The Divine Comedy with Commentary by Cristoforo Landino

...winds. And of the last one where he says:

Although it winds for eleven miles. original: "Tutto che la uolge undici miglia" – Inferno XXX, 86

But seeking the proportion, that which encloses should always be twice as much, as twenty-two is to eleven. Because the third would have forty-four, and proceeding thus, the tenth would be five thousand miles, according to thirty-two The translator notes a likely calculation of diameter/circumference ratios used by the commentator and the greater width of one thousand five hundred miles. So you see that toward the center there would be more width than on the surface. This is also consistent with the description of the heights that he provides above and their supports. But we shall say that it is always eleven miles more than the enclosed space: and thus all the ditches bolge Malebolge, meaning "Evil Pouches" or "Ditches," is the eighth circle of Hell, consisting of ten concentric trenches will equally have a distance of eleven miles, just as when many moats surround a castle with equal distances, where each moat is one and three-quarter miles wide with a diameter of thirty-five miles. And this is also easily understood in his narration where he does not show the ultimate distance, which is only half a mile in width, while the others are all one mile and three-quarters. And this corresponds with the greater width of Hell, which we set at three thousand five hundred and ten. Therefore, the first ditch is thirty miles First part of the Malebolge, and has a diameter of thirty-five miles and a circumference of one hundred and ten. Therefore the first ditch is thirty-one miles, which contains the panderers ruffiani and seducers. The second contains the adulators and flatterers and has a diameter of thirty-one and a half miles. The third, of the simoniacs, is twenty-eight. The fourth, of the diviners, is twenty-four and a half miles. The fifth, of the barrators corrupt politicians, is twenty-one miles. The sixth, of the hypocrites, is seventeen and a half miles. The seventh, of the thieves, is fourteen miles. The eighth, of the fraudulent counselors, is ten and a half miles. The ninth, of the sowers of discord scismatici, is seven miles. Therefore, the circumference of such a diameter will be twenty-two miles. Wherefore Virgil says:

Consider if you can count them / for twenty-two miles the valley winds. original: "Pensa se tu annumerar gli puoi / Che miglia ventidue la valle volge" – Inferno XXIX, 9

The tenth and last of the Malebolge, where the falsifiers and alchemists are, has a diameter of three and a half. Wherefore he says, although it turns eleven miles, it is no less than half a mile across. And certainly, taking from its diameter two half-miles, which they occupy in the circle, there remains a void diameter of two and a half miles; and this last one has from one top of the bank to the other a distance of half a mile. Now the circles of Malebolge could, on a flat plane, enclose one another successively with equal space between each; and being thus, the ten valleys would be one and three-quarter miles wide from the top of one bank to the other. But the place is not on a plane, but on a slope descending toward the center. Wherefore he says in Canto XXIV:

Because all of Malebolge slopes / toward the entrance of the lowest pit / the site of each valley carries / that one bank rises and the other descends. original: "Ma perché Malebolge inver la porta / Del bassissimo pozzo tutte prende / Lo sito di ciascuna valle porta / Che l’una costa surge e l’altra scende" – Inferno XXIV, 37-40

And elsewhere he shows the bottom and the steepness of these valleys, saying:

Here he gently set down his burden / gently along the jagged and steep rock / which would be a difficult pass even for goats. original: "Quivi soavemente spose el carcho / Soave per lo scoglio sconcio et erto / Che sarebbe alle capre duro varco" – Inferno XXXI, 140-142

Therefore it is necessary that the valleys be wider, though only slightly when measured on a plane. Thus it seems to me that the half part of the half-diameter of the widest part of such a site—which comes to be the half of seventeen and a half miles—is the figure of the slope of this site; that is, the end of the Pit of Geryon is eight and three-quarter miles higher than the bank of the Pit of the Giants. From the end of the Pit of Geryon, which is the beginning of Malebolge as I have said, until the center of the earth is thirty-two and a half miles; and subtracting that which Malebolge slopes, which seems to me eight and three-quarter miles, there remain twenty-three and three-quarter miles. And this shall be sufficient to have said of the site of Hell. But likewise, to understand the immense stature of the giants, we will investigate in the verses of the poet several measurements written by him; and first we will note in Canto XXXI what he writes of Nimrod Nebroth:

His face appeared to me as long and large / As the pine cone of Saint Peter’s in Rome / and in its proportion were all his other bones. original: "La faccia sua mi parea lunga & grossa / Come la pina di san Piero a Roma / & a sua proportiõ tutte laltre ossa" – Inferno XXXI, 58-60. The "pine cone" refers to a famous 13-foot-tall Roman bronze sculpture

According to these verses, the height of the head of this giant will be five and two-fifths Florentine cubits braccia fiorentine A "braccio" was a standard unit of measurement in Florence, roughly 58 centimeters or 23 inches; for we know that such is the size of the aforementioned bronze pine cone in Rome. Learned painters in symmetry say that a well-proportioned man is as long as eight of his heads; therefore, this giant would be forty-three cubits or more. This then will be the height of the giants according to the poet's position. It follows that by certain principles set down by him, we may likewise measure the greatness of Lucifer. But first we will note that after the circles and smaller circles and rounds of which we have spoken until now, there remain four spheres of bloody and frozen water, which have as their center the universal center; and in the one furthest from the center is founded the Pit of the Giants; and this is called Caina. Within this is enclosed the second, called Antenora. And in this the third, named Ptolomea; and by Ptolomea is enclosed the one called Giudecca, the smallest of all; of which we will narrate particularly in their place.
This contains within itself the universal center: and in the center.

This contains within itself the universal center; and in the center is Lucifer, who, placed in the ice, emerges from the middle of his chest upward. And of Lucifer, the poet writes:

And I am more comparable to a giant / than giants are to his arms. original: "Et più con un gygante io mi convegno / Che giganti non fan cholle sue braccia" – Inferno XXXIV, 30-31

Dante says, therefore, that his body has more proportion to giants than the bodies of giants have to the arm of Lucifer. And because Dante was of medium stature, estimated at two cubits and seven-eighths, and we concluded above that giants, according to the measure of the face equal to the pine cone of Saint Peter, are forty-three cubits high. Therefore, Dante would fit fifteen times into a giant. Consequently, a giant would fit fifteen times into an arm of Lucifer. It follows that the arm of Lucifer is six hundred and forty-five Florentine cubits. And because we see a well-proportioned man to be the measure of three cubits, and the arm of such a man to be one and one-sixth cubits long, it follows according to such proportion that if the arm of Lucifer is six hundred and forty-five cubits, his body is not far from two thousand cubits. In fact, according to the measurement, it would be exactly one thousand nine hundred and eighty cubits. But because he showed that giants are barely comparable to his arm, we can set it at that number. The same is true if we look at the measure in palms, for every three palms is one cubit, and the measure of the wings, which are about two Florentine cubits. And this is as to the body. But the sphere of Giudecca, in which is the universal center, and from which Lucifer emerges from the middle up, seems to me to have a diameter of half the said two thousand cubits, which is one thousand cubits. Because from the middle of the chest to the top of the head is the measure of two heads; and just as much—that is, the measure of two other heads—should emerge from the top of the legs, since he has the middle of his body at the universal center, which is likewise the center of this sphere, as denoted in these verses:

When we were at the point where the thigh / turns exactly upon the thick of the haunch / the Guide with labor and with anguish / turned his head to where he had his shanks / and grappled to the hair like a man who climbs / so that I thought we were returning to Hell again. original: "Quando noi fumo là dove la coscia / Si volge apuncto in sul dosso dellanche / El duca cõ fatica & con angoscia / Volse la testa ovegli hauea le zanche..." – Inferno XXXIV, 76-81

Thus, there would remain in the sphere the measure of four heads, which are half of the total of Lucifer. Therefore, the diameter of Giudecca will be one thousand cubits. And Ptolomea, which is contiguous to this, will be, I believe, the size of the whole body of Lucifer, which is two thousand cubits. And then Antenora, which encloses this, three thousand cubits; and Caina, which is the largest, will be four thousand cubits. And if you ask what conjecture leads me to this opinion, I answer because in the circles of the rounds and in the ditches of Malebolge, this same rule is seen. Nor have I anything else that can contribute to the location of Hell and the stature of the giants and of Lucifer. Therefore, we will remain in this opinion until another of greater judgment comes and shows us better the description of Dante, which we follow in this. His exit from Hell is quite clear because of a long small stream that ends in the tomb of Lucifer, and on the surface of the earth in the other hemisphere, and on the island where the mountain of Purgatory is, where he writes thus:

There is a place down there as far from Beelzebub / as the tomb extends, which is known / not by sight but by the sound of a rivulet / that descends here through the hollow of a rock / which it has worn with its winding course / and it slopes a little. My Guide and I entered by that hidden way / to return to the bright world / and without caring for any rest / he climbed up first and I second / until I saw the beautiful things / that the heaven carries, through a round opening / and from there we came out to see the stars again. original: "luogo è laggiù da Belzabù remoto..." – Inferno XXXIV, 127-139
And that the exit facing this is Cato, he demonstrates in the first canto of Purgatory with these words:
Who are you, who against the blind stream / have fled the eternal prison? original: "Chi sete voi che contro al cieco fiume / Fuggito hauete la prigione etherna" – Purgatorio I, 40-41
he said, moving those venerable plumes. The End.