The proportion equation, or usually simply proportion, is an equation whose both sides are ratios of (non-zero) numbers:

(1)

Properties of proportions.

• The product of the extreme members of the proportion is equal to the product of the middle members.
• The proportion (1) is equivalent with the proportion $$\frac{a}{c} = \frac{b}{d},$$ i.e., the middle members can be swapped.
• The proportion (1) is equivalent with the proportion $$\frac{a+b}{a-b} = \frac{c+d}{c-d}$$ if the divisors do not vanish.
• If any three members of a proportion are known, then the fourth member may be determined (often by using the first property).
• If the number $b$ satisfies the proportion

  (2)

  
  then $b$ is called the central proportional of $a$ and $c$ . We have $$b = \sqrt{ac},$$ i.e., the central proportional of two real numbers (of same sign) equals to their geometric mean.
• In (2), the number $c$ is called the third proportional of $a$ and $b$ .