and Elementary Theorems of Geometry. 79 



nearest the eye, we say the direction on the perpendicular, 

 from the point of intersection towards our right hand is 

 ' right normal/ and that the opposite direction on the per- 

 pendicular is ' left normal.' 



Directions are said to he ' oblique right ' or ' oblique left/ 

 in respect to the primitive directions on another straight line 

 A A, just according as (when taken from the points in which 

 they cut this line) they lie between a normal and a right 

 primitive, or between a normal and a left primitive. 



If a straight line, which we may conceive produced to in- 

 finity in its primitive directions, be supposed to become rigid, 

 and one point of it to be permanently fixed, the rigid line being 

 otherwise capable of movement in any plane in which it may 

 lie, then it is evident there are but two ways of revolving 

 the line in this plane — one being ' right rotation/ and the 

 same as that in which the hands of a watch would move if the 

 dial-plate were towards us, and in the plane ; the other, or 

 contrary, is called ' left rotation.' 



If AA and BB be two straight lines, and I their point 

 of intersection, then the ' angle IA right to B/ means the 

 angle formed at I by a rigid line having I as a fixed pivot, and 

 revolving from a position in AA by a right rotation until its 

 first arrival into the position BB, the revolving line being 

 supposed produced indefinitely on both sides of the pivot. 



If AA and BB be two straight lines, and I their point 

 of intersection, then the ' angle IA left to B ' means the 

 angle formed at I by a rigid straight line having I as a fixed 

 pivot, and revolving by a left rotation from a position in AA 

 until its first arrival into the position BB, the revolving 

 line being supposed produced indefinitely on both sides of the 

 pivot. 



The ' angle AA right to BB/ means the same as angle 

 IA right to B. The f angle AA left to BB/ means the 

 same as angle I A left to B. 



If AA and BB be two straight lines, and I their point 

 of intersection, then c angle IA right round to IB ' means 

 the angle formed at I by a straight line having one of its 

 extremities in this point, revolved by right rotation from the 

 actual direction iA until it arrives in the actual direction 

 IB. 



If AA and BB be two straight lines, and I their point 

 of intersection, then ' angle IA left round to IB/ means 

 the angle formed at I by a straight line having one of its 

 extremities in this point, revolved by left rotation from the 



