PARALLELISM OF EDGES. 397 



edges of the plane o', which are produced by its in- 

 tersection with tile planes /' and e. From this paral- 

 lelism, as it has been already remarked, it is known 

 that the plane o' is itself parallel to the edge at which 

 the plane I and e meet. 



We have thus obtained two conditions, which en- 

 able us to place the plane o' on the primary form. 



First an edge of that plane is parallel to the edge 

 a b of fig*. 364, and secondly the plane itself is paral- 

 lel to, and consequently may coincide with, the line 

 c w, which represents the edge at which the planes / 

 and c meet. 



If therefore we draw the line q r, parallel to a 6, 

 and passing through the point c, and the line ojt?, 

 parallel to q r, and passing through the point w, we 

 shall, by joining o 7, and p r, obtain the position on 

 the primary form of the plane o'. 



And the ratio of q d to d o, will evidently give the 

 law of decrement by which the plane o 1 has been pro- 

 duced. 



This ratio Mr. Monteiro says is easily deduced, 

 but he does not point out the method of discovering 

 it; it is however very obvious. 



Fig. 365. 



Let the plane dfs t be represented by fig. 365. 

 Produce df, and from the point h, draw h D, parallel 

 to I m, whence d v m If; and because the triangles 

 vfh, Iffy are similar, nf is evidently T of hf\ and 



