118 Mb WALLACE, ON GEOMETRICAL THEOREMS, AND FORMULAE, 



a; 6 sin^ ' 

 Hence we tind - = - ■ p 

 y a siii-D 



- = - .%, and other formula of a like na- 

 « b 



ture, which are comprehended in this table. 



y = 



a 



h 



a 

 a 



y = - 



, b 



b 



c 

 c 



c 

 c 



c 

 c 



c 

 c 



a 

 V 



b 



c 



a 

 c' 



a 

 b 



b_ 

 c 



a 

 c 



a 

 b 



b_ 

 c 



a 

 c 



a 

 b 



h 

 c' 



d 

 c 



IV. 



These formula give the ratios of the six lines x, y, »; x\ y, x, when 

 the lines a, b, c ; a', b', c, or their ratios, are known ; when the angles 

 a, fi, y contained by these lines are given, the lines themselves may be 

 found by known propositions in Trigonometry. To these I shall in the 

 sequel add others. 



16. We have found that 



be . 



X sin o + y sin /3 + s sin 7 = — sin A' ; 



Now y = Y • ~ ^> 

 ^ b a 



X 



a c 

 c ' d 



■.X. 



These values of y and % being substituted in the above equation, it 

 becomes 



, . a h' . r, ad. , he . ,, 



a; {sm a + y . -, sm /3 + - . -j, sm vf = — svvlA. 

 * ha c a " X 



Similar expressions may be had for y and %, and from these the fol- 

 lowing formulae have been obtained : 



