| 
4808. 
trigonometry, are found to be the same 
which Ptolemy considered as sufficient 
for all the purposes of astronomy. He 
has synthetically demonstrated, that the 
ancients possessed no other method, and 
these demonstrations, extended by his 
commentator Theon, were not very com- 
plicated. M. Carnot, after having de- 
maonstrated the first principle according to 
the method of Ptolemy, finds for the 
others’ a more simple method in modern 
trigonometry. 
After comparing it with the Greek au- 
thor, he greatly amplifies this theory, 
which extends to plain and spherical qua- 
drilateral figures, to plain or even wregu- 
Jar polygons, and in short to pyramids. 
These applications are wholly orginal, not 
the smallest hint of them being found, ei- 
ther in the works of Ptolemy himself, or 
his commentator. 
List of New Publications. 
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The next work noticed by the reporter 
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trie, by M. Lacroix. ) 
'M. Hauy, has also published, we are 
informed, a second edition of his #le- 
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says the reporter, for us to enter into a 
detailed account of the plan or execu- 
tion of a work, every part of which the 
author has revised; in order to enrich 
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come to hght, during the short time that 
has elapsed since its first publication. 
Thus-we find im it the theory of ca- 
pillary phenomena, by Laplace; the ex- 
periments of Gay Lussac on the dilata- 
tion of gas, and the researches of M. Biot 
respecting the relation which subsists be- 
tween the refractive power and the che- 
mical composition of certain substances. 
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