La Vita Nuova ("The New Life") is a literary piece written in a prosimetrum style, alternating between prose and poetry, by Dante in 1295. It is the story of the life-changing love of Dante for a young woman named Beatrice Portinari; a character who also figured prominently in his Divine Comedy.
The quotation that the Doctor reads at the end of "Latent Image" is paraphrased from Dante's La Vita Nuova. The Doctor reads:
"In that book which is my memory,
On the first page of the chapter that is the day when I first met you,
Appear the words, 'Here begins a new life'."
The original Italian is more literally translated by D.G. Rossetti in 1861:
"In that part of the book of my memory,
Before which is little that can be read,
There is a rubric, saying, 'Incipit Vita Nova'. (Here beginneth the new life.)"