How Does Scripture Treat Children of Believers?

The legitimacy of infant baptism depends entirely on the question of the manner in which Scripture regards the children of believers and wishes us, consequently, to regard them. If Scripture speaks of these children in the same way as of adult believers, and if the promises which are made to them and the benefits of grace received by them are the same, then the legitimacy and, still more, the duty of infant baptism are securely established; we cannot withhold from children that which is granted to adults. (Pierre Marcel, Doctrine of Infant Baptism)