Two Lectures to the Florentine Academy
On the Shape, Location and Size
of Dante's Inferno
by Galileo Galilei, 1588
Table of Contents
The ice regions
Recapitulation of Dante's journey
Lecture II: Velutello's Inferno
Criticism of Velutello
If it is an amazing and wonderful thing that men have been able, through their long observations, ceaseless vigilance, and perilous explorations, to determine the measure of the skies, their motions fast and slow, their proportions, the sizes of the stars, -- not just the nearby ones but the distant ones as well --, and the geography of the earth and of the seas: things which, either in whole or in the greater part, are sensible to us; how much more marvelous must we esteem the investigation and description of the place and shape of the Inferno, which, buried in the bowels of the earth, hidden from every sense, is known to no one by any experience; where, although it is easy to descend there, it is nonetheless very difficult to return, as our Poet tells us so well when he says
"All hope abandon, ye who enter,"
Inferno III, 9
and his guide says in those lines
"The gates of Hell are open night and day,
Smooth the descent, and easy is the way:
But to return and view the cheerful skies
In this the task and mighty labor lies."
Aeneid VI, 192-195
The absence of any other accounts adds greatly to the difficulty of its description. To explain that infernal theater, it was necessary to have a geographer and architect of the most sublime judgment, as, in the end, our Dante has proved. If he who so sublimely developed the wonderful construction of the heavens, and so exquisitely designed the place of the earth, was reputed worthy the name of divine, then for the reasons already given, hasn't our Poet earned that name yet again?
Dante describes the Inferno, but he leaves it so obscured in darkness that others after him have wearied themselves in long attempts to explain his architecture. Among these are two who have written most prolifically; the one is Antonio Manetti, the other Alessandro Vellutello; but they have written very differently from each other, and very obscurely, both of them, although not, to be sure, through any failing on their part, but by the difficulty of the subject, which does not admit of easy explication in writing. We therefore, obeying the command given to us by one who can command us, have come here today to try whether the living voice, with accompanying drawings, could explain to those who have not understood it the meaning of the one opinion and of the other; and in addition, if there is time, we will add arguments for the one and the other side which could persuade us that either description is in agreement with the intentions of the Poet; doing our best at the end with some other arguments of our own to show how closely they approach to the truth, that is, to the mind of Dante; where perhaps we will make clear how wrongly the virtuous Manetti and together with him the most learned and most noble Florentine Academy have been slandered by Vellutello.
But before we go any further, let your fastidious ears not be offended, accustomed as they are to hearing this place always resonate with those select and decorous words which the pure Tuscan language affords, and pardon us if they may occasionally be assaulted by some declension or ending appropriate to that art which is so serviceable to us, taken either from the Greek or from the Latin language -- for the material of which we shall speak compels us to this.
The order which we shall adopt in explaining Manetti's opinion will be this: first we shall consider the form and total size of the Inferno, both absolutely and in comparison to the whole earth. In the second place we shall see where it is located, that is, where beneath the surface of the earth. Third, we shall see into how many levels it is divided, differing among themselves in greater or lesser distance from the center of the earth, and which of these levels are simple, and which composed of several circles or rings, and how many. In the fourth place, we will measure the intervals which are found between one level and another. Fifth, we will find the breadth across each level, circle, and ring. In the sixth place, having already considered the above principal things, we will briefly retell the journey made by Dante through the Inferno, and in this we will point out some particular things, useful for the perfect knowledge of this place.
Coming then, to the explication of the opinion of Manetti, and first of all to the shape, I say that it is in the shape of a concave surface which we call conical, its vertex is at the center of the world, and the base is against the surface of the earth. But how does this work? We will shorten and facilitate the argument; and considering together the shape, the place, and the size, let us imagine a straight line which comes from the center of the earth (which is also the center of heaviness and of the Universe) to Jerusalem, and an arc which extends from Jerusalem over the surface of the water and the earth together to a twelfth part of its greatest circumference: such an arc will terminate with one of its extremities on Jerusalem; from the other let a second straight line be drawn to the center of the earth, and we will have a sector of a circle, contained by the two lines which come from the center and the said arc; let us imagine, then, that the line which joins Jerusalem to the center staying fixed, the other line and the arc should be moved in a circle, and that in such motion it should go cutting the earth, and move itself until it returns to where it started. There will be cut from the earth a part like a cone; which, if we imagine it to be taken out of the earth, there will remain, in the place where it was, a hole in the form of a conical surface, and this is the Inferno. And from this description we have, first, the form; second, the place, being so positioned that its lowest point is the center of the world and its base or mouth is against that part of the earth which is centered on Jerusalem, as one evidently learns from Dante when, as soon as he has passed over the center to the other hemisphere, he hears from Vergil these words
"Now you are beneath the opposite hemisphere to that
Which canopies the great dry land therein:
Under the zenith of that one is the site
Whereon the Man was slain who without sin
Was born and lived ..."
Inferno XXXIV, 112-115
And in the second canto of Purgatory, being entirely in the other hemisphere, he confirms the same thing, saying
"Already the Sun was joined to the horizon
Whose meridian circle covers
Jerusalem with its highest point."
Purgatorio II, 1-3
The size and depth of the Inferno is as great as the radius of the earth, and its mouth, which is the circle turned about Jerusalem, has for its diameter an equal size, because under the arc of the sixth part of the circle is a chord equal to the radius.
But wanting to know its size in respect to the whole volume of earth and water, we should not just follow the opinion of some who have written about the Inferno, who believe it to occupy the sixth part of the volume, because making the computation according to the methods proved by Archimedes in his book On the Sphere and the Cylinder, we will find that the space of the Inferno occupies a little less than 1/14 part of the whole volume; I say this if that space should extend all the way to the surface of the earth, which it doesn't: on the contrary, the mouth remains covered by a great vault of earth, whose summit is Jerusalem and whose thickness is the eighth part of the radius, which is 405-15/22 miles.
Having understood its form generally in this way, we should divide it into its levels; because its internal surface is not so smooth and simple as would follow from the description which we have given; rather it is divided into certain levels in which various sins are punished with various pains; and of these levels we should now assign the number and the order, and then more specifically the sizes and distances from one to the other, and the division of some of them into various rings, thus distinguished and named by the Poet. This enormous cavern is, then, divided into 8 levels, differing among themselves in greater or lesser distance from the center; such that the Inferno comes to resemble an enormous amphitheater, which narrows, descending from one level to another; except that an amphitheater has at the bottom the stage, but the Inferno terminates its depth almost at the center, which is a single point. These levels go turning round and round the concavity of the Inferno; and the first, the nearest to the surface of the earth, is Limbo; the second is that where the sensuous are punished; in the third are castigated the gluttonous; the fourth holds the prodigal and the avaricious. The fifth level is divided into two circles, the first of which includes the Stygian swamp and the moats around the city, the place assigned to the pains of the wrathful and the sullen; the second the city of Dis, where the heretics are punished. And here one should point out that by levels we do not mean what are called circles by Dante, because we propose that the levels are distinct from each other by greater or lesser distance from the center, which isn't always the case with circles, witness that in the fifth level the Poet places on the same level two circles. But because the other levels are still called circles by the Poet, we can say that in all there are 9 circles and 8 levels. Next therefore follows the sixth level and seventh circle, the torment of the violent, which is divided into 3 rings, so named by the Author. And here we can note the distinction which Dante makes between circles and rings, the rings being parts of the circles, like this seventh one, divided into 3 rings of which the one surrounds the other. And the first and the greatest in circumference, which is a lake of blood, surrounds the next, which is a forest of stumps, which surrounds the third ring, which is a plain of sand. For in the 13th Canto we read
"Here the good master began, `Before you go
Farther, be aware that now you are in this,
The second ring -- and so you shall be until
The horrible sand.'"
Inferno XIII, 16-19
The seventh level and eighth circle contains the whole of Malebolgia, where the fraudulent are punished. The eighth and last level, which is the ninth circle, embraces the four spheres of ice of the traitorous. But passing to the distances from one level to the other, of which there are eight, I say that the first six are equal to one another, and each one is one eighth part of the radius of the earth, that is, 405-15/22 miles. And by so much is Limbo distant from the surface of the earth, in the same way the second level from Limbo, the third from the second, the fourth from the third, the fifth from the fourth, and the sixth from the fifth. The two last distances remain, that is, the distance from the circle of the violent to Malebolgia, which is the depth of the defile of Geryon, and that from Malebolgia to the ice, which is the pit of the giants; and these two distances would have been again the same according to Manetti, equal to each other and to all the others, that is, each one the eighth part of the radius, if he had not observed in Dante places from which one necessarily deduces that these must be unequal. But because Dante says the ninth and last bolgia turns through 22 miles, hearing these words from Vergil in the 29th canto
" ... You found no reason
To delay like this at any other pit.
Consider, if counting them is what you plan,
This valley extends along a circular route
For twenty-two miles."
Inferno XXIX, 7-9.
and in consequence, the diameter must be 7 miles. And the tenth one turning eleven miles, as one sees in the following canto, where it says
"...Were I still light
Enough to move even one inch ahead
Every hundred years, I would have set out
Upon this road already, trying to find
Him in this mutilated people -- despite
The circuit being eleven miles around
And at least half a mile across its track."
Inferno XXX, 82-86
and having in consequence, a diameter of 3-1/2 miles. It follows that the width of the ninth bolgia must be 1-3/4 miles. And giving so much width to each of the others, the first and largest bolgia comes to have a diameter of 35 miles, and so much is the diameter at the end of the penultimate distance, that is, as has been said, the interval from the circle of the violent to Malebolgia. And if the diameter there is this much, making the computation we will find the distance of such a place from the center ought to be 81-3/22 miles, as will be demonstrated next, when we will speak of the width of the bolgias. And if 81-3/22 miles is the last distance, the remainder up to 2/8 the radius of the earth will be the penultimate, that is, 730-5/22 miles. So much therefore is the depth of the defile, the depth of the pit being 81-3/22 miles.
Now, since we should come to the method used by Manetti to investigate the widths of all the levels of the Inferno, we deem it necessary to propound a geometrical proposition, the knowledge of which will help us greatly to the understanding of what it has to say, and it is this:
If between two intersecting lines there be described some parts of the circumference of circles, which have as center the point of intersection of the lines, these circumferences will have among each other the same proportions as the radii of their circles. And this is clear, because they make similar sectors of circles, of which the sides are proportional to the arcs, as is demonstrated in geometry.
Having said this, we turn to the widths. Manetti used the straight lines which we pulled up from the center of the earth, the one to Jerusalem, the other to the extremity, or, as we might say, to the edge of the mouth of the Inferno (when it arrives up to the surface of the earth), and in the arc which is drawn from the one to the other of these, which is in length 1700 miles, he marked 10 spaces, each one of 100 miles, beginning from the mouth; from these he deduced the widths of some of the levels and rings, as we shall see more particularly now. In this way, having taken the end of the first hundred and from this drawn a line to the center of the world, with this he terminated the width of Limbo, that is, the first circle. And because this line with that previously drawn from the edge of the mouth to the center goes narrowing proportionately down to the center, where they meet, and the distance of Limbo from the surface of the earth was said to be the eighth part of the radius, it will follow, by the proposition just propounded, that the width of Limbo is narrowed by the eighth part of that which was at the surface of the earth; and because there it was 100 miles, taking away the eighth part, which is 12-1/2 miles, there will remain the width of Limbo, 87-1/2 miles. Coming back then to the second hundred, from its end toward Jerusalem a second line drawn toward the center terminates the width of the second circle, which being distant from the surface of the earth by 2/8 the radius, diminishing the width by the same proportion, which on the surface is 100 miles, there remains the width of the second circle, 75 miles. And observing the same order in the third and fourth levels, diminishing the width by the proportion of their distance to the surface of the earth, to the third circle Manetti assigned the width 62-1/2 and to the fourth 50 miles. But to determine the width of the fifth level, he took three hundreds in the said arc on the surface of the earth, and this because the fifth level is divided into two circles, and the first of these is divided again into two rings, that is, the Stygian swamp and the moat, but the second circle, that is the city, remains undivided. And because this level is distant from the surface of the earth by 5/8 the radius, diminishing the width by the same proportion, which on the surface of the earth is 300 miles, he deduced the width of the fifth level, 112-1/2 miles, of which the third part, that is 37-1/2, he gave to the swamp, another 37-1/2 to the moat, and the last third to the cemetery of the heretics, inside the city. And in this way, down to this level, there have been used up 7 of the 10 hundreds marked on the arc on the surface of the earth, that is, 4 for the first four circles and 3 for the fifth.
There remain, therefore, 3 hundreds to give the width of the sixth level, which is divided into 3 rings, that is, the lake of blood, the forest, and the sandy plain. Thus it is appropriate to make them all the same, and because this level is distant from the surface by 6/8 of the radius, diminishing the 300 miles that we have at the surface by that proportion, we have 75 miles, of which we will assign 25 to each ring.
Up to this point we have distributed 1000 of the 1700 miles marked on the surface, on the arc from Jerusalem to the mouth of the Inferno, in assigning the widths to the aforesaid circles. There remain to us therefore 700 miles to distribute through the width of the remaining circles, that is, through Malebolgia and the pit of the giants; and this division, because I find it to correspond so exquisitely to the widths which the Poet himself assigns to the pit and the bolgias, induces me, and not without astonishment, to believe that the opinion of Manetti conforms in everything to the idea conceived by Dante for this, his theater.
Coming now to this division, it is good that we should demonstrate that which we promised a little while ago; that is, that if Malebolgia is, in its greatest width, 17-1/2 miles in radius, as one deduces from Dante himself, then there must necessarily be 81-3/22 miles from Malebolgia to the center. It is clear that to the 17-1/2 miles which Malebolgia has as radius in its greatest width there correspond at the surface of the earth 700 miles; from which it follows necessarily, by the aforesaid proposition, that so much greater is the distance from the surface of the earth to the center than the distance of Malebolgia to this same center, as the width of the 700 miles is greater than the width of 17-1/2 miles; but the 700 miles are exactly 40 times greater than the 17-1/2 miles; therefore the distance from the surface of the earth to the center will be 40 times greater than the distance of Malebolgia from the same center. Further, the distance of the surface from the center, that is, the radius of the earth, is 3245-5/11 miles, of which the fortieth part is 81-3/22: the distance therfore of Malebolgia from the center is necessarily 81-3/22 miles. And this is what we were to demonstrate.
Now, coming back to what we had to say about the distribution of the 700 miles to assign the widths to the bolgias and to the pit, I say that we learn from Dante, as we said above, that the width of the pit is one mile in radius, the width of that space which remains between the last bolgia and the pit is 1/4 mile, that of the last bolgia 1/2, and finally the widths of the 9 bolgias remaining are 1-3/4 miles each. And if we find this quantity of miles to imply 700 miles at the surface of the earth, we will be able to affirm without a doubt that Manetti has investigated with marvelous invention the mind of the Poet. And because it has indeed been demonstrated that the distance of the surface of the earth from the center is 40 times greater than the distance of Malebolgia from the same, and that the distances correspond proportionately to the widths, that which in Malebolgia will have width 1, on the surface of the earth will be 40: the distance between the pit and the last bolgia is 1/4 mile, which at the surface of the earth means 10 miles; the last bolgia is 1/2 mile in width; to it corresponds therefore at the surface 20 miles: each of the remaining 9 bolgias has a width of 1-3/4 miles; to each one corresponds therefore at the surface 70 miles; but adding up all together 9 times 70, for the 9 bolgias, with 20 for the tenth bolgia, with 10 for the space between the tenth bolgia and the pit, and with 40 for the radius of the pit, we get exactly 700 miles, which is what was left for us to use up at the surface. We can therefore conclude that Manetti has investigated the mind of our Poet wonderfully.
We have added this discourse, and the demonstration of the distance from Malebolgia to the center, to that which has been written by the friends of Manetti as an explication of his discoveries, it seeming to us, as indeed it is, that they had neglected to explain the most subtle inventions of the noble genius of Manetti.
It remains to us now, to complete our task, to produce the sizes of each of the four ice regions, based on the same Poet. And the method which one must follow to achieve this will be as follows. We have in Canto 34 these words
"The emperor of the realm of grief protruded
From mid-breast up above the surrounding ice.
A giant's height and mine would have provided
Closer comparison than would the size
Of his arm and a giant. Envision the whole
That is proportionate to parts like these."
Inferno XXXIV, 28-33
It being our purpose to investigate the size of the ice regions, and knowing that Lucifer protrudes out of the lowest one (which is what was spoken of in the place cited) up from the middle of the breast, and knowing further that this same Lucifer has his navel at the center of the world, as we learn from the Poet in the same canto, where it says
" .. And then
When we had reached the pivot of the thighs,
Just where the haunch is at its thickest, with strain
And effort my master brought round his head
To where he'd had his legs: and from there on
He grappled the hair as someone climbing would --
So I supposed we were heading back to Hell."
Inferno XXXIV, 76-81
If therefore we know the size of Lucifer, we will also have the distance from the navel to the middle of the breast, and consequently the radius of the lowest sphere of ice. But the size of Lucifer we have from the cited verses to be such that Dante makes a greater comparison with a giant than a giant makes with one arm of Lucifer. If therefore we know the size of Dante and that of a giant, we will be able from that to find the size of Lucifer. But of Dante we have, from those who have written his life, that he was of average stature, which is 3 braccia. It remains to us therefore only to investigate the size of a giant. And in this way we have reduced our problem, which was to find the size of the ice, to having only to investigate the size of a giant; and then, putting it all together, we will be able to achieve our intent; for if the size of a giant is given to us, it will be known what proportion a man has to this, and therefore the proportion that a giant has to an arm of Lucifer. But the proportion that an arm has to the whole body is known, so that the size of Lucifer will be manifest. And with this we will have the distance from the middle of his breast to his navel, and consequently the radius of the lowest sphere of ice, and finally from that sphere we will assign the sizes to the remaining spheres.
The poet writes, speaking of Nimrod, first of the giants that he found in the pit
"To me his face appeared as long and full
As the bronze pinecone of St. Peters's at Rome,
With all his other bones proportional,"
Inferno XXXI, 58-60
If therefore the face of the giant is as great as the Pinecone, it will be 5-1/2 braccia, for this is its size. And because men are ordinarily 8 heads high, even though the painters, sculptors, and among others Albrecht Durer, in his book on human measurement, hold that well proportioned bodies should be nine heads, but because one very rarely finds such good proportions, we propose that the giant should be in height 8 times the height of his head, so that a giant will be 44 braccia in height, since so much is the product of 8 by 5-1/2. Dante therefore, that is, an average man, has to a giant the proportion 3 to 44. But because a man to a giant has greater comparison than a giant to an arm of Lucifer, if we compute "as 3 is to 44, so is 44 to another number," which will be 645, we will have that one arm of Lucifer should be more than 645 braccia. But leaving out that "more," which is uncertain, reserving that computation for the end, we say that one arm of Lucifer is 645 braccia; but because the length of an arm is 1/3 of the total height, the height of Lucifer will be 1935 braccia, for so much is 645 multiplied by 3. But because the comparison is greater between a man and a giant than between a giant and an arm of Lucifer, and we have done this computation as if the proportions were equal, and in this case Lucifer would be 1935 braccia high, adding that "more" which is missing, we can reasonably conclude that Lucifer ought to be 2000 braccia high. And if this is so, the interval between the navel and the middle of the breast will be 500 braccia, because that is the fourth part of the whole body; and so much will be the radius of the lowest sphere of ice. And because there is no place in Dante from which one can deduce the sizes of the other 3 spheres remaining, Manetti judges, as one should reasonably believe, that the others should have the same thickness; and because the one surrounds the other, just as one heaven surrounds another, the radius of the penultimate one will be 1000 braccia, that of the second 1500, and finally the first and largest will have for its radius 2000 braccia. This is as much of the complete explanation of the form, location, and size of Dante's Inferno, according to the opinion of Manetti, as it seemed to me necessary to say. It remains now, for the entire satisfaction of what we promised at the beginning, with a brief narration of the journey made by the Poet through this Inferno, that we should understand some particular things worthy to be known; and at the same time we will point out again the order, number, distances, and widths of the infernal circles, just so that they will be better impressed on your minds.
"Midway on our life's journey, I found myself
In dark woods, the right road lost. To tell
About those woods is hard -- so tangled and rough..."
Inferno I, 1-3
And this was the year of our salvation 1300, a jubilee year, at night, the moon being full. The forest where it happened is, according to Manetti, between Cuma and Naples, and here was the entrance to the Inferno. And we may reasonably suppose it to be here: first, because the circle of the mouth of the Inferno passes precisely by Naples; second, because in this region, or not very far from it, are Lake Averno, the mountains Drago, Acheron, Lipari, Mongibello, and similar other places, which by the horrible effects they produce deserve to be considered infernal places; and finally one may suppose the Poet to have imagined the entrance to the Inferno there to imitate Vergil, his escort, who put it in such a place. So having arrived at the gate of the entrance, over which were written in dark colors the words
"Through me you enter into the city of woes,
Through me you enter into eternal pain,
Through me you enter the population of loss"
Inferno III, 1-3
they begin to descend by a slope, until they arrive at the grotto of the uncommitted, hateful to God and to his enemies. This grotto is a most ample cavern, placed between the surface of the earth and the edge of the Inferno, just like those who dwell there, banned from heaven and from the abyss; here they find those unfortunate ones running behind a banner. Following then their descent, they arrive at the river Acheron. This river passes around the first circle of the Inferno, which is Limbo; and here they find the demon Charon, who ferries the souls in his great boat to the other bank. In this place, because of the shaking of the earth and the flash of red light, the Poet fainted, and then, reawakened by a great thunderclap, he found himself on the other bank; walking then he comes to the path of the first circle, and having entered, together with Vergil, into Limbo, he turns, walking to the right, and sees the innocent babies, who died without baptism, and those who lived morally, but without the Christian faith, who have no other torment there than that they may not have the vision of God; in this circle they find the ardent flame and the noble castle, surrounded by seven circuits of walls. This circle is distant from the surface of the earth by 1/8 the radius, that is, 405-15/22 miles, and its width is 87-1/2. Having circled the tenth part of this, they go down to the second, smaller and lower, where, under Minos, judge of the damned, the hosts of the sensuous are punished by continuous buffeting; and the distance of this circle to the first is as much as the distance of the first to the surface of the earth, that is, 405-15/22 miles, and it is 75 miles wide. Having circled the tenth part of this they go down to the third, distant similarly from the second by 405-15/22 miles, and 62-1/2 miles wide, where the gluttonous under Cerberus are afflicted by continuous rain and hail. They descend then to the fourth, smaller than the third, having a width of only 50 miles, and distant similarly from the third by 405-15/22 miles, where under Pluto the prodigal and the avaricious torment each other by turning themselves, one against the other, with heavy stones. Circling, always to the right hand, the tenth part of this, they find, near to the end, a spring, from which derives a creek which, falling to the fifth circle, makes of itself the Stygian swamp, 37-1/2 miles wide, where under Phlegyas are punished two kinds of sinners, that is, the wrathful above the mud and the sullen below it; and the moats around the city, 37-1/2 miles wide, the torment of the envious and the proud. The other circle is the City of Dis, within which, under the dominion of the Furies, in red hot sepulchres are punished the heretics. They pass from the bank of the swamp to this city, which is 37-1/2 miles wide, on the boat of Phlegyas, circling the tenth part of the swamp, and of the moats, and also of the city, moving always to the right hand. From this level, through a great ravine of rocks, they descend to the sixth, lower than the fifth by 405-15/22 miles, and divided into 3 rings, each one of them 25 miles in width; and in the first, which is a lake of blood called Phlegeton, are punished, under the Minotaur, the violent against their neighbors, whose torment is to be shot with arrows by the Centaurs every time they dare to raise themselves out of the blood. In the second are tormented two sorts of the violent, that is, the violent against themselves, and these are transformed into crooked stumps, on whose leaves the Harpies feed; and the violent against their own interests, and for these the punishment is to be torn apart by black famished dogs. In the third ring, on the burning sand, by the flames which continually rain down there, are afflicted the violent against god, against nature, and against art. Circling these three rings by the tenth part, always to the right hand, being on the sandy plain, they find a narrow stream of blood, which originating from the statue placed by the Poet on Mount Ida in Crete, cascading into the abyss, makes Acheron, Styx, Phlegeton, and Coccys, principal rivers of the Inferno. And Dante, walking along this stream toward the middle, reaches the edge of the defile of Geryon, where, having launched out together with Vergil on the shoulders of the beast, he descends through the dark air to the seventh level, which is the one which is divided into 10 bolgias, and where under Geryon ten kinds of the fraudulent are punished, of which it would take too long to tell all their pains. This level is distant from the one above by 730-15/22 miles, and the depth of the defile is this much. Each one of the bolgias is 1-3/4 miles wide, except the last one, which is 1/2 mile wide, from which to the pit of the giants, placed in the middle, there is a space of 1/4 mile; so that the whole width of Malebolgia is 16-1/2. And the bolgias are all crossed by a narrow embankment or bridge, except for the sixth, over which the bridge, by a certain accident, has fallen down.
Having crossed the bolgias, being arrived at the pit, Dante together with Vergil was lowered by the giant Anteus to the ice, called Caina, which is the first and greatest sphere and which surrounds the others, in which, under Lucifer, the traitorous are punished. And in the first, the traitors against their neighbors; in the second, called Antenor, the traitors against their homeland; in the third, called Ptolomea, the traitors against their benefactors; in the fourth, called Giudecca, the traitors against their lord. The distance of the ice regions from Malebolgia, that is, the depth of the pit of the giants, is 81-1/2 miles. In the middle of the ice is placed Lucifer; having arrived there, Vergil and Dante descend by his fleece to his navel, where the center of the world is, and then ascend up by the hairy thighs, finally passing by his feet into the other hemisphere, where, by a twisting path, they get out, and emerge to see the stars once again. It would remain for us now to look at the opinions of Vellutello, and then the arguments which one could cite for the one or the other opinion; but because the lecture thus far has taken far longer than even I myself would have believed, so as not to bore any longer so many noble listeners, we shall put off our argument to a more opportune time.
In the previous lecture we have, with all the forces at our disposal, set out the opinion of Manetti concerning the location and shape of Dante's Inferno. Today it is our intention to explain, first, the opinion of Alessandro Velutello concerning the same material, and then to add arguments which persuade us to prefer the one or the other. And in order to carry out our first intention more briefly and easily, we judge it convenient to see first in which things they agree, and then in which things they differ.
Vellutello agrees with Manetti first as to the location of the Inferno, each one putting it under that part of the earth which has Jerusalem as its summit; that is, if a straight line be drawn up from the center of the universe to Jerusalem, the Inferno would be distributed equally in all its parts around the said line. Again, they do not differ from each other in the order of the levels, nor in the divisions of these into various circles and rings, in the way that we said the other day. And finally they agree on the size of Malebolgia: and in all this they agree because one clearly has all this from the Poet himself. They differ, though, first in the overall size of the Inferno as a whole; second (which necessarily follows from the first), in the sizes and distances of the particular levels (except, as we just said, in the size of Malebolgia); third, they disagree on the sizes of the giants and of Lucifer; fourth on the shape of the ice regions; fifth, on the size and location of the noble castle which is mentioned by the Poet in Limbo; sixth, they differ in assigning the road which Dante and Vergil took in descending to the center, Manetti believing that, circling through the levels, they would have proceeded so that their left hand would be toward the middle, just the opposite of what Vellutello believed; seventh, they disagree in assigning the number of bridges in Malebolgia.
Thus they are very different, first concerning the overall size of the Inferno as a whole, witness that Vellutello makes it less than the thousandth part of what Manetti does; for Vellutello wants the depth of his Inferno to be not more than one tenth of the radius of the earth, and if such an Inferno were a complete sphere, it would be one thousandth of the whole volume of the earth, as one deduces easily from the Elements of Euclid; but Vellutello's Inferno is less than one fourteenth of such a sphere, just as Manetti's is one fourteenth of the whole earth. Thus it follows, as was just said, that Vellutello imagined his Inferno to be not greater than one thousandth part of that of Manetti.
But how Vellutello obtains one tenth the radius of the earth as the depth of his Inferno, we can understand in what follows, going over the components of this construction of his. And first, we should understand a pit which has a diameter of one mile, both at its top and at its bottom, and one mile is also its depth, and at its bottom there is ice, in the shape of an enormous grindstone (and we are asked to take this example), 750 braccia thick. And this ice should be divided into 4 circles, so that one surrounds the next, and in the middle of the smallest there should be a little pit, again in the shape of a grindstone, whose depth is the thickness of the ice, that is, 750 braccia, and in the middle of this is the center of the world, and Lucifer would be in this little pit. And the other, larger pit, mentioned a moment ago, would be the place where the giants protrude out from the middle of their bodies, as the Poet means when he says
"For, as on Montereggione's wall appear
Towers that crown its circle, here, arrayed
All round the bank encompassing the pit
With half their bulk like towers above it, stood
Horrible giants, whom Jove still rumbles at
With menace when he thunders ..."
Inferno XXXI, 40-45
Thus the mouth of the pit of the giants will be distant from the center of the universe by 1-1/4 miles, that is, one mile for its depth, as was said, and 750 braccia, which is 1/4 mile, for the thickness of the ice and the depth of the little pit where Lucifer is.
Around the mouth of the pit of the giants Vellutello places the valley of Malebolgia, with the same measurements assigned to it by Manetti; such that at its greatest it has a radius of 17-1/2 miles. But because this valley of Malebolgia leans toward the middle, as is obvious in these verses of Dante
" ...But it was true
In each valley that the contour of the land
Made one side higher and the other low,
Because of the way all Malebolgia inclined
Downward toward the mouth of the lowest pit"
Inferno XXIV, 37-40.
Vellutello gives to the bolgias 14 miles of height, so that the first bolgia is farther from the center than the last by 14 miles. Around the highest bolgia rises, with constant radius, that is, with radius 17-1/2 miles, another great pit, called by the Poet the defile, whose rise is placed by Vellutello at ten times greater than the rise of Malebolgia, that is 140 miles. The top of this is imagined to be no wider than the bottom. Around the top opening of this defile he places the 3 rings of the violent, to each one of which he gives 5-5/6 miles of width, so that the whole circle has a width of 17-1/2 miles. And because that was also the radius of the defile, the whole radius of the circle of the violent will be 35 miles, and the whole diameter 70 miles.
There follow then, above the level of the violent, six other levels, the first of which contains the city of Dis, the moats around it, and the Stygian swamp; and their distance from the level of the violent is 70 miles, exactly as much as is imagined for the diameter of the largest ring; and the ascent from the violent to the higher circle is such that the diameter is the same at the bottom as at the top, except that in some places the Poet supposes the bank has collapsed, through a certain accident, and one can descend through one such ravine. To this level, which is immediately above the violent, Vellutello gives a width of 18 miles, of which he assigns 1/2 mile to the city, 1/2 mile to the moats around it, and the remaining 17 miles to the Stygian swamp, which circles the said moats. Thus the diameter at its greatest will be 106 miles. A cliff rises then around the swamp, but it doesn't go straight up like the other ascents out of the pits, which we have heard of up to here, but climbs (to use the right word) at a slope, so that at its lowest place, that is, at the level of the swamp, its diameter is 106 miles, and at its upper mouth it is 140. And the climb of this beach is so steep that climbing 14 miles vertically, it widens by 17 miles. And a similar kind of climb is observed in all the other higher levels.
At the top of this climb a plain goes around which is 1/2 mile wide; and this is the circle of the prodigal and the avaricious, whose diameter comes to 141 miles, that is, 140, as was just said, for the mouth of the cliff through which one climbs to here, and 1 for the two widths of 1/2 mile each which are assigned to this circle. From this circle one passes to that of the gluttonous by a climb made the same way, at a slope which, ascending 14 miles by the perpendicular, widens 17 miles, so that where this bank at its base was 141 miles in diameter, it will be at its extreme mouth 175 miles; around which the circle of the gluttonous distends itself with a width of half a mile, so that its greatest diameter comes to 176 miles.
From this circle, with a similar climb, one comes to that of the sensuous, which also has a width of 1/2 mile; and from this, with another similar climb, one ascends to the first circle, which is Limbo, whose width Vellutello puts at 1/2 mile, like that of the other circles, of which he assigns 1/4 to the width of the noble castle, which he imagines to be placed around the opening, and the other 1/4 mile he gives for the width of a green meadow which encircles the castle. Around the edge of the meadow a bank rises up which, in the manner of the others, ascending at a slope, rises perpendicularly 14 miles while widening by 17 miles more than it is at its base; so the diameter of this opening comes to 280 miles, as, doing the computation, one easily obtains. And Vellutello finds the depth of the Inferno to be just this much, measuring from the mouth of Limbo by the perpendicular down to Malebolgia: witness that he would put the depth of the defile at 140 miles, the distance from the violent to the city of Dis 70, which makes 210, and adding to that five ascents of 14 miles each through the remaining circles makes exactly the sum of 280 miles. Imagine then that the outer edge of Limbo is circled by a plain whose width is 17-1/2 miles, of which he assigns half to the river Acheron, the other half to the grotto of the uncommitted. This is, briefly, the opinion of Vellutello, which perhaps one will comprehend better from the outline of his design; and this invention pleased Vellutello so much that he ridiculed Manetti and together with him the whole Florentine Academy, calling the Inferno of Manetti rather a fantasy and an invention of his own, and of the other Academicians, this thing that conforms precisely to Dante's intentions. And to what extent this is true, it is now time to begin to consider.
And first, if we will consider the one and the other design without having regard to any place in Dante, or any argument that would persuade us that the one or the other is more plausible or believable in representing Dante's intentions, but only contemplating the disposition of the whole and of the parts, and in sum, so to speak, the architecture of the one and of the other, we will see, as it seems to me, how much better is the design of Manetti, composed of parts more similar to each other. And similarly, it seems an incredible thing that the Inferno should be so small that it would not be as much as the thirty thousandth part of the earth, as we, doing the calculation diligently, find that it must be, if one had to believe the opinion of Vellutello; and besides imagining it so small, he nonetheless assigns only the tiniest part to the places where the sinners are punished, giving to the first 4 circles only 1/2 mile of width each.
But let us leave the architecture as it is, and see if such a construction could support itself, which, as it seems to me, we will find that it cannot. For if we assume that the defile rises up with its sides equidistant from each other, the upper parts will find themselves without support to hold them up, and that being the case, they will undoubtedly collapse. For heavy objects, in falling, go along a line which conducts them straight to the center, if in this line they do not find anything that impedes and supports them. But if, for example, we draw lines to the center from the city of Dis, these do not find any impediment, so that this city, being free to fall, and not impeded, finding nothing underneath which would support it, will certainly collapse; and the circle of the violent will do the same, being founded upon walls whose perpendiculars are far from from those which go directly to the center; and if this collapses, all the other higher levels which rely upon them will collapse. But there is yet another problem: that it is not only impossible, if we wish to escape the collapse of the whole Inferno, that the parts above should lack support, but it is also contrary to the Poet, who, knowing what would be necessary to hold up his grand construction, that is, that the upper parts would be held up by the lower parts, wrote, being at the bottom of the descent to the pit of the giants,
"If I had harsh and grating rhymes, to befit
That melancholy hole which is the place
All the other rocks converge and thrust their weight..."
Inferno XXXII, 1-3
If, then, above this hole the other rocks converge and support themselves, it is necessary that the walls which give them support not be out of the perpendicular which goes to the center. This problem does not exist in the architecture of Manetti, witness that he places all the banks and walls directly in a line toward the center, as one sees in the design. The upper circles, however (I speak of the levels above the city) could have some few good points in the architecture of Vellutello, and seem plausible at first sight; that is, that he makes the descents from one to the other not perpendicular, as Manetti does, but at a slant, like the slopes of the mountains, according to the idea of Vellutello, so that one can descend from one level to the next; especially because Manetti makes no mention of the way they took to descend. But I want this same argument to be the refutation of that Vellutello. For if the descents from one level to the other are, as he says, like the slopes of the mountains, one could in consequence descend from one level to the next wherever one wanted to; but we find this to be contrary to what Dante intends, since the descents were only in certain particular places, and in only one place per circle, as one sees at the end of Canto VI, where it says
"And speaking more than I repeat, we two
Continued our way, until the circuit came
To where the path descends -- and there we saw
Plutus, the great Enemy, and confronted him."
Inferno VI, 103-106.
And in the beginning of Canto 7, where Vergil says of Satan to Dante
"Don't let fear harm you; whatever power he has
Cannot prevent us climbing down this rock."
Inferno VII, 4-6
Thus, if the descents were in certain particular places, at each one of which Dante places a guardian demon, then of necessity in other places one could not descend; and this means that in other places the descent would be perpendicular, as Manetti has it, and not like the slopes of the mountains, according to the opinion of Vellutello. And I believe it is like this so that the sinners of the lower levels, where the torments are greater, as the Poet indicates to us at the beginning of the fifth canto
"So I descended from first to second circle --
Which girdles a smaller space and greater pain,
Which spurs more lamentation."
Inferno V, 1-3
so that, I say, these lower sinners cannot escape and flee to the higher levels, to lesser torments; and it seems that this is what Dante meant when he put, at each place where one could go from one level to another, a demon.
It cannot be, then, considering everything together, that Dante's Inferno could have such an architecture, nor such a small size, as has been pretended by Vellutello; and this, beyond the arguments adduced, we will prove again by Dante himself, in the matter of the size. If the Inferno is no deeper than one tenth the radius of the earth, as Vellutello would have it, then having conducted Dante to the first circle, and urging him to quicken his pace, why would Vergil say
" '... Now on:
Our long road urges us forward.' And he entered
The abyss's first engirdling circle, and down
He had me enter it too."?
Inferno IV, 22-24
If Vergil calls the way that they have yet to travel long, he must mean it is long in comparison to that which they have just walked; and if that is so, it cannot be that the journey already made is 9 times greater than that which they have still to make, and in consequence the Inferno, through which they have to descend to the center, cannot be so small as Vellutello would have it.
Here one might oppose that the Inferno cannot be so large as Manetti makes it, since, as some have suspected, it doesn't seem possible that the vault that covers the Inferno could support itself and not fall into the hole, being so thin, as is necessary if the Inferno comes up so high. And especially, beyond being no thicker than the eighth part of the radius of the earth, which is 405 miles more or less, some of it must be removed for the space of the grotto of the uncommitted, and even more must be removed [on the top] for the very great depth of the sea. To this one answers easily that such a thickness is more than sufficient; for taking a little vault which will have an arch of 30 braccias, it will need a thickness of about 4 braccias, which not only is enough, but even if you used just 1 braccia to make an arch of 30 braccias, and perhaps just 1/2, and not 4, it would be enough to support itself; and knowing that the depth of the sea is a very few miles, or better, even less than one mile, if we believe the most expert sailors, and assigning as many miles as seem necessary for the grotto of the uncommitted, a determinate measure not being given by the Poet, if this together with the depth of the sea comes to 100 miles, the said vault will still be very thick, and far more than is necessary to hold itself up.
It seems to me that these arguments can persuade us how much more plausible the Inferno of Manetti is than that of Vellutello, as a description of the whole, and we will find the same thing again in distinctly examining its parts, and first the castle placed in Limbo. It seems to me a difficult thing to imagine it circling 770 miles, as this Vellutello would have it, being surrounded by 7 orders of high walls, and occupying in all a width of 1/4 mile. If nothing else, to build 7 circuits of walls, which would have to be very thick, having to be 770 miles around, as was said, over a ring which is no wider than 1/4 mile, seems to me an impossible business, or at least a thing very badly proportioned, and besides we must still leave space for the inhabitants. There is also another inconvenience: that making the castle so big makes the city then so small that it gets barely one quarter of the circle. For these reasons, who would not believe the castle should be small, as imagined by Manetti, and not circling around the edge of Limbo, but situated within the width of Limbo?
Of 4 other differences which arise between Manetti and Vellutello, I do not find places in Dante which constrain this opinion to be more plausible than that, but there are certainly very probable reasons in favor of Manetti. And first, on the ten orders of bridges with which Vellutello crosses Malebolgia, there is no place in Dante where one can find such a number; but if the Poet does not say that there was even one, nonetheless, since just one order would suffice, I do not know why it is proposed to multiply them without necessity. Besides, if there were 10 orders, it would be too great a marvel that all ten over the sixth bolgia agreed to fall down, especially since, as the Poet affirms, this collapse happened by chance, through a certain accident.
The novel opinion of Vellutello that Lucifer would be 3000 braccia high and not 2000, as Manetti would have it, originating from nothing other than wanting to measure the Pinecone before it was broken, and wanting the giants to be 9 heads high, does not seem very believable to us. On the contrary, it is believable that Dante, if he even measured it, measured the Pinecone as it was in his time, and that he believed the giants to be of ordinary proportion, and not of that rare proportion which would make them 9 heads high.
Similarly, there is neither argument nor authority that persuades us to believe that the ice regions would be like millstones, and not like spheres. On the contrary, since the Poet himself called them spheres in the last canto:
"... your feet this minute press
Upon a little sphere whose rounded skin
Forms the Judecca's other outward face"
Inferno XXXIV, 116-117
it is not without temerity to want to say that they have the shape of millstones, almost as if he has the clever idea that Dante would have lacked the words to express his own conception.
It remains to us to see finally about the path itself through the circles, that is, if it was to the left, as Vellutello affirms, or rather to the right, as Manetti would have it. In this we should again believe Manetti, having in his favor the authority of the Poet, who declares to us that walking he had his left toward the middle, Vellutello being moved to believe the opposite solely by certain verses of the Poet, which can be even better interpreted in favor of Manetti. And these are in the fourteenth canto:
"...And he: `As you know well,
The place is round; although you have come far
Always to the left descending down to the pit...'"
Inferno XIV, 124-126
In these verses, if we put the words `always to the left' together with those before, saying `although you have come far always to the left,' making a pause in the middle of the line, they support the opinion of Vellutello; but if we make the pause at the end of the third line, joining the words `always to the left' with the following ones, in this way: `always to the left descending down to the pit,' they favor the opinion of Manetti. Now in an uncertain interpretation, who would not find it better to make the pause at the end, rather than in the middle of the verse? But leaving the dubious places, let us look at the clear and obvious ones, which support the opinion of Manetti. Dante writes at the end of the ninth canto, when they had just entered into the city:
"He turned to the right, and we continued to walk
Between the anguish and the high parapets,"
Inferno IX, 152-153
and at the end of the tenth
"He turned to the left; and leaving the city wall
Behind our backs we continued on our way
Toward the center.."
Inferno X, 133-134
These places being so clear, as they truly are, constrained Vellutello to say that even though they went to the right within the city, nonetheless in the other circles they walked to the left; which seems very thoughtless.
But since proceeding either to the right or to the left is not very important to our principal intention, which has been to set out the location and shape of Dante's Inferno, and at the same time to defend the ingenious Manetti against the false calumnies that he has unjustly received on this subject, and especially since they have stung not just him alone, but the whole most learned Florentine Academy, to which for many reasons I feel myself most obligated; and having showed, with what little ingenuity I possess, how much subtler is the invention of Manetti, I bring my argument to a close.