Periah

See the Chidushey Ha-Ran, who states that even if one is no longer busy cutting / , i.e., with the milah,/ but /already/ started /doing/ the periah he is /nevertheless/ still classed as being occupied with the milah, since milah and periah are /classed as parts of/ the same action.

in the description of Abraham's circumcision eth is not sued. Rashi quotes Bereshith Rabbah, which explains that Ishmael underwent periah - the removal of an additional membrane below the foreskin - while Abraham did not.

The Midrash, extolling the wisdom and beauty of the human body which is uniquely constructed for the performance of mitzvot, notes that G-d gave people nails on their fingers so they could perform the rituals of melika (a form of schechita of birds in the Mikdash) and periah. Nevertheless, when mohelim developed a more efficient method of performing milah and periah in one step, no objection was raised.

periah was an innovation instituted over the course of time, most likely in response to the drawing down of the foreskin that was known from the time of the Hellenists and was still practiced during the time of the Hadrianic persecutions .. Proof that periah is an innovative requirement is to be found as well in the tradition that the Patriarch Abraham did not practice it.