proportion equation

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

ab=cd  or  a:b=c:d (1)

The numbers a, b, c, d are the members of the ; a and d are the extreme members and b and c are the middle members.  The number d is called the fourth proportional of the numbers a, b and c.


  • The product of the extreme members of the is equal to the product of the middle members.

  • The


    i.e., the middle members can be swapped.

  • The


    if the do not vanish.

  • If any three members of a are known, then the fourth member may be determined (often by using the first property).

  • If the number b satisfies the proportion

    ab=bc (2)

    then b is called the central proportional of a and c.  We have


    i.e., the central proportional of two real numbers (of same sign) equals to their geometric meanMathworldPlanetmath.

  • In (2), the number c is called the third proportional of a and b.

Title proportion equation
Canonical name ProportionEquation
Date of creation 2014-02-23 21:37:10
Last modified on 2014-02-23 21:37:10
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 12
Author pahio (2872)
Entry type Topic
Classification msc 97U99
Classification msc 12D99
Synonym proportion
Related topic Equation
Related topic SimilarityInGeometry
Related topic GoldenRatio
Related topic ContraharmonicProportion
Related topic ConstructionOfFourthProportional
Defines proportion
Defines extreme members
Defines middle members
Defines fourth proportional
Defines central proportional
Defines third proportional