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be a King nor a nobleman; talents, because he had none ; religion, because it prohibited all the crimes for which he had occasion. His energy was only that of ferocity, and he was ferocious because he was a coward. The innumerable assassinations of which he was guilty were as often the effect of his terror as the means of his ambition, and the whole of his ability consisted in constantly pushing on towards his object, without any scruple in the choice of his measures.'

M. Bertrand gives a very minute and satisfactory account of the struggle, in the first sittings of the convention, between the Girondists and the faction of Robespierre ; and on the result of this virulent contest, dextrously managed on the part of Robespierre, but most weakly on that of his adversaries, he remarks;

• Thus Robespierre, evidently guilty, not only of having instigated, directed, and partaken all the enormities of the Revolutionary Commune of Paris, but also of having threatened the Legislative Body, despised and degraded their authority, of having aspired to the Dictatorship, and of having employed the most criminal manæuvres to usurp the Supreme Power; Robespierre, solemnly accused of all these crimes, and opposing only his simple denial to facts of which the whole Capital were witnesses, gaiued the completest victory over his accusers in the Convention, although he was then detested and dreaded by most of that Assembly. But they had occasion for him to consuinmate, and to render popular, the horrible crime which they were meditating ; and the extreme wickedness of that monster, being substituted for innocence, rendered it unnecessary for him to justity himself.'

'Our readers may recollect that the National Convention passed a decree to banish the whole race of Bourbons Capet, and that the partisans of the Duke of Orleans very soon obtained its revocation, or rather its suspension, as far as it respected him and his family : but we are here informed that the parties who proposed it agreed to this alteration only on condition that Philip Egalité and his friends should enter into an engagement to yote for the death of the King. This horrible engagement was made, and secured the majority for the Regicide faction.'

At the commencement of the trial of the King, we are told, his enemies « had taken care to fortify the galleries with their trusty agents, and to place a sufficient number of those abandoned fellows in all the avenues of the Hall. The part allotted to them was to give all the Deputies, as they arrived, to understand that those who did not vote for the death of Lonis would be looked upon as traitors to their country, and would be treated as such ; the gesture which accompanied these words was too plain to be misunderstood, and served as a comment upon them' It is morcover asserted that the section of the Luxcmbourg 'bound themselves by an oath, to stab Louis XVI.

if the Assembly did not condemn him to be brought to the scaffold; and this resolution was addressed to all the other sections, inviting them to take part in it.'

The author presents us with the following observations on the request made to the Convention by the king of Spain, in favour of the head of his family:

· The vast importance to this rising Republic, of separating Spain from the coalition of the several powers, of being recognized by her, of forming an alliance with her, of not being obliged to divide its forces by detaching from them 40,000 men for the defence of the southern frontier; the immense superiority which these 40,000 men would have given to the armies of the Rhine and of Belgium over those of the Emperor and the King of Prussia, the considerable saving which would have resulted from such a junction, and, finally, the dignity which it would have given to the character of the Convention to have acceded to the entreaties of the most powerful Sovereigns of Europe, to which England, and the wishes of all nations gave their support; all these positive advantages ought to have prevailed on this Assembly to have resolved upon sparing the remainder of the King's days, even if he had been guilty of the worst of crimes, and they had themselves been legally competent to bring him to trial : and what more interesting inducement could have offered itself to urge them eagerly to seize the most favourable opportunity that could ever occur of performing a duty which justice and humanity, as well as policy, imperatively prescribed ! But this Tribunal without powers, these Judges without justice, these men without humanity, these monsters required blood alone, they had no other thought than to assassinate, no other wish than to murder as speedily as possible, the devoted Louis XVI. The Ambassador's letter, therefore, had no other effect than to increase the keenness with which they hastened to finish the horrid deed.'

We believe that the mere narrative of the proceedings of the Convention in relation to the king's trial would have better seeured the author's object, and would have more completely called forth the indignation and detestation of the reader, than the course which he has adopted; namely, that of refuting, as he proceeds, each false charge, and that of commenting on each unfair proceeding; a course only proper when it appears that some regard has been had for justice, and which is misplaced when the whole proceeding is the most barefaced mockery of it, and the greatest outrage ever put on it. Such a mode was still less requisite, in consequence of the masterly and unanswerable defence of the unfortunate monarch by Desèze.

Though the truly commendable feelings and partialities of M. Bertrand sometimes betray him into inconsistencies, and render it unsafe for the reader to place an implicit trust in all his representations, yet so scrupulous does he appear to be in stating facts, and so considerable is the mass of them which he Rev. JULY, 1803.



has brought together, that his labours, though rather humble in a literary point of view, will be highly prized by those who seek important information, and will entitle him to the acknow. legements of the public. We think, however, that more pains should have been bestowed in preparing them for the public cye; and that the translator, also, should have paid a greater at. tention to the polish and the correctness of his style.

The last volume consists of documents in the original French) cited in the course of the work, and of the reply to animadversions on the former volumes by the late M. Malleta du-Pan, with the correspondence between the author and Mr. Fox, which were formerly published. (See M. Rev. loc. cit.)

ART. III. Analytical Institutions, in four Books; originally written

in Italian. By Donna Maria Gaetana Agnesi, Professor of the Mathematics and Philosophy in the University of Bologna. Translated into English by the late Rev. John Colson, MA. F.R.S., and Lucasian Professor of the Mathematics in the University of Cambridge. Now first printed, from the Translator's Manuscript, under the Inspection of the Rev. John Hellins, B.D.F.R.S., and Vicar of Potter's-Pury, in Northamptonshire. 4to. 2 Vols, 21. 2s. Boards. Wingrave. INCE the general progress of learning and information over

civilized Europe, many female poets, historians, and philo. sophers have appeared : but mathematicians of the softer sex are very rare. In modern times we recollect only two, the Marchioness de Chatelet, and Donna Maria Gaetana Agnesi : whom we incidentally introduced to our readers in the Appendix to our xxxıud Vol. N.S. p. 516.

The original of the work now before us was printed in Bologna, in the year 1748 ; and Mr. Colson, thinking highly of the merit of this female mathematician, undertook a translation of her Institutions : but he lived not long enough to present it to the world, and it is now for the first time published, at the expence of Mr. Baron Maseres, under the care of Mr. Hellins.

As the world would naturally be desirous of knowing any circumstances relating to a lady, who, on the most abstruse of subjects, could write more than 60o quarto pages, the editor has combined several accounts of her : of which the most full and satisfactory is taken from the Appendix to our 33d Volume already mentioned, and to which we have only to refer.

The first volume of this production treats on the Analysis of finite Quantities, and contains, under that title, the ordinary ope4


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rations of Multiplication, Division, Involution, Evolution, the management of Fractions, the theory of Equations, the construction of Loci, Solid problems and their Equations, the method of Maxima and Minima, Tangents, and points of contrary Flexure, as dependent (according to the words of the translator) on common Algebra only.

The second volume relates to the Analysis of Quantities in finitely small, and treats of Tangents, Regression of Curves, Evolutes, the Integral Calculus, Rectification of Curves, Quadratures, &c.; the Inverse method of Tangents, the construction of differential Equations, the reduction of differential Equations, &c.

By this short enumeration of the contents, the reader will perceive that the mathematical learning of la Signora Agnesi was of considerable extent and depth; and, indeed, when we reflect on the situation, sex, and age of the author, we find much matter for admiration : yet the book, abstractedly con. sidered, does not please us. We express not a wish that the original work had never been written; for it probably did good in its time, and aided the advancement of science : but we should not have given our vote in favour of publishing the translation ; because it can do no good now, or, to speak more precisely, there are other books of a like nature and less bulk which can do more good. It is not wise and safe to suppress the publication of any new work, from an individual's opinion of its inutility: but there was no danger of the analytical treasures collected by Signora Agnesi being hidden from mortal sight; they had been displayed in their original garb; and, if we mistake not, a translation into French had been executed by M. Cousin. If any curious artifices and methods were here revealed, the learned Mathematician could resort to them, or extract them; and we by no means think that the work forms an excellent elementary treatise, and one that is proper for the student : since it contains many false notions and erroneous reasonings, is diffuse without being explicit, prolix rather than explanatory, minute but not accurate; and since examples to its rules are more frequent than illustrations of its theories. Science has made such advances, that the student cannot be expected to read ten treatises on the same subject; and the instructed mathematician certainly will not. For what dem scription of persons, then, is this production calculated ? is there a middle class, between mathematicians and students de. sirous of becoming mathematicians ? The compositions of original writers and of inventors deserve notice, and will be read, because they may add to our knowlege of the human mind, in shewing the steps in the intellectual process by which


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their inventions were produced: but we feel little curiosity to peruse a book which consists of a collection of methods, not one of them due to the author of the publication : except, indeed, he should be able to give it an air of originality, by new illustrations or more excellent arrangements.—We shall extract a few passages, by which the power and propriety of the fair writer's explanations, as well as the extent and depth of her knowlege, may in some degree be estimated :

• Positive and negative quantities distinguished.-Of these quantities some are positive, or said to be greater than nothing; others are less than nothing, and therefore are called negative. To explain this by an example. The goods in our own possession may be called positive, but those which we owe to others are negative, because they must be subtracted from the positive, and therefore will diminish their sum total. Wherefore, as the capitals in our possession are positive, and are answerable for our debts ; so the debts we owe will be negative quantities. In like manner, if a body or point in motion is directed towards a certain mark, and in its passage describes a space, this space may be called positive ; but afterwards if it receives an opposite direction, it will indeed describe a space, but this space will be negative in respect of the mark to which it ought to go. Wherefore, in Geometry, if a line drawn one way is assumed as positive, (for this is quite arbitrary,) a line drawn the contrary way will be negative.'

On reading such a passage, we were rather surprized when we recollected that Baron Maseres is said in the preface to have patronized this book.


* Simple quantities are multiplied by writing them one after and ther, without any sign between, (unless sometimes the mark X,) and the resulting quantity is called the Product, as also the quantities so multiplied are called the Factors or Multipliers. But as to the sign which is to be prefixed to the products, the general rule is this; that if the quantities to be multiplied are both positive or both negative, then the positive sign must always be prefixed to the product: but if one of those quantities, whichever it is, is positive, and the other negative, then the negative sign must always be prefixed to the product. The reason of this is, because multiplication is nothing else but a geometrical proportion, of which the first term is unity, the second and third terms are the two quantities which are to be multiplied together, and the fourth term is the product. And therefore being placed in a row, unity for the first term, one of the multipliers for the second, and the other multiplier for the third; therefore, by the nature of geometrical proportion, the fourth must be such a mul. tiple of the third, as the second is a multiple of the first. If the second and third terms are positive, for example, if it is 1.a::b. to a fourth ; the first term or unity being positive, the fourth must there. fore be positive. But if the second is negative, and the third positive, that is, if 1.-a::b. to a fourth ; whereas this fourth must be such

a multiple


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