However we look at it, the figure cut in this story by della Croce is not heroic.
Between the years 1474 and 1476, Vannozza bore Roderigo two sons, Cesare Borgia (afterwards Cardinal of Valencia and Duke of Valentinois), the central figure of our story, and Giovanni Borgia (afterwards Duke of Gandia).
Lucrezia Borgia, we know from documentary evidence before us, was born on April 19, 1479.
But there is a mystery about the precise respective ages of Vannozza's two eldest sons, and we fear that at this time of day it has become impossible to establish beyond reasonable doubt which was the firstborn; and this in spite of the documents discovered by Gregorovius and his assertion that they remove all doubt and enable him definitely to assert that Giovanni was born in 1474 and Cesare in 1476.
Let us look at these documents.

They are letters from ambassadors to their masters; probably correct, and the more credible since they happen to agree and corroborate one another; still, not so utterly and absolutely reliable as to suffice to remove the doubts engendered by the no less reliable documents whose evidence contradicts them.
The first letters quoted by Gregorovius are from the ambassador Gianandrea Boccaccio to his master, the Duke of Ferrara, in 1493.

In these he mentions Cesare Borgia as being sixteen to seventeen years of age at the time.

But the very manner of writing--"sixteen to seventeen years"-- is a common way of vaguely suggesting age rather than positively stating it.

So we may pass that evidence over, as of secondary importance.
Next is a letter from Gerardo Saraceni to the Duke of Ferrara, dated October 26, 1501, and it is more valuable, claiming as it does to be the relation of something which his Holiness told the writer.