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REPORT ON CERTAIN BRANCHES OF ANALYSIS. 295 



mathematical education, by placing this most important branch 

 of analytical science, the very key-stone of all the appHcations 

 of mathematics to natural philosophy, within the reach of every 

 student who has mastered the elements of geometry and the 

 first principles of algebra. 



We have before had occasion to notice the work of the late 

 Professor Vince upon this subject, which was generally used 

 in the Universities of England for some years after the com- 

 mencement of the present century. Its author was a mathema- 

 tician of no inconsiderable powers, and of very extensive know- 

 ledge, but who was totally destitute of all feeling for elegance 

 in the selection and construction of his formulae, and who had 

 no acquaintance with, or rather no proper power of appreciating, 

 those beautiful models of symmetry and of correct taste which 

 were presented by the works of Euler and Lagrange. But 

 though this treatise was singularly rude and barbarous in its 

 form, and altogether inadequate to introduce the student to a 

 proper knowledge either of the objects or of the powers of this 

 science, yet it was greatly in advance of other treatises which 

 were used and studied in this country at the period of its pub- 

 lication. Amongst these may be mentioned the treatise on Tri- 

 gonometry which is appended to Simson's Euclid, which was 

 more adapted to the state of the science in the age of Ptolemy 

 than at the close of the eighteenth century *. 



The Plane and Spherical Trigonometry of the late Professor 

 Woodhouse appeared in 1810, and more than any other work 

 contributed to revolutionize the mathematical studies of this 

 country. It was a work, independently of its singularly oppor- 

 tune appearance, of great merit, and such as is not likely, not- 

 withstanding the crowd of similar publications in the present 

 day, to be speedily superseded in the business of education. 

 The fundamental formulae are demonstrated with considerable 

 elegance and simplicity ; the examples of their application, both 

 in plane and spherical trigonometry, are well selected and very 

 carefully worked out ; the uses of trigonometrical formulae, in 

 some of their highest applications, are exhibited and pointed 



* Similar remarks might be applied to treatises upon trigonometry which 

 were published both before and after the appearance of Professor Wood- 

 house's Trigonometry. The author of this Report well recollects a treatise of 

 this kind which was extensively used when he was a student at the Univer- 

 sity, in which the proposition for expressing the sine of an angle in terms of 

 the sides of a triangle, was familiarly denominated the Hack triangle, in con- 

 sequence of the use of thick and dark lines to distinguish the primitive tri- 

 angle amidst the confused mass of other lines in which it was enveloped, for 

 the purpose of obtaining the required result by means of an incongruous 

 combination of geometry and algebra. 



