Charles Buck Theological Dictionary
Were thus denominated, because, in profession, they condemned the errors of the Arians, but in reality maintained their principles, only palliating and concealing them under softer and more moderate terms. They would not allow, with the orthodox, that the Son was of the same substance, but only of a like substance with the Father; and thus, though in expression they differed from the orthodox in a single letter only, yet in effect they denied the divinity of Jesus Christ. 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 those who teach that the eternal generation is necessary. Such, at least, are the respective opinions of Dr. Clarke and Bishop Bull.
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Buck, Charles. Entry for 'Semi-Arians'. Charles Buck Theological Dictionary. https://www.studylight.org/dictionaries/eng/cbd/s/semi-arians.html. 1802.