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homogeneous

[hoh-muh-jee-nee-uh s, -jeen-yuh s, hom-uh-] /ˌhoʊ məˈdʒi ni əs, -ˈdʒin yəs, ˌhɒm ə-/
adjective
1.
composed of parts or elements that are all of the same kind; not heterogeneous:
a homogeneous population.
2.
of the same kind or nature; essentially alike.
3.
Mathematics.
  1. having a common property throughout:
    a homogeneous solid figure.
  2. having all terms of the same degree:
    a homogeneous equation.
  3. relating to a function of several variables that becomes multiplied by some power of a constant when each variable is multiplied by that constant: x 2 y 3 is a homogeneous expression of degree 5.
  4. relating to a differential equation in which a linear combination of derivatives is set equal to zero.
Origin
1635-1645
1635-45; < Medieval Latin homogeneus, equivalent to homogene- (stem of Greek homogenḗs of the same kind; see homo-, gene) + -us -ous
Related forms
homogeneously, adverb
nonhomogeneous, adjective
nonhomogeneously, adverb
nonhomogeneousness, noun
unhomogeneous, adjective
unhomogeneously, adverb
unhomogeneousness, noun
Can be confused
homogeneous, homogenous.
Synonyms
1. unvarying, unmixed, alike, similar, identical.
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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British Dictionary definitions for homogeneously

homogeneous

/ˌhəʊməˈdʒiːnɪəs; ˌhɒm-/
adjective
1.
composed of similar or identical parts or elements
2.
of uniform nature
3.
similar in kind or nature
4.
having a constant property, such as density, throughout
5.
(maths)
  1. (of a polynomial) containing terms of the same degree with respect to all the variables, as in x² + 2xy + y²
  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
  3. (of an equation) containing a homogeneous function made equal to 0
6.
(chem) of, composed of, or concerned with a single phase Compare heterogeneous
Also (for senses 1–4) homogenous
Derived Forms
homogeneity (ˌhəʊməʊdʒɪˈniːɪtɪ; ˌhɒm-) noun
homogeneously, adverb
homogeneousness, 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
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Word Origin and History for homogeneously

homogeneous

adj.

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
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homogeneously in Medicine

homogeneous ho·mo·ge·ne·ous (hō'mə-jē'nē-əs, -jēn'yəs)
adj.

  1. Of the same or similar nature or kind.

  2. 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.
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