VII. (3) By parity, the necessity of baptism is the same as that of circumcision. Now circumcision was to be administered to
infants according to the command of God. Therefore also infant baptism. The truth of the major is proved
(a) because baptism is put in the place of circumcision and succeeds it in the New Testament (from Col. 2:12, where Paul discovers circumcision in baptism).
(b) From the end of each—circumcision was a sacrament of initiation that they might be received into the covenant; baptism is the same.
(c) From the thing signified by each, which is the internal circumcision of the heart and the grace of regeneration.
(d) The grace of God is not diminished and restricted in the New Testament, but rather enlarged. If therefore the infantile age is an obstacle in baptism on account of the defect of reason, there was the same impediment in circumcision.
For if the blessings of God were not even then fruitlessly offered by circumcision, why should the same not be thought of baptism? Nor is it to be said either that “the circumcision of infants was expressly commanded, but not infant baptism.” It is one thing to be contained expressly; another implicitly in a general command (as we said before). Or that “the argument does not proceed rightly because there are various differences between circumcision and baptism.” The analogy of both sacraments ought to be attended to not in all, but in the principal condition related to the confirmation of the gratuitous covenant and declared in the New Testament (to wit, that both sacraments were a sign of the covenant, a symbol of initiation and a badge of profession, by which anciently the Jews were distinguished from the Gentiles and now Christians are distinguished from unbelievers). The differences (usually adduced) are of another kind which do not touch the very essence of the sacrament and its end.
Francis Turretin, Institutes of Elenctic Theology, ed. James T. Dennison Jr., trans. George Musgrave Giger, vol. 3 (Phillipsburg, NJ: P&R Publishing, 1992–1997), 19.20.7 (p. 416–17).