Ten is the perfect number in the same way in which Eight is: it is the number in which the circle is closed, and the beginning is reborn from the end. This is so obvious that the early writers hardly ever mentioned it, exercising their minds to praise its perfection in more subtle ways.
We’ve already discussed Pythagoras’ tectractys of the decad, in which Ten is expressed as the sum of the first four numerals: 1 + 2 + 3 +4. In his treatise refuting the Manichean heresy, Augustine discovers a more obviously Christian arrangement: “This number Ten signifies perfection; for to the number Seven, which embraces all created things, is added the Trinity of the Creator”.
The architecture of Dante’s Commedia is organized according to the sum of seven plus two equal nine plus one equals ten. In Hell, sins fall into three ethical categories (the Sins of the Leopard, the Lion, and the Wolf), and their perpetrators are disposed in seven circles: four of Incontinence, one of Violence and two of Fraud. To these Dante adds two circles of wrong belief: one of unbelief (the Limbo of the Pagan Worthies) and another of perverted belief (the Circle of the Heretics). Finally, he adds the Vestibule of the Futile, who have neither faith nor the capacity to decide (and thus to undertake moral action, as it was anciently defined).
This makes, then, ten main divisions in Hell, disposed according to the same numerical scheme (7+2=9 +1=10) as we find in the other books of the Comedy. There are seven Cornices of Purgatory, each allotted to one of the Seven Deadly Sins. These in turn are divided once more into three broad categories (Love Perverted, Love Defective, and Excessive Love of Secondary Goods). The Seven Cornices are approached from the Two Terraces of the Ante-Purgatory, and followed by the Earthly Paradise at the summit of the Mountain. Heaven, similarly, consists of a total of ten spheres: the seven planetary spheres, beyond which lie the spheres of the fixed stars and the Primum Mobile, beyond which lies the outermost sphere, the Empyraeum, that is, the true Heaven of God.