0.1 Piero di Cosimo, Hunt, tempera and oil on wood, 70.5 × 169.5 cm, New York, Metropolitan Museum of Art, 75.7.2 (photo: Metropolitan Museum; creative commons) 4
0.2 Piero di Cosimo, Return from the Hunt, tempera and oil on wood, 70.5 × 168.9 cm, New York, Metropolitan Museum of Art, 75.7.1 (photo: Metropolitan Museum; creative commons) 5
1.1 Subdivisions of the two realms of existence into metaphysical entities and epistemological states according to the image of the Line in Plato’s Republic (design: author) 22
1.2 Athenian black-figured neck-amphora depicting a chariot and a charioteer driving a white horse and a black horse, c. 500 BC, excavated in Italy (Magna Graecia), London, British Museum (photo provided by, and reproduced here by permission of: the British Museum © The Trustees of the British Museum; all rights reserved) 26
1.3 Plato’s construction of the equilateral triangle and the square using six elementary scalene triangles (Tsca) and four elemental isosceles triangles (Tiso), respectively (design: author) 33
1.4 Alternative constructions of the equilateral triangle and the square, involving only two elemental triangles (A and B), the undivided figures (C and D), other elementary figures (E and F) (design: author) 34
1.5 A possible explanation underpinning Plato’s constructions: the hypotenuse of Tsca and both the catheti of Tsca are the radii of the circle circumscribing the corresponding final figures (design: author) 35
1.6 Raphael, The School of Athens, fresco, Musei Vaticani, ca. 1509–1510, detail of Plato (left-hand side) and Aristotle (right-hand side) standing one beside the other (photo provided by, and reproduced here by permission of: the Musei Vaticani © Governatorato SCV—Direzione dei Musei.) 41
4.1 Angelica Kauffmann, Pliny the Younger and his Mother at Misenum in 79 CE, oil/canvas, 103 × 127 cm, Princeton University Art Museum, Princeton, NJ (photo: author) 92
4.2 Joseph Wright, The Corinthian Maid, oil/canvas, 106.3 × 130.8 cm, Paul Mellon Collection, National Gallery of Art, Washington, DC (photo: National Gallery of Art) 96
4.3 Ghiberti, attrib., Madonna and Child, painted terracotta, 81.3 × 59 × 21.6 cm, Cleveland Museum of Art (photo: Cleveland Museum of Art) 99
4.4 Anonymous, Brunelleschi’s Death Mask, plaster, approximately 35 × 26 cm, Museo dell’Opera del Duomo, Florence (photo: author) 100
4.5 Desiderio da Settignano, attrib., Niccolo da Uzzano?, painted terracotta, 46 × 44 cm, Museo Nazionale del Bargello, Florence (photo: author) 101
4.6 Verrocchio, attrib., Giuliano de’ Medici, terracotta, 61 × 66 × 28.3 cm, Andrew W. Mellon Collection, National Gallery of Art, Washington, DC (photo: National Gallery of Art) 103
4.7 Andrea del Verrocchio and Orsino di Niccolò Benintendi, model, Bust of Lorenzo de’ Medici, painted terracotta, 65.8 × 59.1 × 32.7 cm, National Gallery of Art, Washington, DC (photo: National Gallery of Art) 104
4.8 Anonymous, Lorenzo de’ Medici’s Death Mask, patinated plaster, approximately 14 × 10 cm, Museo degli Argenti, Palazzo Pitti, Florence (photo: author) 105
5.1 Stage for Dionysus in Hero’s Automata, Cod. Marcianus gr. Z 516, fol. 202r (photo: Biblioteca Marciana) 110
5.2 Frontispiece of Baldi’s De gli automati (1589) 112
5.3 Harun al-Rashid’s gift to Charlemagne, illustrated in Les grandes chroniques de France, Département des manuscrits, Français 2610, fol. 110r (photo: Bibliothèque nationale de France) 118
5.4 Counterweight drawing on differential drums in Baldi’s De gli automati 124
5.5 Modeling the automaton’s circular motion as a rolling cone, Cod. Marcianus gr. Z 516, fol. 199r (photo: Biblioteca Marciana) 126
5.6 Stage of Dionysus with Victory in Baldi’s De gli automati 128
6.1 Bernardo Buontalenti, Grotta Grande, 1583–1593, Giardino di Boboli, Palazzo Pitti, Firenze (foto: Fred Romero) 134
6.2 Francesco di Giorgio Martini, Illustrazione di una mina esplosiva, Opusculum de architectura, c. 1474–1482, penna e inchiostro su pergamena, 274 × 229 mm, British Museum, Londra, particolare (foto: British Museum) 135
6.3 Georg Agricola, Diversi tipi di vene metallifere, De re metallica libri XII, 1556, xilografia su carta, 34 cm di altezza, Getty Research Institute, Los Angeles (foto: Getty Research Institute) 139
6.4 Cesare Cesariano, Condutture di scarico, Di Lucio Vitruvio Pollione de architectura libri dece, 1521, xilografia su carta, 43 cm di altezza, Getty Research Institute, Los Angeles (foto: Getty Research Institute) 141
6.5 Luys Collado, Diverse configurazioni di mine esplosive, Prattica manuale dell’arteglieria, 1606, xilografia su carta, 27 cm di altezza, ETH-Bibliothek, Zurigo (foto: ETH-Bibliothek) 143
6.6 Andreas Libavius, Tipologie di alambicchi, Commentariorum alchymiae, 1606, xilografia su carta, Bayerische Staatsbibliothek, Monaco di Baviera (foto: Bayerische Staatsbibliothek) 145
6.7 Antonio da Sangallo the Younger, Sistema di ventilazione nelle contromine, Bastione Ardeatino, c. 1537, Roma (disegno: Morgan Ng) 148
6.8 Francesco de Marchi, Camere di contromina di dimensione crescente, Architettura militare, c. 1550, penna e inchiostro con acquarello su carta, 43 cm di larghezza, Yale Center for British Art, Paul Mellon Collection, New Haven, particolare (foto: Yale Center for British Art) 150
6.9 Georg Agricola, Il complesso termale a Tritoli, De ortu et causis subterraneorum, 1558 (1ª ed. 1546), The Wellcome Library, Londra (foto: The Wellcome Library) 151
6.10 Giuliano da Sangallo, Sala ottagonale nel Bastione di San Martino, c. 1512, Cittadella Nuova, Pisa (foto: Mario Ciampi) 153
6.11 Giovanni Battista da Sangallo, Ricostruzione ipotetica dell’impianto di una stanza termale antica, metà del XVI secolo, MS Corsini 50.F.1, Biblioteca dell’Accademia Nazionale dei Lincei e Corsiana, Roma (foto: Biblioteca dell’Accademia Nazionale dei Lincei e Corsiana) 154
6.12 Resti di un ipocausto delle terme di Histria, Scizia Minore (foto: Cristian Chirita) 157
7.1 Entrance to the Ear of Dionysius, Syracuse 168
7.2 Athanasius Kircher, ‘Ichnographia Specus Syracusanae Dionysij Tyranni ex vivo saxo delineatae,’ Musurgia universalis sive ars magna consoni et dissoni, Rome 1650, vol. 2, 292 (photo: Bibliotheca Hertziana—Max Planck Institute for Art History) 170
7.3 Athanasius Kircher, ‘Iconismus XV’, Musurgia universalis sive ars magna consoni et dissoni, Rome 1650, vol. 2, fol. 264 (photo: Bibliotheca Hertziana—Max Planck Institute for Art History) 171
7.4 Robert Plot, The Natural History of Oxford-shire, Oxford 1677, ad. pag. 16 (photo: Getty Research Institute) 172
7.5 Cornelis Bloemaert, ‘Echo’, from Michel de Marolles, Temple des Muses, Paris, 1655, 291 (photo: Getty Research Institute) 176
8.1 Leonardo da Vinci, Deluge, c. 1513–1516, drawing, black chalk, pen and ink, wash, with touches of white heightening, 270 × 408 mm, Windsor Castle, Royal Collection RCIN 912376 (photo: Windsor Castle, Royal Collection) 180
8.2 Michelangelo, Diluvio universale, c. 1508–1510 fresco, Rome, Sistine chapel ceiling 181
8.3 Leonardo da Vinci, Geologic map of the Mediterranean, c. 1515 drawing, pen and ink and wash on coarse brown paper, Codex Atlanticus, fol. 901r, 86–104 × 155–229 mm, detail, Milan, Ambrosiana Library (photo: Ambrosiana Library) 183
9.1 Leonardo da Vinci, The Madonna of the Rocks, c. 1483–1491, oil on panel. Credit: © RMN-Grand Palais (Musée du Louvre, Paris) / Michel Urtado 193
9.2 Leonardo da Vinci, Deluge, c. 1517–1518, black chalk on rough ‘oatmeal’ paper, Windsor (Royal Library). Credit: Royal Collection Trust/© Her Majesty Queen Elizabeth II 197
9.3 Temptation and Fall of Adam and Eve, cast in 1015 for the bronze doors of Bishop Bernward, Hildesheim (Cathedral of St. Mary) 199
9.4 Piero di Cosimo, A Hunting Scene, 1488–late 1490s, tempera and oil on panel, New York (The Metropolitan Museum of Art). Credit: © The Metropolitan Museum of Art, New York 201
9.5 Fra Filippo Lippi, Adoration of Christ with St. Romuald and the Young Baptist, c. 1459, tempera on panel, Berlin (Gemäldegalerie, Staatliche Museen zu Berlin). Credit: Photo Scala, Florence/bpk, Bildagentur für Kunst, Kultur und Geschichte, Berlin 202
9.6 Parmigianino, Study of Tree Trunks and Foliage, 1523–1527, pen and brown ink heightened with white, on blue paper, Florence (Gabinetto dei Disegni e delle Stampe delle Gallerie degli Uffizi). Credit: Gabinetto dei Disegni e delle Stampe delle Gallerie degli Uffizi, Florence 205
9.7 Albrecht Altdorfer, Weeping Willows in an Alpine Landscape, c. 1511, pen and black ink in two tones on light brown paper, Vienna (Graphic Collection of the Academy of Fine Arts). Credit: Graphic Collection of the Academy of Fine Arts, Vienna 206
9.8 Piero di Cosimo, The Forest Fire, 1495–1505, oil on panel, Oxford (Ashmolean Museum). Credit: Ashmolean Museum, Oxford 208
9.9 Leonardo da Vinci, Vault, Sala delle Asse, c. 1498, tempera on plaster, Milan (Castello Sforzesco) 212
9.10 Leonardo da Vinci, Monochrome fragments, Sala delle Asse, c. 1498, tempera on plaster, Milan (Castello Sforzesco) 213
9.11 Leonardo da Vinci, Virgin and Child with St. Anne, c. 1503–1519, oil on panel, Paris (Musée du Louvre). Credit: Photo © RMN-Grand Palais (Musée du Louvre)/René-Gabriel Ojéda 215
9.12 Battista Naldini, View of Tivoli, 1560–1561, pen and brown ink, over stylized traces and black chalk. Berlin, Staatliche Museen zu Berlin, Kupferstichkabinett. Credit: Staatliche Museen zu Berlin, Kupferstichkabinett, Berlin 217
9.13 Opicinus de Canistris, Map, Vat. Lat. 6435, fol. 53v, c. 1337. Rome (Biblioteca Apostolica Vaticana) 219
10.1 Botticelli, Venus and Mars, tempera and oil on panel, 69.2 × 173.4 cm, National Gallery, London (Credit: © National Gallery, London/Art Resource, NY) 228
10.2 Unknown, Bacchus reclining in the arms of a goddess, c. 60–50 BCE fresco, Sala di Grande Dipinto scene VI, Villa of the Mysteries, Pompeii (Alamy: Image ID: P408WN; by permission) 233
10.3 Table, Empedocles’ Cosmic Cycle (Gordon Campbell original design) 235
10.4 Unknown, Hercules and Omphale, fresco, Museo Archeologico Nazionale di Napoli, c. 25–35 AD, from the House of The Prince of Montenegro (VII, 16, 13), Pompeii (Alamy: Image ID: M18DC3; by permission) 245
11.1 Piero di Cosimo, The Forest Fire, c. 1505, oil on panel, 71.2 × 202 cm, Ashmolean Museum, Oxford, WA1933.2 (photo: Ashmolean; © Ashmolean Museum, University of Oxford; by permission) 251
11.2 Piero di Cosimo, The Forest Fire, detail (photo: author) 251
11.3 Luca Signorelli, Empedokles (?), 1500–1503, fresco, Orvieto Cathedral, chapel of the Madonna di San Brizio (photo: Scala/Art Resource, NY) 255
12.1 Albrecht Dürer, Rape of Europa, 1494–1495, Graphische Sammlung Albertina, Vienna (photo: Erich Lessing/Art Resource, NY) 275
12.2 Albrecht Dürer, Hercules, ca. 1498, Kupferstichkabinett, Staatliche Museen, Berlin, Germany, inv. 399–2 (photo: bpk Bildagentur/Staatliche Museen, Berlin/Jörg P. Anders/Art Resource, NY) 279
12.3 Sandro Botticelli, Pallas and the Centaur, early 1480s, Uffizi, Florence, inv. 29 (photo: Erich Lessing/Art Resource, NY) 281
12.4 Monogrammist BXG, Wild Man and his Family, second half of the fifteenth century, Albertina, Vienna, DG 1928/332 (photo courtesy the museum; © Albertina, Wien) 284
12.5 Leonardo da Vinci, Study of Human Proportion: The Vitruvian Man, ca. 1492, Accademia, Venice, inv. 228 (photo: Cameraphoto Art, Venice/Art Resource, NY) 289