Young's Elements of Plane and Spherical Trigonometry, 365 



quences that must flow from it. The total and speedy decline of 

 mathematical science will be the inevitable result. 



These reflections have originated in a comparison of Mr.Young's 

 excellent treatise on Trigonometry with some other works that have 

 made their appearance within the last ten or twelve years, and a 

 comparison of all these with the standard works that preceded them. 

 We have more than once taken occasion to express the opinion we 

 were led to form of this gentleman's course of analytical mathe- 

 matics * ; and though in some respects the nature of the work itself 

 affords less scope for the exercise of that happy faculty which 

 Mr. Young possesses for exposing the paralogisms and supplying 

 satisfactory solutions of the elementary difficulties of science, — 

 yet in many parts we see traces of that same peculiar attention 

 to logical and philosophical accuracy which distinguished his for- 

 mer writings. The great value of this work, we conceive, consists 

 in its unity of purpose, the continuity of its plan, and the very close 

 attention paid to the student's power of completing the whole se- 

 ries of processes which are involved in the solution of the problem 

 under consideration. Though a sufficient number of examples is 

 always a desideratum in every elementary book, the clear develop- 

 ment of the whole process is greatly more important ; but in Trigo- 

 nometry, examples are so easily formed, and the results so easily 

 verified, that we think there is less necessity for this kind of ampli- 

 fication than in any other branch of elementary mathematics. We 

 therefore think Mr. Young has done judiciously in rather giving 

 examples of completely -worked questions under each head, than in 

 adding a great number of unwrought questions, merely as an ex- 

 ercise for the student in performing operations for which he has no 

 model, nor, to him, an intelligible rule. Having done this, we think 

 the number of exercises given in the present work, will furnish am- 

 ple practise for the most unapt of his readers. 



The manner of considering the signs of the trigonometrical lines 

 is, though not new, yet very happily developed ; and the derivation 

 of the formulae of plane trigonometry, altogether, is exceedingly 

 well chosen. No one expects to find much in the way of novelty of 

 method in this branch of the science ; and all that can be expected 

 is, a neatly condensed selection from the various writings already 

 extant, and a systematic connexion between these several compo- 

 nent parts. We could have wished, however, that the very elegant 

 formulae for one case of plane triangles, which was first given by 

 Mr. Anthony Thacker, (editor of the Gentleman's Diary,) in his 

 Mathematical Miscellanies (1743), and which has been subsequently 

 used with great effect by Professor Wallace in the Edinburgh Trans- 

 actions, vol. x. p. 168, had found a place in Mr. Young's book. 

 We trust that in a second edition he will comply with this hint. 



In the Spherical Trigonometry, the fundamental theorems are 

 laid down with great clearness and perspicuity, and the subsequent 

 formulae are derived both briefly and elegantly. This forms the 

 second part; and it is confined to that portion of spherical trigonome- 

 try which has direct and immediate reference to the practical solu- 



* See Phil. Mag. & Annals, N.S. vol. x. p. 287, &c 



