St. Peter's example as an authority for Whitsuntide baptisms
And that we do not contend for this on our own conviction but retain it on Apostolic authority, we prove by a sufficiently apt example, following the blessed Apostle Peter, who, on the very day on which the promised coming of the Holy Ghost filled up the number of those that believed, dedicated to God in the baptismal font three thousand of the people who had been converted by his preaching. The Holy Scripture, which contains the Acts of Apostles, teaches this in its faithful narrative, saying, “Now when they heard this they were pricked in the heart, and said unto Peter and to the rest of the Apostles, what shall we do, brethren? But Peter said unto them, Repent and be baptized every one of you in the name of Jesus Christ, unto the remission of your sins, and you shall receive the gift of the Holy Ghost. For to you is the promise, and to your children and to all that are afar off, even as many as the Lord our God shall call unto Him. With many other words also he testified and exhorted them saying, Save yourselves from this crooked generation. They then that received his word were baptized, and there were added in that day about three thousand.”
Source: Letters (New Advent)