320 REVIEWS — GEOLOGICAL SURVEY OF CANADA. 



Chambers' course. "Whether it he possible or not, 

 imagine a Hne drawn bisecting the angle A, then 

 applying the 4th proposition to the triangles BAD, 

 C A D, the angle B is at once shewn equal to the 

 angle C. But the equality of B to C does not in / 



the least depend on the possibility of drawing AD, / 

 and it would be just as much equal if A D were / 

 erased, i. e., if it had not been drawn. 13 



This proof could not be admitted because Euclid commences with 

 three postulates, and does not allow any line to be drawn, or supposed 

 drawn, without having two points to draw it through. Another proof 

 also published by Messrs. Chambers, is obtained by imagining 

 another triangle equal in all respects to be compared with the original 

 one, but this also is not admissible, because we have as yet no means 

 of drawing such triangle j if, however we consider such triangle to be 

 merely a back view of the original one, or the hole out of which the 

 triangle has been cut, there may be no objection to it as a 'proofs 

 although as a method we prefer the demonstration given above, which 

 does not involve rotation or other mechanical artifice, or effecting of 

 geometrical construction in a manner not admitted by Euclid. 



REVIEWS. 



Geological Survey of Canada. Report of progress for the years 

 1853-54-55-56. Printed by order of the Legislative Assembly : 

 JohnLovell: Toronto, 1858. 



Notwithstanding the dearth of dramatic incidents and matters of 

 striking or adventitious interest connected with the Province during 

 the last ten years, it is patent to all who have reflected upon the sub- 

 ject, that a much larger share of European thought has been accorded 

 to Canada during that period, than at any previous epoch within the 

 present century. This, of course, has arisen from a combination of 

 various causes ; but amongst these, it may be safely asserted, that the 

 labors of our Geological Survey have played no unimportant part. 

 The references that have been made to these labors by various leading 

 authors in Great Britain, France and Germany, more especially, and 

 the extracts and quotations from the Reports which one continually 

 sees both in home and foreign journals, are sufficient to establish this. 



