Art.  51,  The  difference  of  two  positive  quantities,  as  in
Arithmetic,  is  always  less  than  the  greater  quantity.     Thus,  5a

The  difference  of  two  negative  quantities  is  always  greater,
algebraically  considered,  than  the  minuend.  Thus,  — 5a — ( — 2a)
=— 3  a.
The  difference  between  a  positive  and  a  negative  quantity,
found  by  subtracting  the  latter  from  the  former,  is  always  grealei
than  either  of  them.     Thus,  2a — ( — a)=2a.
Examples:  1.  The  latitude  of  A  is  10°  N.  (+);  the  latitude
of  B  is  5°  S.  ( — );  what  is  their  difference  of  latitude  ]     Ans,  15^,

2.  At  7  A.  M.  of  a  certain  day,  the  thermometer  stood  at  — 9^
that  is,  9  degrees  below  zero ;  at  2  P.  M.,  at  +15°,  that  is,  15
degrees  above  zero  ;  w^hat  was  the  change  of  temperature  betweeA
these  hours  1  Ans.  24°.
MULTIPLICATION.
Art.  52,  Multiplication,  in  Algebra,  is  the  process  of  taking
one  algebraic  quantity  as  often  as  there  are  units  in  another.
The  quantity  to  be  multiplied  is  called  the  Multiplicand.
The  quantity  by  which  we  multiply  is  called  the  Multiplier.
The  result  of  the  operation  is  called  the  Product.
The  multiplicand  and  multiplier  are  generally  called  factors.
Art.  53.  To  understand  the  subject  of  algebraic  multiplica-
tion, it  is  necessary  that  the  pupil  should  be  made  acquainted  with
the  following  preliminary  prinx^iple  :

The  product  of  two  factors  is  the  same,  whichever  be  made  the
multiplier.
To  prove  this,  suppose  we  have  a  sash  containing  a  vertical
and  b  horizontal  rows.  It  is  evident  that  the  whole  number  of
panes  in  the  sash  will  be  equal  to  the  number  in  one  row,  taken
as  many  times  as  there  are  rows.
