If we transliterate the Latin it would be In name Father and Son and Spirit Holy. Et means and, not both, so in each case the et means and.Is it correct to say that sign of the cross as, “In the name of the Father; both of the Son and of the Holy Spirit” since the Latin sign of the cross is, “In nomine Patris et Filii et Spiritus Sancti.”, where “et … et” means “both … and”,and the corresponding part in the sign of the cross translating to “both of the Son and of the Holy Spirit”?
Yes, but the Church gives us, “In the name of the Father, and of the Son, and of the Holy Spirit.” I would say that, “In the name of the Father; both of the Son and of the Holy Spirit,” sounds quite awkward.In Latin, however, word order does not necessarily matter, and you have to accommodate the Latin into what would sound best in English. Patris, Filii etc. are all in the genitive case, so they would mean “of the father” and “of the son”. The articles are also implied here, as there are no articles in Latin. Et … et is also a common phrase in Latin to mean both … and, for example, “Vita gaudiumque et in terra et in caelo.” would mean “There is life and joy both in heaven and on earth.”