536 Nofice^ rcspecliug New Books. 



an air ofmvsterv and dignity, whicli distracts and overawes the iininitiateil 

 student, in tiie place of giving him that encoiu-agenient and sympatiiy, which 

 he certainly requires, in his first feeble efforts in the pursuit of abstract 

 knowledge. The geometry of Euclid is a highly artificial system, which 

 can only be read, thoroughly, by a person who is already a mathematician, 

 and who can enter into its metaphysical subtleties, and beautiful yet operose 

 demonstrations. The principle of motion gives a simplicity and clearness 

 to many geometrical conceptions, but from an imagined inconsistency in 

 tiie use of such a method, Euclid employs it neither for the purpose of 

 demonstration nor illustration. The method of sujierposition, which in 

 reality lies at the very basis of geometrical demonstration, and, in many 

 cases, gives a graphic interest to an investigation, is employed in the fourth 

 proposition of his first book, and then, as if ashamed of the lowly origin of 

 geometry, he scarcely uses it afterwaids. Many of his problems are solved 

 by methods which are never used in practice; for example, when a given 

 portion is to be cut off from a straight line, instead of supposing the given 

 portion to be simply transferreil to, or placed upon the straight line, &c., 

 which we really do in practice, Euclid must describe circle after circle, in 

 order to accomplish the problem. The doctrine of similar triangles is, un- 

 questionably, one of the most important propositions in the whole range of 

 geometry, yet the student is not permitted to understand this proposition, 

 until he has gone through the fifth book, which, to a large class of students, 

 must for ever I'cmain a sealed book. It is desirable that [iractical n)en 

 should comprehend the leading propositions in solid geometry; but Eu- 

 clid's method of treating this subject is so operose and refined as to place 

 it beyond the reach of persons whose time for study is limited, or whose 

 mathematical talents are not of a superior order." — Preface, pp. vii. viii. 



Now we have no hesitation in saying (and we say it to those who 

 are able to judge whether we are right or not) that there is not one 

 single assertion in this long extract which is not directly false, or 

 else so gross a perversion of the truth as to be false under the ordi- 

 nary meaning of the terms emjiloyed. We do not think the perver- 

 sion was deliberate, but the result of total misconception : a perver- 

 sion of the intellect rather than of the moral sense. He is an enthu- 

 siast in the cause of " common sense ;" and he has only exercised 

 the advocate's privilege. His own rejiutation is bound up in the 

 cause ; and he makes the best he can of it. 



We shall close our extracts with one which developes Mr. Tate's 

 style of teaching and mode of demonstrating geometrical truth very 

 clearly. It is a dialogue between the teacher and pupil. 



" Nearly all the geometrical knowledge contained in this work may be 

 conveyed to the pupil in this manner. 



" Teacher. What is the line .^ b called? a b 



" PjipiL It is called a straight line. 



" T. Of the two straight lines a b and d c, a. b d .c 



which is the greater? 



" P. The line a b is the greater. 



" T. How should you ascertain this with certainty ? 



" P. By laying the line d c upon a b. 



" T. What sort of line is a f b {see fig. Art. 2.)? 



" P. It is a crooked line. 



" T. True; but it is also called a curved line. 

 Whether is the curved line a r b or the straight line a b the shorter? 



