind embraced physics, geometry, metaphysics, ethics, and the belles lettres, from the time that he began to read with reflection; and it is certain that he aspired at being a master in all these departments of literature. His bold and elevated imagination seemed to give him likewise a turn for poetry; but he neglected it for the sciences. He settled at an early period at Paris, where the natural eloquence which animated his conversation procured him friends and patrons. What first drew the attention of the public to him as an author, and gave him a high reputation among a certain class of readers, was a small volume written against the Christian religion, and intitled Pensées Philosopiques; which was reprinted afterwards under the title of Étrennes aux Esprits forts.

This book appeared in 1746, 12mo. The adepts of the new philosophy compared it; for perspicuity, elegance, and force of diction, to the Pensées de Pascal. But the aim of the two authors was widely different; Pascal employed his talents and his erudition, which was profound and various, to support and illustrate the great truths of our holy religion, which Diderot attacked by all the disingenuous arts of an unprincipled sophist. The Pensées Philosopiques, however, became popular. It contributed to promote the object of that conspiracy which had been for some time formed against every thing which ennobles human nature (See Jacobins in this Supplement). It was therefore applauded by Voltaire and D'Alembert, and read, of course, by every man and woman of taste in Paris.

Our author was more usefully employed in 1746, when, together with Messrs Bédous and Toussaint, he published a general Dictionary of Medicine, in five volumes folio. This work, it must be confessed, has considerable merit; for though there are in it several articles superficial and erroneous, there are many others of such deep and accurate disquisition, as deservedly recommended it to men of science.

It was about this time that an intimacy was formed between Diderot and D'Alembert, and that, under the direction of Voltaire, they formed the idea of a Dictionnaire Encyclopédique. The great objects which they had in view when they entered upon this work are now universally known. D'Alembert was a profound mathematician, Diderot had considerable knowledge in the physical sciences, more especially mechanical philosophy, and Voltaire was a matter of the belles lettres.

It is not to be supposed that such men would publish anything very defective in these departments of science; but an Encyclopedia must treat of religion; and to every kind of religion they were all sworn enemies. They engaged, however, a very worthy, though not very acute, clergyman, to furnish the theological articles; and for other branches of knowledge, they were promised the assistance of several men of letters, and of a variety of artists.

Diderot took upon himself the description of arts and trades; one of the most important departments of the work, and the most acceptable to the public. To the particulars of the several processes of the workmen he sometimes added reflections, speculations, and principles, adapted to their elucidation. But besides his own department, he furnished articles on almost every other subject.

By those who knew not the great aim of the undertakers of this work, it has been regretted that Diderot was not less verbose, less of the dictators, and less inclined to digressions. He has also been censured for employing needlessly a scientific language, and for having recourse to metaphysical doctrines, frequently unintelligible, which occasioned him to be called the Lycophron of philosophy; for having introduced a number of definitions incapable of enlightening the ignorant, and which the philosopher seems to have invented for no other purpose than to have it thought that he had great conceptions; while, in fact, he had not the art of expressing perspicuously and simply the ideas of others. But these complaints arise from mistaking entirely the purpose for which he wrote.

It has been completely proved, that one great object for which the philosophers, as they called themselves, undertook the compilation of the Encyclopédie was to sap the foundation of all religion. This was to be attempted, not directly and avowedly; for bare-faced atheism would not then have been suffered in France. A cloak, therefore, was to be worn, and the poisoned dagger to be concealed under it. Whilst the well-meaning divine was supporting, by the best arguments which he could devise, the religion of his country, Diderot and D'Alembert were overturning those arguments under titles which properly allowed of no such difficulties. This necessarily produced digressions; for the greatest genius on earth could not, when writing on the laws of motion, attack the mysteries of Christianity without wandering from his subject: but that the object of these digressions might not pass unnoticed by any class of readers, care was taken to refer them from the articles where the question was discussed by the divine. That when employed in this way, Diderot seems to write obscurely, is indeed true; but the obscurity is not his. His atheism was so plain, that for the most part D'Alembert, or some other leader of the gang, had to retouch his articles, and throw a mist over them, to render their intention the less obvious.

Even with all this care and studied obscurity, the design of the Encyclopédie was too palpable not to be seen, and too wicked not to give offence. Certain wild positions on government and on religion occasioned the imposition to be suspended in 1752. At that time there were no more than two volumes of the dictionary published; and the prohibition of the succeeding ones was only taken off at the end of 1753. Five new volumes then successively appeared. But in 1757 a new storm arose, and the book was suppressed. The remainder did not appear till about ten years after; and was then for a while only privately distributed; some copies having been seized by government, and the printers shut up in the battile. The merit, however, of some of the articles is confessedly great; and the first edition was quickly sold off.

Thus was this great work in the press from 1751 to 1767; during which period, Diderot and D'Alembert were accustomed to frequent the coffee-houses of Paris, and to enter with keenness into religious disputes: the former attacking Christianity; and the latter, under the mask of piety, defending it; but always yielding to the arguments of his opponent. This practice was put a stop to by the police; and Diderot, when reproached by the lieutenant with preaching atheism, replied, "Ce la est vrai, je suis athée, & m'en fai gloire."

Finding his impious conversations interrupted, and the publication of the Encyclopédie rendered tedious by the vigilance of government, he thought of propagating his notions by other vehicles. Alternately serious and sportive, solid and frivolous, he published, at the very time he was working on the Dictionary of Sciences, several productions, which could scarcely have been expected from a man so completely employed. His Bijoux Indiscrets, 2 vols 12mo, are of this number—a disgusting work, even to those young people who are unhappily too eager for following after licentious romances. Even here a certain philosophical pedantry appears in the very pages where it is most misplaced, and never is the author more awkward than where he intends to display a graceful ease.

The Fils Naturel, and the Père de Famille, two comedies in prose, which appeared in 1757 and 1758; are not of the same kind with the Bijoux Indiscrets. They are moral and affecting dramas, where we see at once a nervous style and pathetic sentiments. The former piece is a picture of the trials of virtue, a conflict between interests and passions, wherein love and friendship play important parts. It has been said, that Diderot borrowed it from Goldoni; but if that be the case, the copy does honour to the original; and, with the exception of a small number of scenes, where the author mixes his philosophical jargon with the sentiments of the heart, and some sentences out of place, the style is affecting and natural enough. In the second comedy, a tender, virtuous, and humane father appears, whose tranquillity is disturbed by the parental solicitudes, inspired by the lively and impetuous passions of his children. This philosophical, moral, and almost tragic comedy, has produced considerable effects on several theatres of Europe. The dedication, to the princess of Nassau Saarbruck, is a little moral tract of a singular turn, without deviating from nature. This piece, written with a true dignity of style, proves that the author possessed a great fund of moral sentiments and philosophical ideas. At the end of these two pieces, published together under the title of Théâtre de M. Diderot, are dialogues containing profound reflections and novel views of the dramatic art. In his plays he has endeavoured to unite the characters of Ariosto and Plato; and in his reflections he sometimes displays the genius of Aristolette.

This spirit of criticism is exhibited, but with too much licence, in two other works, which made a great noise. The former appeared in 1749, 12mo, intitled Letters on the Blind for the Use of those who See. The free notions of the author in this work cost him his liberty. He underwent a six months imprisonment at Vincennes. Having naturally strong passions and a haughty spirit, and finding himself on a sudden deprived of liberty and of all intercourse with human beings, he was threatened with the loss of his reason. The danger was great; and to prevent it, they were obliged to allow him to leave his room, to take frequent walks, and to receive the visits of a few literary men; among whom J. J. Rousseau, at that time his friend, went and administered consolation to him, which he ought not to have forgotten.

The letter on the Blind was followed by another On the Deaf and Dumb, for the Use of those who can Hear and Speak; 1751, 2 vols, 12mo. Under this title the author delivered reflections on metaphysics, on poetry, on eloquence, on music, &c. In this essay there are some good things, among others absurd and imperfect. Though he strives to be perspicuous, yet he is not always understood; and this is more his fault than that of his readers. Of what he has composed on abstract subjects, it has been said that it is a chaos on which the light shines only at intervals. The other productions of Diderot betray the same defect of clearness and precision; and the same uncoast emphasis, for which he has always been blamed.

The principal of them are, 1. Principles of Moral Philosophy, 1745, 12mo; of which the Abbé de Fontaine speaks well, though it met with no great success. It was our philosopher's fate to write a great deal, and not to leave a good book, or at least a book well composed. 2. History of Greece, translated from the English of Stanyan, 3 vols, 12mo; an indifferent translation of an indifferent book. 3. Pieces on several Mathematical Subjects, 1748, 8vo. 4. Reflections on the Interpretation of Nature, 1754, 12mo. This interpreter is very obscure. 5. The Code of Nature, 1755, 12mo; which is certainly not the code of Christianity. 6. The Sixth Sense, 1753, 12mo. 7. Of Public Education; one of that swarm of publications produced by the appearance of Emilius, and the abolition of the Jesuits. Though all the ideas of this author could not be adopted, yet some of them are very judicious, and would be highly useful in the execution. 8. Panegyric on Richardson. Full of nerve and animation. 9. Life of Seneca. This is the last work which he acknowledged; and it is one of those by Diderot that is permitted with most pleasure, even in rectifying the judgments he passes on Seneca and other celebrated men. The Abbé Barruel says, that he was the author of Syllabus de la Nature, which is usually given to Robinet; and it is certain, that if he was not the author, he furnished hints, and revised the whole. Yet the junto of atheists were themselves ashamed of the first edition of that work; and after all Diderot's care to improve it, the subsequent editions are, notwithstanding his boasted knowledge of the laws of nature, contemptible in the eyes of a real mechanical philosopher.

When a new edition of the Encyclopédie was resolved on, Diderot, the editor of the former edition, thus addressed the bookellers who had undertaken to republish it. "The imperfections (says he) of this work originated in a great variety of causes. We had not time to be very scrupulous in the choice of our coadjutors. Among some excellent persons, there were others weak, indifferent, and altogether bad. Hence that motley appearance of the work, where we see the rude attempt of the schoolboy by the side of a piece from the hand of a master; a piece of nonsense next neighbour to a sublime performance. Some working for no pay, soon lost their first fervour; others, badly recomposed, served us accordingly. The Encyclopédie was a gulf into which all kinds of scribblers promiscuously threw their contributions; their pieces ill conceived, and worse digested, good, bad, contemptible, true, false, uncertain, and always incoherent and unequal; the reference, that belonged to the very parts assigned to a person, never filled up by him. A refutation is often found where we should naturally expect a proof. There was no exact correspondence between the text and the plates. To remedy this defect, recourse was had to long explanations. But how many unintelligible machines, for want of letters to denote the plates!" To this confession Diderot added particular details on various parts; such as proved that there were in the Encyclopédie subjects to be not only retouched, but to be composed afresh; and this was what a new company of literati and artists set themselves to work upon in the Encyclopédie Méthodique.

This immense work is not yet completed; and therefore we cannot speak of it as a whole; but it is surely not less verbose than the former edition, nor do the aims of its editors appear to be purer. That it contains much valuable information in chemistry, and indeed in every department of physical science, no candid man will controvert; but its articles on abstract philosophy are prolix and obscure; and it betrays the same impertinence, the same eager desire to corrupt the principles of the rising generation, and the same contempt for every thing which can make mankind happy here or hereafter.

Notwithstanding his numerous publications, Diderot was never rich. Soon after the publication of the last volumes of the Encyclopédie, upon which he had been employed for upwards of twenty years, his circumstances were so straitened, that an expedient was to be devised for their improvement. He had long corresponded with the late Empress of Russia, whom he persuaded to consider him as the greatest, or one of the greatest economists of France. In the course of the correspondence he had mentioned his own library as one of the most valuable in Europe; and when Catherine wanted to purchase it and make him librarian, he said that his constitution could not support the cold climate of St. Petersburg. She offered to let him keep it during his lifetime in Paris; and the library was sold for an immense price. When her ambassador wanted to see it, after a year or two's payments, and the visitation could be no longer put off, Diderot was obliged to run in a hurry through all the bookellers' shops in Germany to fill his empty shelves with old volumes. He had the good fortune to save appearances; but the trick took air, because he had been niggardly in his attention to the ambassador's secretary. This, however, did not hinder him from visiting his imperial pupil, to whom he told a poor story, in hopes of getting his daughter married with parade, and patronized by her majesty; but it was seen through, and he was disappointed.

In the year 1784 Diderot's health began visibly to decline; and one of his domestics, perceiving that his death was at no great distance, acquainted him with his apprehensions, and addressed him on the importance of preparing for another world. He heard the man with attention, thanked him kindly, acknowledged that his situation required seriousness, and promised to weigh well what he had said. Some time after this conversation he desired that a priest might be brought; and the same domestic introduced to him M. de Farfa, Curé de St. Sulpice. Diderot saw this ecclesiastic several times, and was preparing to make a public recantation of his errors. Condorcet and the other adepts now crowded about him, persuaded him that he was cheated, that his case was not so dangerous as it was said to be, and that he only wanted the country air to restore him to health. For some time he resisted their attempts to bring him back to atheism, but was at last prevailed upon to try the effect of the country air. His departure was kept secret, and he was concealed in the country till the 2d of July, when he died. His dead body was secretly brought back to Paris, and a report was spread and believed that he died suddenly on rising from the table, without remorse, and with his atheism unshaken.

To draw a formal character of this wretch is surely superfluous. His friends extol his frankness, his disinterestedness, and his integrity; but except his gross avowal of atheism, which may in France be called frankness, this character is belied by every transaction of his life. He married, and had a daughter, as has been already mentioned; M. Bausé, referred to by Abbé Barruel, coming one day into Diderot's house, found him explaining to this daughter a chapter of the gospels. When he expressed some surprize at this conduct, Diderot said: "J'entends ce que vous voulez dire;" Differential mais au fond, quelles meilleures leçons pourrois-je lui donner, ou trouverais-je mieux?" It was a common assertion of Diderot's, that between him and his dog "il n'y avoit de difference que habit." In uttering this sentiment, he resembled not Pope's Indian with untutored mind,

"Who thinks, admitted to that equal sky, "His faithful dog shall bear him company."

The Indian hopes to carry his dog with him to heaven; but Diderot hoped to die like a dog, and to be as if he had never been.

DIFFERENTIAL method, is the art of working with the differences of quantities. By this method any term of a series may be found from the several orders of differences being given; or vice versa, any difference may be found from having the terms of the series given: it likewise shows how to find the sum of such a series. And it gives rules to find by interpolation any intermediate term, which is not expressed in the series, by having its place or position given.

When any series of quantities is proposed, take the first term from the second, the second from the third, the third from the fourth, &c.; then all these remainders make a new series, called the first order of differences. In this new series take the first term from the second, the second from the third, the third from the fourth, &c., as before; and these remainders make another series, called the second order of differences. In like manner, in this series, take the first term from the second, the second from the third, &c.; and these will make a series called the third order of differences; and after this manner you may proceed as far as you will. Thus in the following proposition A, b, c, d, e, &c. is the series; B, B', B", B"', &c. the first order of differences; C, C', C", C"', &c. the second order of differences; D, D', D", &c. the third order; E, &c. the fourth order, and so on. But the first terms of these several orders of differences, as B, C, D, E, &c. are those that are principally made use of in calculations by this method.

PROP. I. If there be any series, A, b, c, d, e, &c. and if there be taken the first differences B, B', B", &c. the second differences C, C', C", &c. the third differences D, D', D", &c. and so on.

Then if T stand for the first term of the nth differences, ± T = A - b + n × \( \frac{n-1}{2} \) - \( \frac{n-1}{2} \) × \( \frac{n-2}{3} \) + \( \frac{n-1}{2} \) × \( \frac{n-2}{3} \) × \( \frac{n-3}{4} \) - &c. that is, + T, when n is even, and - T when n is odd.

The several orders of differences being taken as before directed, will stand thus. Then,

\[ \begin{align*} A &\quad B &\quad C &\quad D &\quad E \\ b &\quad c &\quad d &\quad e &\quad f \\ B' &\quad C' &\quad D' &\quad E' &\quad F' \\ B'' &\quad C'' &\quad D'' &\quad E'' &\quad F'' \\ B''' &\quad C''' &\quad D''' &\quad E''' &\quad F''' \end{align*} \]

series A, b, c, d, e, &c. 1st diff. b - A, c - b, d - c, e - d, &c. 2nd diff. c - 2b + A, d - 2c + b, e - 2d + c, &c. 3rd diff. d - 3c + 3b - A, e - 3d + 3c - b, &c. 4th diff. e - 4d + 6c - 4b + A, &c.

That is, B = b - A, C = c - 2b + A, D = d - 3c + 3b - A, E = e - 4d + 6c - 4b + A, &c. or - B = A - b, C = A - 2b + c, D = A - 3c + 3b - d, E = A - 4d + 6c - 4b + c, where, putting T successively equal to B, C, D, E, &c. and n = 1, 2, 3, 4, &c. the prop. will be evident.

Cor. Hence

A = A, the first term. B = -A + b, the first difference. C = A - 2b + c, the 2nd difference. D = A - 3c + 3b - d, the 3rd difference. E = A - 4d + 6c - 4b + c, the 4th difference. F = A - 5e + 10f - 10g + 5h, the 5th difference, &c.

PROP. II. If A, b, c, d, e, &c. be any series, and there be taken B, C, D, E, &c. the first of the several orders of differences;

Then, the nth term of the series will be = A + \( \frac{n-1}{1} \) B + \( \frac{n-1}{2} \) × \( \frac{n-2}{2} \) C + \( \frac{n-1}{2} \) × \( \frac{n-2}{2} \) × \( \frac{n-3}{3} \) D + \( \frac{n-1}{2} \) × \( \frac{n-2}{2} \) × \( \frac{n-3}{3} \) × \( \frac{n-4}{4} \) E + &c.

For from the equations in the last Prop. viz. B = b - A, C = c - 2b + A, &c. we have, by transposing, b = A + B, = -A + 2b + C = -A + 2A + 2B + C (expunging b); that is, c = A + 2B + C, d = A - 3b + 3c + D = A - 3A - 3B + 3A + 6B + 3C + D (expunging b and c); that is, d = A + 3B + 3C + D. Also e = A + 4b - 6c + 4d + E (expunging b, c, d) = A + 4A + 4B - 6A - 12B - 6C + 4A + 12B + 12C + 4D + E; that is, e = A + 4B + 6C + 4D + E, &c.

Then putting A, b, c, d, e, &c. for the nth term, and n successively = 1, 2, 3, 4, &c. the series will be evident.

Cor. 1. If d, d', d'', &c. be the first of the first, second, third order, &c. of differences; then

The nth term of the series A, b, c, d, &c. will be = A + \( \frac{n-1}{1} \) d + \( \frac{n-1}{2} \) × \( \frac{n-2}{2} \) d' + \( \frac{n-1}{2} \) × \( \frac{n-2}{2} \) × \( \frac{n-3}{3} \) d'' + &c.

For B = d, C = d', D = d'', &c. And the coefficients are the same of the nth - 1th power.

Cor. 2. Hence also it follows, that any term of a given series may be accurately determined, if the differences of any order happen at last to be equal.

Cor. 3. Hence

A = A, the first term. b = A + B, the 2nd term. c = A + 2B + C, the 3rd term. d = A + 3B + 3C + D, the 4th term. e = A + 4B + 6C + 4D + E, the 5th term. f = A + 5B + 10C + 10D + 5E + F, the 6th term. g = A + 6B + 15C + 20D + 15E + 6F + G, the 7th term, &c.

PROP. III. If a, b, c, d, e, &c. be any series, and d', d'', &c. the first of the several orders of differences; then

The sum of n terms of the series is = na + \( \frac{n-1}{2} \) d + \( \frac{n-1}{2} \) × \( \frac{n-2}{2} \) × \( \frac{n-2}{3} \) d' + \( \frac{n-1}{2} \) × \( \frac{n-2}{2} \) × \( \frac{n-3}{3} \) × \( \frac{n-2}{3} \) × \( \frac{n-3}{4} \) × &c. For in the series of quantities,

\[ \begin{align*} \text{1st diff.} & : a, b, c, d, \ldots \\ \text{2nd diff.} & : d', d'' \\ \text{3rd diff.} & : d''', d'''' \\ \text{4th diff.} & : d''''', \ldots \end{align*} \]

Therefore (by Cor. 1. Prop. II.) the \(n + 1\)th term of the series, \(a, a + b, a + b + c, a + b + c + d, \ldots\) or the \(n\)th term of the series, \(a, a + b, a + b + c, a + b + c + d, \ldots\) is

\[ o + na + n \times \frac{n - 1}{2} d + n \times \frac{n - 2}{2} d' + \ldots \]

But the \(n\)th term of the series \(a, a + b, a + b + c, \ldots\) is the sum of \(n\) terms of the series \(a, b, c, d, \ldots\) and therefore equal to \(na + n \times \frac{n - 1}{2} d + n \times \frac{n - 2}{2} d' + \ldots\).

For a fuller account of this method, and its application to curves, we refer the reader to Emerson's works, from which these three propositions are taken.