102 ARITHMETIC. 



3. Divide 234*6 by "]. Ans. 301-714285. 



4. Divide 13*5 169533 by 4-297, Ans 3-145. 



OF PROPORTION IN GENERAL 



JN UMBERS are compared together to discover the re- 

 lations they have to each other. 



There must be tvv^o numbers to form a comparison : the 

 number which is compared, being written first, is called 

 tlie antecedent ; and that to which it is compared, the conse^ 

 quent. Thus of these numbers 2 : 4 : : 3 : 6, 2 and 3 are 

 called the antecedents *, and 4 and 6, the consequents. 



Numbers are compared to each other two different ways : 

 one comparison considers the difference of tfee two numbers, 

 and is called arithmetical relation^ the difference being some- 

 times named the arithmetical ratio ; and the other considers 

 their quotient, and is termed geometrical relation, and the quo- 

 tient the geometrical ratio. So of these numbers 6 and 3, 

 the difference or arithmetical ratio is 6 — 3 or 3 j and the 

 geometrical ratio is -- or 2. 



If tw^o or more couplets of numbers have equal ratios, 

 or differences, the equality is named proportion ; and their 

 terms similarly posited, that is, either all the greater, or 

 all the less, taken as antecedents, and the rest as conse- 

 quents, are called proportionals. So the two couplets 2, 4^ 

 and 6, 8, taken thus, 2, 4, 6, 8, or thus, 4, 2, 8, 6, are 

 arithmetical proportionals j and the two couplets 2, 4, and 



8, 16, 



