Do I have the right birth record???

[Piano Dee]

I found this record Ruvo del Monte, PZ for what I think is my great grandfather. His name was Vincenzo Grieco and parents were Giuseppe and Arcangela Vasta (spelling?). His name appeared as Vito Vincenzo on one of his children's birth records. His death certificate indicates he was born around 1864. Can anyone translate the attached with the date of birth, parents and anythng else that seems relevant. I'm having a tough time with the handwriting. Thanks!!!

[paola52]

May 2 1864
Giuseppe Grieco, son of Vincenzo, peasant, 26, living in Ruvo declares that May 1 a son was born to him and his wife Arcangela Vasti, 26, living with him in their house in Ruvo
He gives the chlid the name Vito Vincenzo.
Side notation: the child was baptized May 3 in the parish of Santa Maria Assunta
Ciao
Paola

[Piano Dee]

Thank you Paolo