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单词 ProportionEquation
释义

proportion equation


The proportion equation, or usually simply, is an equation whose both are ratios (http://planetmath.org/Division) 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

    ac=bd,

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

  • The

    a+ba-b=c+dc-d

    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

    b=ac,

    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.

Titleproportion equation
Canonical nameProportionEquation
Date of creation2014-02-23 21:37:10
Last modified on2014-02-23 21:37:10
Ownerpahio (2872)
Last modified bypahio (2872)
Numerical id12
Authorpahio (2872)
Entry typeTopic
Classificationmsc 97U99
Classificationmsc 12D99
Synonymproportion
Related topicEquation
Related topicSimilarityInGeometry
Related topicGoldenRatio
Related topicContraharmonicProportion
Related topicConstructionOfFourthProportional
Definesproportion
Definesextreme members
Definesmiddle members
Definesfourth proportional
Definescentral proportional
Definesthird proportional
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