466 Notices respecting New Boohs. 



objection is, that the number of logical forms frequently occurring 

 in judgments is by no means so small as stated by the old logicians. 

 They have no proper place for the equations of Algebra, or for 

 statements about Eelationships. In what intelligible sense can 

 7 + 5=12 be called a singular judgment ? (p. 145). The list of the 

 categories, being derived from an imperfect list of logical forms, 

 cannot be perfect. It may be described, to use one of Kant's own 

 phrases, as the result of a search after pure concepts undertaken 

 haphazard, the completeness of which, as based on induction only, 

 can never be guaranteed. 



Lessons on Form. By E. P. Weight, Teacher of Mathematics, 



University College School, London. 8vo, pp. 103. Longmans 



and Co. :' 1882. ' 

 This short treatise aims at teaching the first elements of Geo- 

 metry in an informal manner, as compared with the inartinetism of 

 Euclid, after the method of Pestalozzi. Commencing with the 

 forms of the principal regular solids, it passes to the analysis of 

 the relations among straight lines intersecting one another, and of 

 the angles which they thus make, whether two are parallels cut by 

 a secant or whether no two are parallel. In the three chapters 

 treating of these matters formal proofs are sparingly introduced, 

 the treatment being rather descriptive than demonstrative. Chap- 

 ter 4 is a short initiation into the study of the triangle : the con- 

 ception of similar triangles, having commensurable sides, being 

 early introduced. The subject of the varieties of the Quadrilateral 

 and the method of measuring areas occupy the remaining two chap- 

 ters of the First Part. 



Part II. treats of the metrical properties of triangles, as depend- 

 ing on Pythagoras's Principle, of which several proofs are given. 

 The consideration of regular Polygons and of the Circle, as their 

 limit, closes the treatise. 



Prom this brief analysis of the scheme and contents of the book, 

 it will be seen that pupils who have been guided to master it in- 

 telligently will have acquired a considerable amount of Geometrical 

 know ledge ; and this, as it is hoped, with little or no drudgery. 

 The skilful teacher will know how to select those parts particularly 

 which seem most suited to the degrees of development and ap- 

 titudes of the learners. That he will find the book most helpful 

 and suggestive in a mode of instruction out of the usual routine 

 path will be evident. This smaller work may be regarded as intro- 

 ductory to Mr. Wright's larger and more formal ' Elements of 

 Plane Geometry ', now in its fourth edition, a fact which stamps 

 it as a standard treatise. 



