( HAPTER II 



GEOMETRIC CONCEPTIONS. THE POINT 

 I. OOdBDOfAl I. BTM Blffl 



18. Coordinates of a point. Position, like magnitude, is 

 relati\<. and ran he given for a geomet ric I'linm- only lv 

 reference to some fixed geometric figures (planes, lines, or 

 points) which are regarded as known, just as magnitude 

 can be given only by reference to some standard magni- 

 tudes which are taken as units of measurement. Tin- pofli- 

 tion of tin- city of New York, for example} when ^m-n 1\ its 

 latitude and longitude, is referred to the equator and tin- 

 meridian of dreenu K -h, -the position of tllCSO two hues 



being known, that of New York is also known. So also 

 the position of Baltimore may be given 1>\ its distance and 

 direction from Washington; while a particular point in a 

 room may be located by its distances from the floor and 

 two adjacent walls. 



If, as in the last illustration, a point is to be fixed in x/>/z<?e, 

 then three magnitudes must he known, referring to three fixed 

 positions. If. on the other hand, the point is on a known 

 >urf;icc, as New York or Baltimore on th- surface of tin- 

 earth, then only two magnitudes need be known, referring to 

 two fixed positions on that surface; while it the point is on 

 a known line, only one magnitude, refenin_r to one fixed 

 position on that line, is needed to tix its position. 



These various magnitudes which ser\e to fix the position 



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