The Consuls remained in the Audience Chamber all confused, both by the difficult methods of the original masters and by this last method of Filippo's, which they thought absurd, for it appeared to them that he would ruin the work in two ways: first, by making the vaulting double, which would have made it enormous and unwieldy in weight; and secondly, by making it without a framework. On the other hand, Filippo, who had spent so many years in study in order to obtain the commission, knew not what to do and was often tempted to leave Florence. However, wishing to prevail, he was forced to arm himself with patience, having insight enough to know that the brains of the men of that city did not abide very firmly by any one resolution. Filippo could have shown a little model that he had in his possession, but he did not wish to show it, having recognized the small intelligence of the Consuls, the envy of the craftsmen, and the instability of the citizens, who favoured now one and now another, according as it pleased each man best; and I do not marvel at this, since every man in that city professes to know as much in these matters as the experienced masters know, although those who truly understand them are but few; and let this be said without offence to those who have the knowledge. What Filippo, therefore, had not been able to achieve before the tribunal, he began to effect with individuals, talking now to a Consul, now to a Warden, and likewise to many citizens; and showing them part of his design, he induced them to determine to allot this work either to him or to one of the foreigners. Wherefore the Consuls, the Wardens of Works, and those citizens, regaining courage, assembled together, and the architects disputed concerning this matter, but all were overcome and conquered by Filippo with many arguments; and here, so it is said, there arose the dispute about the egg, in the following manner. They would have liked Filippo to speak his mind in detail, and to show his model, as they had shown theirs; but this he refused to do, proposing instead to those masters, both the foreign and the native, that whosoever could make an egg stand upright on a flat piece of marble should build the cupola, since thus each man's intellect would be discerned. Taking an egg, therefore, all those masters sought to make it stand upright, but not one could find the way. Whereupon Filippo, being told to make it stand, took it graciously, and, giving one end of it a blow on the flat piece of marble, made it stand upright. The craftsmen protested that they could have done the same; but Filippo answered, laughing, that they could also have raised the cupola, if they had seen the model or the design. And so it was resolved that he should be commissioned to carry out this work, and he was told that he must give fuller information about it to the Consuls and the Wardens of Works.
Going to his house, therefore, he wrote down his mind on a sheet of paper as clearly as he was able, to give to the tribunal, in the following manner: "Having considered the difficulties of this structure, Magnificent Lords Wardens, I find that it is in no way possible to raise the cupola perfectly round, seeing that the surface above, where the lantern is to go, would be so great that the laying of any weight thereupon would soon destroy it. Now it appears to me that those architects who have no regard for the durability of their structures, have no love of lasting memorials, and do not even know why they are made. Wherefore I have determined to turn the inner part of this vault in pointed sections, following the outer sides, and to give to these the proportion and the curve of the quarter-acute arch, for the reason that this curve, when turned, ever pushes upwards, so that, when it is loaded with the lantern, both will unite to make the vaulting durable. At the base it must be three braccia and three quarters in thickness, and it must rise pyramidically, narrowing from without, until it closes at the point where the lantern is to be; and at this junction the vaulting must be one braccio and a quarter in thickness. Then on the outer side there must be another vault, which must be two braccia and a half thick at the base, in order to protect the inner one from the rain. This one must also diminish pyramidically in due proportion, so that it may come together at the foot of the lantern, like the other, in such wise that at the summit it may be two-thirds of a braccio in thickness. At each angle there must be a buttress, making eight in all: and in the middle of every side there must be two buttresses, making sixteen in all: and between the said angles, on every side, both within and without, there must be two buttresses, each four braccia thick at the base. The two said vaults, built in the form of a pyramid, must rise together in equal proportion up to the height of the round window closed by the lantern. There must then be made twenty-four buttresses with the said vaults built round them, and six arches of grey-stone blocks, stout and long, and well braced with irons, which must be covered with tin; and over the said blocks there must be iron ties, binding the said vaulting to its buttresses. The first part of the masonry, up to the height of five braccia and a quarter, must be solid, leaving no vacant space, and then the buttresses must be continued and the two vaults separated. The first and second courses at the base must be strengthened throughout with long blocks of grey-stone laid horizontally across them, in such wise that both vaults of the cupola may rest on the said blocks. At the height of every nine braccia in the said vaults there must be little arches between one buttress and another, with thick ties of oak, to bind together the said buttresses, which support the inner vault; and then the said ties of oak must be covered with plates of iron, for the sake of the staircases. The buttresses must be all built of grey-stone and hard-stone, and all the sides of the cupola must be likewise of hard-stone and bound with the buttresses up to the height of twenty-four braccia; and from there to the top the material must be brick, or rather, spongestone, according to the decision of the builder, who must make the work as light as he is able. A passage must be made on the outside above the windows, forming a gallery below, with an open parapet two braccia in height, proportionately to those of the little tribunes below; or rather, two passages, one above the other, resting on a richly adorned cornice, with the upper passage uncovered. The rain water must flow from the cupola into a gutter of marble, a third of a braccio wide, and must run off through outlets made of hard-stone below the gutter. Eight ribs of marble must be made at the angles in the outer surface of the cupola, of such thickness as may be required, rising one braccio above the cupola, with a cornice above by way of roof, two braccia wide, to serve as gable and eaves to the whole; and these ribs must rise pyramidically from their base up to the summit. The two vaults of the cupola must be built in the manner described above, without framework, up to the height of thirty braccia, and from that point upwards in the manner recommended by those masters who will have the building of them, since practice teaches us what course to pursue."
Filippo, having finished writing all that is above, went in the morning to the tribunal and gave them that paper, which they studied from end to end. And although they could not grasp it all, yet, seeing the readiness of Filippo's mind, and perceiving that not one of the other architects had better ground to stand on—for he showed a manifest confidence in his speech, ever repeating the same thing in such wise that it appeared certain that he had raised ten cupolas—the Consuls, drawing aside, were minded to give him the work, saying only that they would have liked to see something to show how this cupola could be raised without framework, for they approved of everything else. To this desire fortune was favourable, for Bartolommeo Barbadori having previously resolved to have a chapel built in S. Felicita and having spoken of this to Filippo, the latter had put his hand to