A \.l / Y 1 1>' GKOMKTl: Y 



. i 



mi.-. Thus the proj-. tion , PQR8T upon An is tin- pro- 

 jection of PQ 4- the projection of yl\ 4- -, upon AB-, 



pnij. PQRST upon ^1B 3fA^+ NK + KL 4- #= 3/77 ; 



hut .V// ii the projection of the straight line PT \vhk-h joins 

 th- tirst initial to last terminal point of the broken line. In 

 the same way it may be shown that the projection of any 

 broken line upon a straight line equals the projection, upon 



same straight line, of the straight line which joins the 

 extremities of the broken line. It follows, therefore, that 

 the projection of the perimeter of any closed polygon upon 



given line is zero. 

 If O r r y 4 , and 6 be the angles that PQ< QR, R8, 



.uil PT respectively make with the line AB, then the 

 projection of the broken line upon AB may also be expressed 

 



proj / 



The projections of two parallel segments of equal length 

 up. ,11 any given line in space are equal. It therefore fol- 

 lows that: 



(1 ) The projection of a segment of a line upon any straight 



PQ cos B l -I- QR cos a + US cos 8 -}- 



