COSMIC PHILOSOPHY 



point by supposing two similar and equal isos- 

 celes triangles, of which the one is turned over 

 and placed upon the other, so that the apex and 

 one side of the one will coincide with the apex 

 and opposite side of the other. Then the other 

 sides and the bases must respectively coincide, 

 otherwise the two triangles would not be similar 

 and equal, and the conditions of the case would 

 be violated. All the sides being thus equal, each 

 to each, the two triangles must everywhere co- 

 incide, and consequently the two basal angles 

 must be equal, both in the triangle which has 

 been turned over and in the one which has kept 

 its original position. Now, each step of this de- 

 monstration is a cognition of the equality of a 

 pair of relations of length or of direction ; and 

 in each case this cognition is established, not 

 by any anterior demonstration, but by direct in- 

 spection. Or, in other words, when it is said 

 that two lines of equal length, starting from the 

 same point, and running in the same direction, 

 must coincide at their farther extremities, the 

 truth of the statement is at once recognized 

 simply because the states of consciousness which we 

 call the ideas of the two lines are totally indis- 

 tinguishable from each other. This immediate 

 perception of the equality — or, in some cases, 

 of the inequality — between two or more rela- 

 tions of position or magnitude is the goal to- 

 ward which every geometrical demonstration 

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