Generally, Dante is regarded as structuring his work on Aristotelian division; but indeed he is far more Platonically based than Aristotelian. In fact, the structure of Dante's work rests on the Medieval structure of the Liberal Arts which, itself, is dependent on an earlier educational model of the Divided Line as laid out in Plato's Republic.
Margherita Fiorello nicely outlines this structure of the Liberal Arts as correspondent to Medieval Alchemy:
The Liberal Arts consisted of two sections; the Quadrivium and the Trivium. The Quadrivium ("four roads") was composed of four sections; arithmetic, geometry, music, astronomy. The Trivium ("three roads") was composed of three sections; grammar, logic, rhetoric.
They were not the same as the divisions we now mark between, say, sophomores and juniors, but were, rather, disciplines which one learned through studying certain texts. The Quadrivium trained the mind to an intellectual rigor, or strength. The Trivium trained the heart (or "third eye" - the "chakra", or "ajna" as the Eastern mystics called it) to perceive through love.
The Quadrivium is itself a reconstitution of the ancient Platonic image of the Divided Line. Tudor B. Munteanu argues at his blog that the Divided Line was NOT based on the Golden Proportion Division:
In my understanding, however, it seems that the Divided Line was an image best left in the mind; difficult to concretize visually - namely b/c Plato seems to overlap the second (pistis) with the third (dianoia) as the connecting "middle term" of the Golden Proportion. They are the same in size, operating on the same thing (objects), connecting the world of the visible to the world of the intelligible. The rift might seem vast, but is no more vast than the line between the lower half of the vesica piscis and the upper half. The rift is the canyon between the violent and the malebolges of Nether Hell down which Geryon carries the two poets. In the Divided Line the middle term of b connects the world of the physical (a) with the world of the metaphysical (c) - this model carries through to the doctrine of the Incarnation in the Catholic world view, Christ being, being both man and god, stands for the "middle term" between earth and heaven. Similarly, belief (pistis) and understanding (dianoia) work intimately with one another to connect the visible world of images with the intelligible world of forms. The whole guardian must be trained in gymnastic and music equally, the ruler must be both philosopher and king equally, the pilgrim (Dante) must become both bishop and emperor equally, physical and metaphysical, dead and living both.
Dante himself acknowledges this paradoxical existence in Canto XXVII when he is faced with walking through the fire - the last trial on the ascent up Purgatory. He says of his fear
per chi/io divenni tal, quando lo'ntesi,
qual e colui che ne la fossa e messo.
I was like a corpse put in the grave,
the words I heard so touched my heart with fear.
- XXVII, 14 - 15
What terrifies him is the impossibility of the paradox. How does one die and remain alive? The only thing that those on this side of the world of the visible perceive is that the body dies - horribly; we see "too sharply in (our) mind bodies (that) die burning at the stake." (XXVII, 17 - 18). The trick is to cross through that fire, as Augustine later suggests in the "Confessions" in order to see that life exists on the other side. Only then can we graduate from children to adults.
Adulthood implies autonomy - we move from being subordinate to the law to being lawmakers - children to men - slaves to freemen. Thus the Liberal Arts' whole purpose is to prepare us to make that spiritual/intellectual move; to prepare men destined to vote in a republic to be able to vote. In similo modo Plato suggests that the movement from Gyges to Er occurs only through an education that prepares us to see "beyond the veil" to what undergirds the created world like the stern of a trireme - the spindle of necessity. Just as Er passes through death (like Coleridge's Mariner) and returns to the world to tell others, to the cave to rescue prisoners, so too does the pilgrim Dante return to write his poem. His poem is the testimony of the other world, like Er's testimony of the afterlife or the risen Christ's testimony to the Apostles.
The last section of the work, Paradiso, is the pleasure which guides him - seeing at last that God and man are one - an action only possible after going through the educational agony of the first two sections of the Liberal Arts.
*work in progress*