in Ecclesiastical History, a branch of the ancient Arians, consisting, according to Epiphanius, of such as, in appearance, condemned the errors of that heresiarch, but yet acquiesced in some of his principles, only palliating and hiding them under softer and more moderate terms. Though they separated from the Arian faction, they could never be brought to acknowledge that the Son was "homoiousios," that is, consubstantial, or of the same substance with the Father; they would only allow him to be "homoiousios," that is, of a like substance with the Father, or similar to the Father in his essence, not by nature, but by a peculiar privilege.

The Semi-Arianism of the moderns consists in their maintaining that the Son was from all eternity begotten by the will of the Father, contrary to the doctrine of the orthodox, who seem to teach that eternal generation is necessary. Such, at least, are the respective opinions of Dr Clarke and Bishop Bull.