ARITHMETIC.

CRITERIA OF DIVISIBILITY.

I. A NUMBER is divisible by 2, 4, or 8, when the number formed by the last one, two, or three figures on the right, is divisible by 2, 4, or 8 respectively.

II. Every number ending with 5 or 0, is divisible by 5 or 10 respectively.

III. Every number is divisible by 3 or 9 when the sum of the digits is divisible by 3 or 9 respectively.

IV. Every number is divisible by 11 when the difference between the sum of the figures in the odd places and the sum of those in the even places is divisible by 11.

V. Every compound number will divide a given quantity when its component factors will divide that quantity.

12.

=

a2 + b2 + c2 + 2 a b + 2 ac + 2bc.

a3± 3 a2 b + 3 a b2± b3.

(a + b + c)3 = a3 + b3 + c3 + 3 (a2 b + a b2 + a2 c
+ ac2 + b2c+be2)+6abc.

a3 ± l3 = (a + b) (a2 + ab + b2).
13

13.

14.

General Properties.

sum of the roots.
product of the roots.

a ± b

24. a+b: a b = c ± dc d, or

c ± d

=

or sum of antecedents is to the sum of the consequents as one of the antecedents is to its consequent.

28. If V∞ v,

Ꮴ =

Cv; C being a constant quantity.

29. If V∞ inversely as v,

C

ย

34. Arithmetic mean = semi-sum of the extremes.