1. On the origins of the baptistery see Ferdinand Schevill, Medieval and Renaissance Florence, rev. ed., vol. 1 (New York: Frederick Ungar, 1961; repr. Harper Torchbooks / Academy Library, 1963), 241–42. On the belief that Florence was founded by Julius Caesar and his veterans see Hans Baron, The Crisis of the Early Italian Renaissance (Princeton, NJ: Princeton University Press, 1955; rev. ed. 1966), 49–52.
2. The dating of Brunelleschi’s experiment is based on the fact that in 1413 the humanist Domenico da Prato refers to him as “the perspective expert, ingenious man, Filippo di Ser Brunellesco, remarkable for skill and fame.” See Ross King, Brunelleschi’s Dome: How a Renaissance Genius Reinvented Architecture (New York: Bloomsbury, 2000), 34.
3. On the competition for the baptistery’s doors see Richard Krautheimer and Trude Krautheimer-Hess, Lorenzo Ghiberti (Princeton, NJ: Princeton University Press, 1956), chap. 3, as well as King, Brunellechi’s Dome, chap. 2.
4. The quote is from Mariano di Jacopo Taccola, “From a Record of a Speech by Brunelleschi (1420s),” in Brunelleschi in Perspective, ed. Isabelle Hyman (Englewood Cliffs, NJ: Prentice-Hall, 1974), 31.
5. On the difference between Brunelleschi and Ghiberti in their approach to the project see Antonio di Tuccio Manetti, Life of Brunelleschi, trans. Catherine Engass, ed. Howard Saalman (University Park: Pennsylvania State University Press, 1970), 46–48.
6. Today, Ghiberti’s bronze panels are acknowledged as one of the great masterpieces of the Renaissance, adorning the eastern doors of the baptistery as part of what Michelangelo called “the gates of paradise.” Brunelleschi’s design can be seen as well, preserved in Florence’s Bargello museum.
7. Among the most notable of the Florentine humanists of Brunelleschi’s generation were the classicist Niccolo Niccoli (1364–1437), the historian Leonardo Bruni (1370–1444), and Poggio Bracciolini (1380–1459), a papal secretary and polymath who rediscovered Lucretius’s De Rerum Natura in a remote monastic library.
8. For a lively and insightful account of early Italian humanism, and of Poggio Bracciolini in particular, see Stephen Greenblatt, The Swerve: How the World Became Modern (New York: W. W. Norton, 2012).
9. On Brunelleschi’s sojourn in Rome, see King, Brunelleschi’s Dome, chap. 2.
10. See Giorgio Vasari, “Filippo Brunelleschi,” in Vasari, The Lives of the Artists, trans. and ed. Julia Conaway Bondanella and Peter Bondanella (Oxford: Oxford University Press, 1991), 118.
11. Quotes are from Manetti, Life of Brunelleschi, 52–54. On the surveying methods described by Fibonacci and likely used by Brunelleschi see Martin Kemp, “Science, Non-Science and Nonsense: The Interpretation of Brunelleschi’s Perspective,” Art History 1, no. 2 (1978): 134–61, pp. 143–46; and Jehane R. Kuhn, “Measured Appearances: Documentation and Design in Early Perspective Drawings,” Journal of the Warburg and Courtauld Institutes 53 (1990): 114–32, pp. 117–22.
12. Manetti, Life of Brunelleschi, 52.
13. Manetti, 50.
14. The painting has since been lost, but Manetti provides a detailed description in his Life of Brunelleschi, 43–44.
15. The diameter of a Venetian ducat was around two centimeters, or four-fifths of an inch. The circumference, accordingly, was slightly more than six centimeters.
16. On Brunelleschi’s experiment see Samuel Y. Edgerton, Jr., The Renaissance Rediscovery of Linear Perspective (New York: Basic, 1975), 124–29; John White, The Birth and Rebirth of Pictorial Space (London: Faber and Faber, 1967), 113–21; and David Wootton, The Invention of Science: A New History of the Scientific Revolution (New York: HarperCollins, 2015), 165–72. Manetti’s account can be found in his Life of Brunelleschi, 44.
17. The word is derived from perspectiva ars, the Latin term for the science of optics. Some scholars argue that the principles of perspective had been known in antiquity, and some surviving paintings do indeed show an awareness of the importance of adjusting the size of an object to its intended distance from the viewer. For example, Vitruvius, the ancient authority on architechure, explains in De Architectura the principles of stage-set paintings known as scenographia, which some argue resemble linear perspective. There are, however, no surviving works from the ancient world in which perspective is applied systematically to an entire composition.
18. See King, Brunelleschi’s Dome, 34.
19. Quoted in Michael Baxandall, Painting and Experience in Fifteenth Century Italy: A Primer in the Social History of Pictorial Style (New York: Oxford University Press, 1972; 2nd ed., 1988), 124–25.
20. On the painting’s mention in the inventory of Lorenzo the Magnificent’s effects after his death in 1492 see White, Birth and Rebirth of Pictorial Space, 119. The importance of mirrors to Brunelleschi’s experiment was first noted by his younger contemporary the Florentine architect and sculptor Filarete. See Wootton, Invention of Science, 165.
21. For more about the significance of mirrors in Brunelleschi’s experiment see Wootton, 169–72.
22. For detailed discussions of Brunelleschi’s experiment see Edgerton, Renaissance Rediscovery of Linear Perspective, 143–52; White, 113–17; and Wootton, 165–72.
23. On Brunelleschi’s design of the Church of San Lorenzo, and his adherence to strict geometrical proportions that he believed were derived from the ancients, see H. W. Janson and Anthony F. Janson, History of Art: The Western Tradition, 6th ed., vol. 2 (Upper Saddle River, NJ: Pearson / Prentice-Hall, 2004), 421–23.
24. For a reconstruction of Brunelleschi’s painting of the Piazza della Signoria see White, Birth and Rebirth of Pictorial Space, 117–21. Wootton also discusses it in The Invention of Science, 166. Manetti’s description can be found in his Life of Brunelleschi, 44–46.
25. On Brunelleschi’s and Donatello’s influence on Masaccio, and his journey to Rome, see Vasari, “Life of Masaccio,” in Lives of the Artists, 101–109. The quote is from 109.
26. It hardly needs saying that Brunelleschi’s lost painting of the baptistery, which he used in his 1413 experiment, was also constructed in accordance with the principles of linear perspective. Whether that painting should be considered a work of art or merely an experimental device is debatable.
27. The discussion of the two paintings follows Edgerton, Renaissance Rediscovery of Linear Perspective, 27. Edgerton calls the practice of presenting all heads at a fixed level “isocephaly.”