# homogeneous

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

/ ˌhoʊ məˈdʒi ni əs, -ˈdʒin yəs, ˌhɒm ə- /

### adjective

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

Related forms

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019

## Examples from the Web for homogeneous

## British Dictionary definitions for homogeneous

## homogeneous

/ (ˌhəʊməˈdʒiːnɪəs, ˌhɒm-) /

### adjective

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

Also (for senses 1–4): homogenous

Derived Formshomogeneity (ˌhəʊməʊdʒɪˈniːɪtɪ, ˌhɒm-), nounhomogeneously, adverbhomogeneousness, noun

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 homogeneous

## homogeneous

1640s, from Medieval Latin homogeneus, from Greek homogenes "of the same kind," from homos "same" (see homo- (1)) + genos "kind, gender, race, stock" (see genus). Earlier in this sense was homogeneal (c.1600).

Online Etymology Dictionary, © 2010 Douglas Harper

## Medicine definitions for homogeneous

## homogeneous

[ hō′mə-jē′nē-əs, -jēn′yəs ]

### adj.

Of the same or similar nature or kind.

Uniform in structure or composition throughout, as of a chemical mixture.

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