my Discourse on the Inequality of Mankind, I was deemed an Atheist and Mifanthrope: after my Letter to Mr. d'Alembert, on the Theatres, I was celebrated as the Defender of Christian Morals: after Eloifa, I was fuppofed to be paffionate and tender at prefent I am a monfter of impiety; and fhall, probably, by and by, be a miracle of devotion.

"Thus fluctuating is the public opinion concerning me; those who adopt it being as ignorant why they deteft me now, as why they once refpected me. As to myself, however, I have al ways remained the fame; more zealous, perhaps, than enlightened in my refearches, but fincere in all, even against myself; fimple and well-meaning, but fenfible and weak; often doing wrong, yet always refpecting what was right; connected by friendship, never by circumstances, and ever more strongly influenced by fentiment than intereft; requiring nothing from others; unwilling to rehder myself dependent on any; fubmit-. ting to their prejudices as little as to their will, and preferving my own as free as my reafon : fearing God, without being afraid of hell; reasoning on matters of religion without licentioufnefs, approving neither impiety nor fanaticifm; but hating Perfecutors ftill worfe than infidels; without difguifing my fentiments from any one; without affectation, without artifice, without deceit; telling my faults to my friends, my fentiments to all the world, and to the public thofe truths which concern it, without flattery, and without pride, equally careless whether I fhould please or offend it. Such are my crimes, and fuch my merits.

"At length, totally difgufted with that intoxicating vapour of reputation, which inflates the imagination without fatisfying the mind; wearied with the importunities of indolent Vifitants, who overburthened with their own time, were prodigal of mine; and fighing after that neceffary repofe of which my heart is fo fond, I had joyfully laid down my pen. Satisfied with the reflection that I had never taken it up but for the good of my fellow-creatures, I required only, as the reward of my zeal, that I might be permitted to live unmolested in my retreat, and to die in peace. In this, however, I was mistaken; the Officers were fent to apprehend me; and juft at the moment when I flattered myfelf the troubles of my life were at an end, my greatest misfortunes begun. There is something fingular in all this; yet this is nothing.

"A.Citizen of Geneva hath a book printed in Holland, and, by an arret of the Parliament of Paris, this book is burnt by the common hangman, without any refpect fhewn to the Sovereign, whofe privilege it had obtained. A Proteftant proposes, in a proteftant country, certain objections to the church of Rome,

and

and he is fentenced by the parliament of Paris. A Republican makes objections, in a republican government, againft monarchy, and he is condemned by the parliament of Paris. The parliament of Paris muft furely have strange notions of their own jurifdiction, to imagine themselves the legal Judges of all

mankind.

"The fame parliament, ever fo remarkably ftrict in the order of their proceedings, when individuals of their own nation are concerned, break through them all in paffing sentence on a poor ftranger. Without knowing whether he was really Author of the book attributed to him, whether he acknowleged it, or caused it to be printed, without any regard to the unhappiness of his fituation, or pity for his bodily infirmities, they began their procefs by ordering him to be clapped into prison. Thus they would have had him taken out of his bed, and dragged from his houfe, to be thrown among infamous criminals, to rot in a jail. Nay, who knows but they might have burnt him at the stake, without fuffering him to speak in his own defence; for what reason is there to think, they would have proceeded more regularly afterwards than at firft, in a profecution fo violently commenced, as to be almost without example, even in the countries of the Inquifition? Thus it is, in my cafe alone, that this fagacious tribunal forgets its prudence; it is against me alone, that a people, who boaft fo much of their politenefs, and by whom I thought myself beloved, act with the strangest barbarity; it is thus the country I have preferred as an afylum above all others, juftifies me in giving it that preference! I know not how far fuch proceedings may be confiftent with the law of nations; but I know very well, that where they are practifed a man's liberty, and perhaps his life, lies at the mercy of the firft Printer who pleases to fet his name to a book.

"A Citizen of Geneva owes no refpect to fuch unjuft Magiftrates, who order perfons to be apprehended, and committed to prifon, upon a fcandalous information given them, without citing the accused to appear and answer for himself. Not having been cited to appear, he is not obliged to it. But being thus proceeded against by force and violence, he is juftified in flying from perfecution. He shakes the duft off his feet, therefore, and leaves an inhospitable country, where the strong are fo ready to opprefs the weak, and to load the ftranger with chains, without hearing his defence, without knowing whether the act he is accused of be criminal, or, being fo, whether he hath, indeed, committed it.

"He abandons with regret the pleafing folitude he had chofen, leaving all his poffeffions, his few, but valuable friends

behind.

behind. Weak and infirm as he is, he is obliged to undergo the fatigues of a long journey; hoping at the end of it to breathe in a land of liberty; he approaches his own country, flattering himself his reception there will confole him for his pait difgrace. But what am I going to fay? My heart finks, my hand trembles, and my pen falls to the ground: Let me be filent, therefore, on this affecting fubject.

"And, wherefore, am I thus treated? I do not fay for what reafon? but on what pretence?-The Magistrates have been rafh enough to judge me guilty of impiety, without reflecting, that the book, containing the pretended inftances of it, is in the hands of the whole world. What would they not give, effectually to fupprefs this authentic teftimony against them, that they might be able more boldly to fay it contains what they pretend to have found there! But this proof of my innocence will remain, in fpite of all their efforts to fupprefs it; and pofterity will be furprized, in looking for the enormous crimes imputed to the Author, to find at worst only, the errors and mistakes of a fincere friend to virtue."

Our ingenious and perfecuted Author goes on to mention the other aggravating circumftances of his oppreffion; hinting at Writers now living, who are more favourably dealt by, notwithstanding the principles they have inculcated in their works. are notorioufly fuch as he is unjustly accufed of: thefe, however, he forbears to name, as it is not his intention to injure others, but only to fhew the fingular hardfhip of his own cafe.

He obferves, that it is a ridiculous abfurdity for a Roman catholic Bishop, who condemns indifcriminately all that are not of his church, to cenfure any particular doctrine of a Proteftant Writer, as if he would not even permit thofe, whom he configns to the devil, to go to him their own way. He affects alfo to think it a mighty ridiculous thing, for fo many great States to enter into a league, as it were, againft fo mean an object as the fon of a Watch-maker. This reflection, however, we think ridiculous enough in our Author. We fhould have thought he had fuffered fufficiently, to be convinced of his own importance; which would not be a jot the lefs at prefent, had he been the fon of a Chimney-fweeper. A Writer, whofe works are become fo univerfal, and whofe opinions are fo well received as thofe of Mr. Rouffeau, is, fingly, a man of more confequence, and may be more useful or pernicious to governments, than a score of Cardinals, or a whole junto of ordinary Minifters of State.

But the true caufe of our Author's perfecution in France, he himfelf conceives to be this. In a note, whi.h was inferted in

1

his Eloifa, he had very unadvisedly spoken against the Janfenifts, predicting, that when they fhould get the upper hand, they would be more perfecuting than their enemies ;-he had alfo refused to write against the Jefuits. At a time, when it was not yet determined to extirpate that fociety, this was overlooked, but not forgotten; thofe perfons by whom the Parliament hath been excited to the prefent proceeding, having waited this opportunity of taking ample vengeance. On this account our Author rallies the Archbishop, on being fecretly made the dupe of that party, which he has had fortitude enough fo long to combat openly with fuccefs.

As a tranflation of this piece is advertised, and the prefent article already fufficiently long, we fhall defer entering upon the merits of our Author's defence at prefent: this may probably be the fubject of a future article. In the mean time, we have only to obferve, that the whole of this epiftle is written with fpirit, and is worthy the pen of Mr. Rouficau.

K-n-k

The Nature and notable Use of the most fimple Trigonal Numbers. With two Arithmetical Tables, that over and above the folution of feveral important Problems, give the Square-root out of every Square, expreffed by an integer Number, and feated between the Unity and forty thousand Millions; and the Cubic-root of every Cube, expreffed by an integer Number, and feated between the Intiger and two hundred fixteen thousand Millions. Tranflated

from the Latin of E. de Joncourt, A. M. and Profefior of Philofophy; by the Author himself. Hague printed for Hufon. 410.

TH

HERE is fomething extremely agreeable in contemplating the Properties of Numbers. It opens an extenfive field, where the faculties of the human mind may range at large, in fearch of pleasure and utility. Many noble difcoveries have been made, and many compendious methods of calculation invented, by this engaging ftudy. The common operations of Trigonometry, for inftance, were extremely fatiguing till Lord Napier, by a happy discovery of the property of numbers, formed the Logarithmic Tables, by which thefe operations are performed with the greatest facility.

The work before us is an attempt of the fame kind, confifting of tables of trigonal numbers, calculated principally to facilitate the extraction of the fquare and cube roots; the other arithmetical operations may be readily performed by thefe tables, which are easily conftructed, in the following manner.

The

The natural numbers 1, 2, 3, 4, 5, 6, 7, 8, &c. being difposed in a column, and the numbers 1, 3, 6, 10, 15, 21, 28, 36, &c, placed oppofite to them in a second column, a series of the moft fimple triangular or trigonal numbers will be generated, correfpondent to a series of natural numbers, as in the following example.

The first trigonal number 1, is equal to the first natural number 1; the second trigonal 3, equal to the fum of the two first natural numbers 2+3; the third trigonal, 6, equal to the fum of the three firft natural numbers 1+2+3=6; &c. In the fame manner the large tables of trigonals, given us by this ingenious Author were conftructed.

From the very nature of the construction, it evidently appears, that the fum of any two trigonals following each other, is equal to the fquare of the natural number belonging to the larger trigonal: thus, for inftance, the fum of the trigonals 36 and 28, is 64, which is equal to the fquare of 8, (the natural number belonging to the greater trigonal 36) =8×8. Thus, by an easy process of addition, the fquare of any whole number less than 20,000, may be very eafily found. But tho' the tables before us extend no farther than 20,000, yet the Author has fhewn, by an eafy artifice, how any number, to 200,000, may be squared.

The rule which the Author has laid down for extracting the fquare-root is this: divide the given refolvend into two equal parts, and feek the half thereof among the trigonals; the number immediately above that half points to the natural number, or root required.Thus, if 49 were the given refolvend, the half will be 24, and the trigonal number immediately above, or greater than 24, is 28, and its natural number 7, the root required. But as moft refolvends are furds, that is, have no true root, the Author has fhewn, by an eafy process, how the root may be approximated to any degree of accuracy.

To this work is annexed a table of the firft 600 cubes, and their roots, by means of which the Author has fhewn how the

cube