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OQHAPTER XX. 
MATHEMATICS AND NATURAL PHILOSOPHY. 
THE present year does not afford us a great number of works in the mathema- 
tical department, but it is distinguished by the names of men of great celebrity in 
science, and of one who is generally, known by his fortunes in the political world. 
Carnot, the ex-director of France, was known as a mathematician, by his small 
work on Fluxions; his reputation will be increased by his Geometry of Position, im 
which he has laboured with great assiduity to reconcile together algebra and geo- 
metry, and correcting same erroneous opinions which had been long maintained by 
very eminent mathematicians. This may be considered as the most important pub- 
lication that we have to announce. ‘Jhe reputation of Baron Maseres, not only | 
as an author, but as a patron of science, is firmly established, and whilst he is con- 
tinuing with such ardour and industry his great work on Logarithms, he can find 
time for tracts, in which the very important question of the generation of equations 
is discussed with great precision, and the question is placed on its true footing. 
The Baron is one of the few persons who has studied Vieta with attention, and is 
qualified to appreciate justly the merits of the founder, we might say, of true alge- 
bra. Dr. Small, of Edinburgh, in a work or no great bulk, has displayed indefa- 
tigable industry. Such calculations eould not have been examined without equal 
talents and labour. We have introduced Montucla into this volume, because from 
accident he could not appear in the last. His history forms an important era in 
mathematical science, but it contains much too great a variety of topics, and its 
general merits were previously too well established for us to enter into a minute de- 
tail of every particular. The author, however, could not be passed over withont | 
some account of a life occupied in science, but which, from the melancholy eyents 
of the late years, was too much embarrassed in matters foreign from study, to. per- 
mit him to give his work that perfection at which he aimed. Lalande, in succeed- | 
ing to him, performed the office of friendship, but was evidently overwhelmed by | 
his many numerous engagements. The French are at present attached more to 
these studies than the English: in the midst of their preparations for war they seem 
to be duly sensible of their merits; and from their numbers we may expect either 
many new discoveries, or great improvements, in the mode of communicating in- 
struction. 
Art. I. Histoire des Mathematiques. History of Mathematics s in which are described 
their Origin and Progress to the present Day ; the principal Discoveries made in every 
Part of the Mathematics; the Disputes that have been:raised among Mathematicians; and the 
principal A&ions of those who have been most famous. Second Edition. By J: F. Mone 
Tucta, of the National Jastitution of France. $ vols. 4to. 
THE former work of this celebrated- world, and everyone must regret that 
writer is well known in the mathematical he did not live to ‘finish this work, and 
