'2* i \ i/ ) //< QBOmSTBY [di II. 



in this line and ft units from O to\\.ird X may he desi^nat^d 

 by ""8, where the sign 4- gives the <Hr, <-ti,,t of ih,- point, 

 and tlu number 8 its distance, from 0. 1'nder these < ir 

 en instances the point /* lying 8 units on the other side of 

 would be designated by ~3. 



In the same way there corresponds to every real number, 

 positive or negative, a definite point of this directed straight 

 line; the numl>ere are called the coordinates of the points; 

 and <>. from \\hich the distances are measured, is called the 

 origin of coordinates. 



21. Cartesian coordinates of points in a plane. Suppose 

 t\\o directed straight lines X' OX and Y'OY are given. 

 fixed in the plane and intersecting in the point 0. These 

 _ri\en lines are called the coordinate axes, X' OX being 

 the x-axis, and Y'OY being the y-axis; their point of inter- 

 section is the origin of coordinates. Any other two lines, 

 + parallel respectively to these fixed 



nr f lines, and at known distances from 



/ them, will intersect in one and hut 



r one point P, whose position is thus 



x' O/ X y definitely fixed. If these lines 



through P meet the axes in Jlf and 



/ A L respectively, then the directed 



distances LP and MP, measured 



parallel respectively to the axes, are the Cartesian coordinates 

 <f the point P. The distance LP, or its equal OM, is the 

 abscissa of P, and is usually represented by x. while MP, or 

 its equal OL, is the ordinate of P, and is usually represented 

 by y. The point P is d<- 1 by the symbol (r,y), often 



written P = (,y), the abscissa always bein ( _r written first, 

 then a comma, then the ordinate, and l>oth letters being 



