27 In the power of the same Holy Spirit Peter also, the chief of the Apostles and the bearer of the keys of the kingdom of heaven, healed Æneas the paralytic in the Name of Christ at Lydda, which is now Diospolis, and at Joppa raised from the dead Tabitha rich in good works. And being on the housetop in a trance, he saw heaven opened, and by means of the vessel let down as it were a sheet full of beasts of every shape and sort, he learned plainly to call no man common or unclean, though he should be of the Greeks. And when he was sent for by Cornelius, he heard clearly the Holy Ghost Himself saying, Behold, men seek you; but arise and get you down, and go with them, nothing doubting; for I have sent them. And that it might be plainly shown that those of the Gentiles also who believe are made partakers of the grace of the Holy Ghost, when Peter had come to Cesarea, and was teaching the things concerning Christ, the Scripture says concerning Cornelius and them who were with him; While Peter yet spoke these words, the Holy Ghost fell on all them which heard the word; so that they of the circumcision also which came with Peter were astonished, and when they understood it said that on the Gentiles also was poured out the gift of the Holy Ghost.
Source: Catechetical Lectures (New Advent)