Book IV. This book is in a sense the beginning of the treatise, and is sometimes cited later on as the first. Its three predecessors, he says in § 1, had been written some time before. They had contained a statement of the truth concerning the Divinity of Christ, and a summary refutation of the various heresies. He now commences his main attack upon Arianism. First (§ 2) he repeats what his difficulty is; that human language and thought cannot cope with the Infinite. Then (§ 3) he tells how the Arians explain away the eternal Sonship of Christ.
As a defence against this tampering with the truth, the Church has adopted the term Homoousion (§§ 4-7); Hilary explains and defends its use. In § 8 he shows, by a collection of the passages of Scripture which they wrest to their own purposes, that such a definition is necessary, and in §§ 9, 10 that their use of these passages is dishonest. In § 11 he tells us exactly what the Arian teaching is, and sets it forth in one of their own formularies, the Epistola Arii ad Alexandrum (§§ 12, 13).
In § 14 this doctrine is denounced; it does not explain, but explains away. The proclamation made through Moses, Hear, O Israel, the Lord your God is One, upon which the Arians take their stand, reveals only one aspect of the truth (§ 15). It does not exhaust the truth; for God is represented as not one solitary Person in the history of creation (§§ 16-22), in the life of Abraham (§§ 23-31), and in that of Moses (§§ 32-34). And this again is the teaching of the Prophets, as is shown by passages selected from Isaiah, Hosea, and Jeremiah (§§ 35-42). All the evidence thus collected shows that in the Godhead there is both Father and Son, and that the Son is God.
Source: On the Trinity (New Advent)