1S-75.] 



- OF COO/:/'/ \ .1 TK8 



1 -". 



i 



n 



8111 at 







are the required formulas of transformation from one 

 of oblique axes to another having the same origin. 



NOTE. If it U desired to change the origin, and also the direction of 

 axes, the neoeaiiry formulas may be obtained by combining Art. 71 

 72, Art. 73, or Art. 74, depending upon the given and required 



EXERCISES 



1. Show, by specializing some of the angles , */. 6. and 4 in Art. 74, 

 formulas [26] include both [25] and [24] as special cases. 



I - equation of a certain locus, when referred to a pair of axes 

 are inclined to each other at an angle of 60, is 7x* - 2xy + 4 jr* = 5; 

 will this equation become if the axes are each turned through an 

 of SO ? What if the r-axis is turned through the angle - 30* 

 the y-axis is turned through + 30? 



75. The degree of an equation in Cartesian coordinates is 

 changed by transformation to other axes. Every form u la 

 transformation obtained ([23] to [2tj] ) has replaced x and 

 respectively, by expressions of the first degree in the new 

 inates a/, y'. Therefore any one of these transforma- 

 replaces the terms Containing x and y by express- 

 lie same degree, and so cannot raits the degree of the 

 given equation. NYithcr can anyone of these transforma- 

 lie degree of the given equation; for if it did. 



These formulas can also be read directly from Fig. 00 by first project- 

 tag OM and then the broken line OM'PM upon a line perpendicular u* 

 and afterwards projecting MP and also the broken line JsTOJT J upon a per- 



pendicular to OX 



sin*,gire[a6]. 



The 



g eq 



in each case, and divided by 



TAX. AX. UBOM. 



