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