Witsius on the Persons for Whom Christ Engaged and Satisifed

Herman Witsius discusses the work of Christ at great length in his The Economy of the Covenants Between God and Man. In his chapter entitled Of the Persons for whom Christ engaged and satisfied he makes five conclusions, two of which I will repeat below:

[Firstly] That the obedience and sufferings of Christ, considered in themselves, are, on account of the infinite dignity of the person, of that value, as to have been sufficient for redeeming not only all and every man in particular, but many myriads besides, had it so pleased God and Christ, that he should have undertaken and satisfied for them.

However, Witsius further notes:

[Fifthly] That…Christ, according to the will of God the Father, and his own purpose, did neither engage nor satisfy, and consequently in no manner die, but only for all those whom the Father gave him, and who are actually saved. This is that truth which is controverted…