How does Dante use the numbers 3, 9, and 10 in The Inferno?

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Of these numbers, three is the most significant in Dante's Divine Comedy, particularly in Inferno

The Divine Comedy as a whole is divided into three sections: Inferno, Purgatio, and Paradiso, the three places people can go after they die. The poems take place over three days, between Good Friday and Easter Sunday, the most significant period of time in Christianity, when Jesus was crucified and three days later, rose from the dead to save all humankind from sin. The Catholic Church also believes in the Holy Trinity of the Father (God), Son (Jesus), and the Holy Spirit. All three of the poems in The Divine Comedy are divided into 33 Cantos and each Canto is written in terza rima (three line stanzas with a rhyme scheme). In other words, the number three is reflected in the content and form of the poems.

To give a more specific example from Inferno, in Canto I, Dante is accosted by three ferocious beasts that represent three temptations that can lead people from the righteous path into "the dark wood of error." The Leopard represents fraud (lines 33-36), the Lion violence and greed (lines 43-47), and the She-Wolf "incontinence," or lack of control over sensual impulses (lines 48-54). 

The number nine, of course, is a multiple of three, and Dante's Inferno features the nine circles of hell. In the ninth circle, which is for the worst sinners who experience the most draconian punishments, Satan resides, holding three of history's worst sinners (and traitors) in three mouths (more threes). The sinners are Brutus, Cassius, and Judas.

The number ten is a perfect and holy number. Ten is a sort of antidote for all of the threes, which most seem associated with temptation and evil despite being drawn from the idea of the Trinity. Overall, the uses of these religiously significant numbers give readers a sense of Dante's familiarity with and devotion to his faith. 

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Dante's Divine Comedy is divided into three sections: Hell, Purgatory and Paradise. Each section is further divided into 33 poems (called cantos). Dante meets three beasts, Satan has three mouths, and three is a symbolic number in Christian theology for the Trinity - the three parts of the Godhead: Father, Son and Holy Spirit. The three major types of sin are incontinence, violence, and fraud. The hound that guards the gates of hell, Cerberus, has three heads. There are many other important "3s".

Hell is divided into nine circles which each represent a different type of sin (nine is the square root of three). The circles are sub-divided into upper and lower circles and circle number 8 is sub-divided into 10 types of frauds. Dante believed that fraud was a sin that could only be committed by man, so therefore God hated fraud more than anything else. Fraud included panderers, flatterers, corrupt church practices (having to pay for receiving the sacraments of the church), sorcery, etc. 

Ten is a number of completeness or perfection in the Bible. The number of "canti" in the poem is 100, the square of the perfect number, 10. There are 10 commandments, there were 10 plagues sent by God to punish Egypt, and the Anti-Christ's realm is predicted to consist of 10 kingdoms, among many other significant illustrations of this perfect number.

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