4 INTRODUCTION. 



Scholium. Articles 16, 17, 18, might have been deduced from 

 art. 15, but they are all easily admitted as axioms. We must how- 

 ever observe that this proposition does not extend to the case of 

 for a divisor. 



19. Theorem. A multiple fraction is equal to the 

 quotient of the numerator divided by the denominator. 



Or, JL-a:b, for iLizi-a (9); and b.±=h.l.a (17); but 

 b . bo b b 



b. — =1 (8); and b. — rtzri.aizrt, therefore 6.-— =« (14), and a : bzz 

 bo b 



Scholium. Hence — is a common symbol for a : b. 

 b 



20. Theorem. A quantity, multiplied by a simple frac- 

 tion, is equal to the same quantity divided by its denomi- 

 nator. 



Or a.-T-iza : 6; for a.—- zz-— (9), and -— -rza : b (19), therefore a. — 

 b b b b b 



=fl : b (14). 



21. Theorem. A quantity, divided by a simple frac- 

 tion, is equal to the same quantity multiplied by its deno- 

 minator. 



1 lie 



Or a : -— iz: ab, for if a : ---zie,rt~c — (12)— — zic ; h (20), and 

 b b b b 



multiplying^ by b, abzzczza I — — 

 b 



22. Theorem. A quantity multiplied by a multiple 

 fraction is equal to the same quantity multiplied by the 

 numerator, and then divided by the denominator. 



Or a — zzab ; c; for a — zza.b — zza&. — znah : c (20). 

 c c c c 



23. Theorem. A quantity divided by a multiple frac- 

 tion is equal to the same quantity multiplied by the de- 

 nominator, and divided by the numerator. 



