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'the Essay on Transversals is not less curious. The fun- Camot's Essay 

 -. i . • i /• t • i-i . 1. /• j • xi_ n> on Transver- 



damental principle of this likewise may be round in the Ajreo- sa i s _ 



metry of Position ; and it was one of the two, on which 

 Ptolemy built all his Spherical trigonometry. The word 

 transversal is here employed to signify any right line, cut- 

 ting the three sides of a right-lined triangle or their prolon- 

 gations. An equation of remarkable simplicity expresses 

 the ratio between the segments of the sides. Mr. Carftot 

 immediately deduces from it three other formulae of the same 

 nature, which, transferred afterward to spherical trigono- 

 metry, are found to be the same as Ptolemy had deemed suf- 

 ficient for the purposes of astronomy. He demonstrated 

 them synthetically, according to the method of the ancients ; 

 and his demonstrations, enlarged by his commentator Theon, 

 are not very complex. Mr. Carnot, after having demon- 

 strated the first principle exactly in the same manner as Pto- 

 lemy, finds in our modern trigonometry more simple means 

 for the others. 



After having coincided with the Greek mathematician, he 

 extends thetheory in various ways, applying it to plane and 

 spherical quadrangular figures ; to every polygon, plane or 

 even oblique; and lastly to pyramids : applications that are 

 perfectly new, and of which not the least trace is to be 

 found either in Ptolemy, or in his commentator. 



Mr. Lacroix has published a fifth edition of his Elements 5th edition of 



Mr. Haiiy has published a second of his Elements of Na- Lacroix, 

 tural Philosophy. The great and rapid success of the first Hat^Ele- ° f 

 edition renders it unnecessary for us to enter particularly ments of Natu* 

 into the plan and execution of a work, which its author has ral Phlloso P h y< 

 revised throughout, to enrich it with all the new discoveries, 

 that have taken place in such a short interval. Thus we 

 find in it Mr. Laplace's theory of capillary phenomena; 

 Mr. Gay-Lussac's experiments on the dilatation of gases; 

 and the researches of Mr. Biot into the relation between the 

 refractive power of different substances and their chemical 

 composition, which he has just finished. 



Lectures 



