different between homogeneous vs quantic

English

Alternative forms

• homogenous (may be considered incorrect; see usage note at homogenous)

Etymology

From Medieval Latin homogeneus, from Ancient Greek ???????? (homogen?s, “of the same race, family or kind”), from ???? (homós, “same”) + ????? (génos, “kind”). Compare homo- (“same”) and -ous (adjectival suffix).

Pronunciation

• (UK) IPA^(key): /?h?.m?(?)?d?i?.n??s/, /?h??.m?(?)?d?i?.n??s/
• (US) IPA^(key): /?ho?.mo??d?i?.nj?s/, /?ho?.m??d?i?.nj?s/, /?ho?.mo??d??.nj?s/

Adjective

homogeneous (not comparable)

1. Of the same kind; alike, similar.
2. Having the same composition throughout; of uniform make-up.
   • 1946, Bertrand Russell, History of Western Philosophy, I.25:

     Their citizens were not of homogeneous origin, but were from all parts of Greece.

3. (chemistry) in the same state of matter.
4. (mathematics) Of which the properties of a smaller set apply to the whole; scalable.

   The function ${\displaystyle f(x,y)=x^{2}+y^{2}}$ is homogeneous of degree 2 because ${\displaystyle f(\alpha x,\alpha y)=\alpha ^{2}f(x,y)}$.

Antonyms

• heterogeneous

Derived terms

Related terms

• homogeneity
• homogenise, homogenize

Translations

Further reading

• homogeneous in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
• homogeneous in The Century Dictionary, New York, N.Y.: The Century Co., 1911.
• homogeneous at OneLook Dictionary Search

English

Etymology

From Latin quantus (“how much”).

Noun

quantic (plural quantics)

1. (mathematics) A homogeneous polynomial in two or more variables.
   • 1858, Arthur Cayley, A Fourth Memoir on Quantics, 1859, Philosophical Transactions of the Royal Society of London, Volume 148, page 421,

     When the two quantics are the first derived functions of the same quantic of any odd order, the lineo-linear invariant does not vanish, but it is not an invariant of the single quantic.

   • 1859, George Salmon, Modern Higher Algebra, page 52,

     74. The discriminant of a binary quantic, or the eliminant of a system of binary quantics, is an invariant.

     We can see a priori that this must be the case, for if a given quantic has a square factor, it will have a square factor still when it is linearly transformed; or if a system of quantics have a common factor, they will still have a common factor when the equations are transformed.

   • 1895, Edwin Bailey Elliott, An Introduction to the Algebra of Quantics, 2011, Facsimile Edition.

References

• quantic in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.