Art.  259.  Since  the  ratio  of  two  numbers  is  expressed  by  a
fraction,  of  which  the  antecedent  is  the  denominator,  and  the  con-
sequent the  numerator,  it  follows,  that  whatever  is  true  with
regard  to  a  fraction,  is  true  with  regard  to  the  terms  of  a  ratio.
Hence,

1  St.  To  multiply  the  consequent,  or  divide  the  antecedent  of  a  ratie
by  any  number,  multiplies  the  ratio  by  that  number,  (Arith.,  Part
8rd,Arts.  142,145.)


RATIO  AND  PROPORTION.  229

2nd.  To  divide  the  consequeiit,  or  to  multiply  tlie  antecedent  of  a
ratio  hy  any  number,  divides  the  ratio  hy  that  number.  (Arith.,  Part
3rd.,  Arts,  143,  144.)

3rd.  To  multiply,  or  divide,  both  the  antecedent  and  consequent  of
a  ratio  hy  any  number,  does  not  alter  the  ratio,     (Art.  118.)

Art.  260*  When  the  terms  of  a  ratio  are  equal  to  each  other,
the  ratio  is  said  to  be  a  ratio  of  equality.  When  the  second  term
is  greater  than  the  first,  the  ratio  is  said  to  be  a  ratio  of  greater
inequality,  and  when  it  is  less,  the  ratio  is  said  to  be  a  ratio  of
less  inequality.
Thus,  the  ratio  of  2  to  2  is  a  ratio  of  equality.
The  ratio  of  2  to  3  is  a  ratio  of  greater  inequality.
The  ratio  of  3  to  2  is  a  ratio  of  less  inequality.
Hence,  a  ratio  of  equality  may  be  expressed  by  1 ;  a  ratio  of
greater  inequality,  by  a  number  greater  than  1 ;  and  a  ratio  of
less  inequality,  by  a  number  less  than  1.
