Definitions

from The American Heritage® Dictionary of the English Language, 4th Edition

  • n. A member of the Semi-Arian party in the fourth century A.D. that held that Jesus the Son and God the Father were of similar but not of the same substance.

from the GNU version of the Collaborative International Dictionary of English

  • adj. Of or pertaining to Homoiousians, or their belief.
  • n. One of the semi-Arians of the 4th century, who held that the Son was of like, but not the same, essence or substance with the Father; -- opposed to homoousian.

from The Century Dictionary and Cyclopedia

  • Having a similar nature.
  • [capitalized] Relating to the Homoiousians or their belief.
  • n. [capitalized] One of the Semi-Arians, followers of Eusebius, who maintained that the nature of Christ is similar to, but not the same with, that of the Father: opposed to Homoöusian.

Etymologies

From Greek homoiousios, of similar substance : homoio-, homeo- + ousiā, substance (from ousa, feminine present participle of einai, to be; see es- in Indo-European roots).
(American Heritage® Dictionary of the English Language, Fourth Edition)

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