The Role of Numbers in the Comedy  

 Throughout the comedy, the numbers three, seven, and ten show up continually.  We see the three structurally, as there are three books, 33 cantos per book, and a terza rima rhyme scheme that is based off of threes (aba, bcb, cdc),  There are 9 (3x3) circles of the inferno and satan has three faces.  Violence is broken down into three parts: Towards others, towards self, and towards God.  There are 9 levels of hell and the ante-hell makes 10.  There are nine levels of purgatory and the earthly paradise makes it 10.  There are also 9 heavens in paradise, and Empyrean makes it 10.  The three primarily represents the trinity of Christianity: Father, Son, and Holy Spirit.  The Divine Comedy was written as a religious work and thus the trinity is an easy explanation for the use of threes.  

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Sources- Numbers in the Divine Comedy. Dante's Uses of Threes in the Divine Comedy.