• Florence in the early 1400s still retained a rural aspect. Wheatfields, orchards and vineyards could be found inside its walls, while flocks of sheep were driven bleating through the streets to the market near the Baptistery of San Giovanni. But the city also had a population of 50,000, roughly the same as London’s, and the new cathedral was intended to reflect its importance as a large and powerful mercantile city.

• Florence had become one of the most prosperous cities in Europe. Much of its wealth came from the wool industry started by the Umiliati monks soon after their arrival in the city in 1239.

• Bales of English wool – the finest in the world – were brought from monasteries in the Cotswolds to be washed in the River Arno, combed, spun into yarn, woven on wooden looms, then dyed beautiful colours: vermilion, made from cinnabar gathered on the shores of the Red Sea, or a brilliant yellow procured from the crocuses growing in meadows near the hilltop town of San Gimignano. The result was the most expensive and most sought-after cloth in Europe.

• Competition between architects was an old and honoured custom. Patrons had been making architects compete against one another for their commissions since at least 448 BC, when the Council of Athens held a public competition for the war memorial it planned to build on the Acropolis.

• Goldsmiths were the princes among the artisans of the Middle Ages, with a large scope to explore their numerous and varied talents. They could decorate a manuscript with gold leaf, set precious stones, cast metals, work with enamel, engrave silver and fashion anything from a gold button to a shrine, reliquary or tomb.

• It is no coincidence that the sculptors Andrea Orcagna, Luca della Robbia and Donatello, as well as the painters Paolo Uccello, Andrea del Verrocchio, Leonardo da Vinci and Benozzo Gozzoli – some of the brightest stars in a remarkable constellation of Florentine artists and craftsmen – had all originally trained in the workshops of goldsmiths.

• Visitors to Florence can make up their own minds about their respective virtues because the two panels are now preserved in the Museo Nazionale del Bargello.

• The Chronica de origine civitatis, an early history written in about 1200, claimed that the city was founded by Julius Caesar. A century later, in his Convivio, no less an authority than Dante called Florence ‘that beautiful and famous daughter of Rome’. The humanist philosopher Leonardo Bruni agreed with this proud lineage but identified the founder not as Julius Caesar – an imperialist tyrant uncomfortably reminiscent of Giangaleazzo Visconti – but rather as Lucius Cornelius Sulla, who established the city some twenty years before Caesar’s reign, during the height of the Roman Republic.

• In calculating the proportions of columns and pediments he determined the measurements specific to the three architectural orders (Doric, Ionic and Corinthian) that had been invented by the Greeks and then imitated and refined by the Romans. These orders were governed by precise mathematical ratios, a series of proportional rules that regulated aesthetic effect. The height of a Corinthian entablature, for example, is a quarter of the height of the columns on which it stands, while the height of each column is ten times its diameter, and so forth.

• The name of the painter Cimabue means ‘ox-head’, and Giotto was so unattractive that Giovanni Boccaccio devoted a tale to his appearance in the Decameron, marvelling at how ‘Nature has frequently planted astonishing genius in men of monstrously ugly appearance’.

• Boccaccio, who never married, had criticised Dante for having done so, claiming that a wife was a hindrance to study.

• Despite his youthful promise as a metalworker he had, at the age of forty-one, accomplished relatively little in practical terms.

• Perspective is the method of representing three-dimensional objects in recession on a two-dimensional surface in order to give the same impression of relative position, size or distance as the actual objects do when viewed from a particular point. Filippo is generally regarded as its inventor, the one who discovered (or rediscovered) its mathematical laws.

• Only in the first decades of the fourteenth century did the ancient methods of perspective reappear when Giotto began using chiaroscuro – a treatment of light and shade – to create realistic three-dimensional effects.

• Filippo was naturally incensed by this treatment, and the experience served to confirm his low opinion of what, ten years later, he would call ‘the ignorant crowd’.

• By 1400, however, it had become the custom to divide the hour into sixty minutes, and each minute into sixty seconds. The pace of life was increasing.

• Drunk in moderation, it was said to improve the blood, hasten digestion, calm the intellect, enliven the spirit and expel wind. It might also have given a fillip of courage to men clinging to an inward-curving vault several hundred feet above the ground.

• In 1420 calculations were based on ancient theories about the various ‘humours’ of trees in the same way that the medicine of the day – equally suspect – was concerned with the interaction of humours in the body. Elm, for example, the wood used in the crossbeam, was said to be ‘dry’, therefore it did not ‘agree’ with the plane tree or the alder, which were ‘moist’ and so ought never to be used in the same structure as elm – a most dubious set of assumptions on which to rest a sandstone beam weighing over 1,000 pounds.

• Plumbers (whose name comes from the Latin plumbum, ‘lead’) were employed at most cathedrals in the Middle Ages in order to rustproof iron or make lead tiles for the steeples.

• Thus, whatever its structural function, the wooden chain ultimately became a means for Filippo to expose Lorenzo’s incompetence to both the wardens and the people of Florence.

• Equally important to the building of the dome was the quality of the mortar, in which Manetti claims Filippo also took a personal interest. Throughout the Middle Ages mortar was made from mixing sand and water with quicklime (calcium oxide), a substance obtained by heating limestone in a kiln.

• to be laid and therefore fewer masons were needed. Twenty-five of them were sacked in April 1426, though in this case the redundancies may have resulted from a labour dispute. Manetti claims the master masons ‘selfishly unionised themselves’ – an act contrary to Florentine law – and went on strike for higher pay.

• The wealthy Alberti clan had been banished from the city seventeen years earlier, when Leon Battista was only four, and he had subsequently been raised in Padua and Bologna. Later famous for his books on painting and architecture, in 1428 he was known for spectacular feats of physical prowess such as piercing an iron breastplate with an arrow and leaping over the shoulders of ten men in succession. Among numerous other accomplishments he was a horse-tamer and the author of treatises on both the arts of navigation and the manners of his pet dog. He invented a disk to compose ciphers (a sort of prototype of the Enigma machine) as well as an astrolabe to survey the ruins of Rome. No subject seemed to escape his attention: Greek, Latin, law, mathematics, geometry. But he took a special interest in architecture, particularly in Filippo’s dome, over the top of which, according to legend, he was able to throw an apple.

• Undaunted by these difficulties, the planners of Santa Maria del Fiore had ordered that three colours should encrust the cathedral: the greenish black stone known as verde di Prato; the red stone marmum rubeum; and, finally, a brittle white marble called bianchi marmi. This last stone would cover the eight enormous brick ribs of the cupola, and in June 1425 the Opera del Duomo signed a contract for 560 tons of it.

• It was first exploited by the Romans, who used it for the Apollo Belvedere (which would be excavated at Frascati in 1455) and in the Arch of Constantine. Later Michelangelo would carve some of his most famous statues from it, including his David and the Pietà. In fact, Michelangelo spent a good many months of his life in the steep, dazzlingly white mountains around Carrara, reopening and inspecting old Roman quarries and fantasising about carving gargantuan shapes into the hillsides. Carrara marble was justifiably the most sought-after in Europe: hard, clean-breaking and a chaste white, it was perfect for carving and ornamentation.

• Filippo had built Il Badalone and contracted for the load of marble entirely out of his own pocket. Altogether he lost 1,000 florins on the venture – the equivalent of ten years of his salary as capomaestro and roughly one-third of his total wealth. It must have been a cruel blow for a man who had envisioned reaping lucrative financial rewards from his invention. Even worse, his reputation as the modern Archimedes was tarnished – a reputation that would be undermined still further a few years later, when another of his clever plans was to rebound disastrously.

• So famous was Florence for homosexual activity that during the fourteenth century the German slang for ‘sodomite’ was Florenzer.

• adolescent by Florentine law. In fact, like all adolescents, he would not be emancipated from his father’s authority until the age of twenty-four, and some of these ‘adolescents’ could even remain under the control of their fathers until they were twenty-eight.