# homogeneous

[hoh-muh-jee-nee-uhs, -jeen-yuhs, hom-uh-]

- composed of parts or elements that are all of the same kind; not heterogeneous: a homogeneous population.
- of the same kind or nature; essentially alike.
- Mathematics.
- having a common property throughout: a homogeneous solid figure.
- having all terms of the same degree: a homogeneous equation.
- relating to a function of several variables that becomes multiplied by some power of a constant when each variable is multiplied by that constant: x2y3 is a homogeneous expression of degree 5.
- relating to a differential equation in which a linear combination of derivatives is set equal to zero.

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## Origin of homogeneous^{}

## Synonyms

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

## homogeneous

- composed of similar or identical parts or elements
- of uniform nature
- similar in kind or nature
- having a constant property, such as density, throughout
- maths
- (of a polynomial) containing terms of the same degree with respect to all the variables, as in x ² + 2 xy + y ²
- (of a function) containing a set of variables such that when each is multiplied by a constant, this constant can be eliminated without altering the value of the function, as in cos x / y + x / y
- (of an equation) containing a homogeneous function made equal to 0

- chem of, composed of, or concerned with a single phaseCompare heterogeneous

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Also (for senses 1–4): homogenous

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## Word Origin and History for homogeneously

## homogeneous

Online Etymology Dictionary, © 2010 Douglas Harper

## homogeneous

(hō′mə-jē′nē-əs, -jēn′yəs)- Of the same or similar nature or kind.
- Uniform in structure or composition throughout, as of a chemical mixture.

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The American Heritage® Stedman's Medical Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.