Figures

1.1 Anonymous, Diagram for chapter 85. MS 5081, 24 r. Rome: Biblioteca Casanatese 12

1.2 Charles Errard, after Pier Francesco Alberti, Diagram for Chapter 85 in Leonardo da Vinci, Trattato della pittura, Paris, 1651 13

1.3 Charles Errard, after Pier Francesco Alberti, Diagram for Chapter 159 in Leonardo da Vinci, Trattato della pittura, Paris, 1651 22

1.4 Charles Errard, after Nicolas Poussin, Diagram for Chapter 327 in Leonardo da Vinci, Trattato della pittura, Paris, 1651 23

1.5 Charles Errard, after Pier Francesco Alberti, Diagram for Chapter 85 in Leonardo da Vinci, Trattato della pittura, Paris, 1651 27

2.1 Leonardo da Vinci, Balance to measure the intensity of percussion, ca. 1495. London, Victorian and Albert Museum, Codex Foster II, f. 107v 45

2.2 Leonardo da Vinci, Balance to measure the intensity of percussion produced by water flow, ca. 1487–90. Milan, Biblioteca Ambrosiana, Codex Atlanticus, f. 126 v-a [349 r] 46

2.3 Leonardo da Vinci, Balance to study the intensity of percussion produced by water flow, ca. 1500? Milan, Biblioteca Ambrosiana, Codex Atlanticus, f. 151 r-a [407 r] 47

2.4 Leonardo da Vinci, Studies on percussion and rebound motion, 1508 or 1509. London, British Library, Codex Arundel, P 125r, f. 118r 50

2.5 Leonardo da Vinci, Studies on percussion and rebound motion in the yo-yo, 1493–1495. Madrid, Biblioteca Nacional, Codex Madrid I, f. 174v 52

2.6 Leonardo da Vinci, Studies on percussion and rebound motion in the yo-yo, 1508 or 1509. London, British Library, Codex Arundel, P 116 r, f. 2r  55

3.1 Leonardo da Vinci, “I want to see how much more force water exerts on its bottom than on its banks.” Codex Madrid I, f. 150 r, around 1495 65

3.2 Leonardo da Vinci, “What water will pour with the greatest violence, that from the nozzle a, b, or c?” Codex Madrid I, f. 152 r. 66

3.3 Two containers with different volumes; if they contain equal heights of water, the ranges of the two outflowing jets are equal too. Codex Atlanticus, f. 109 v-a [303 v], ca. 1490 67

3.4 Diagram of the experience of an emptying barrel, described by Leonardo on Manuscript C, f. 5 v, 1490–91 69

3.5 A likely ideal experiment for studying the effect of a container’s volume on the ranges of outflowing jets. Codex Madrid I, f. 151 r, around 1495 72

3.6 A large and a narrow container, with the same height. Leonardo asks: “Which of the two does throw farther from itself, n or m?” Codex Forster II-b, f. 117 v, ca. 1495 73

3.7 The sketch of a narrow, vertical container that Leonardo imagines “like a ‘cane’ of infinite height.” Manuscript I, f. 14 r, ca. 1497–99 74

3.8 The action that water exerts on the mobile wall of its container is counterbalanced by the weight of a hanging object, Codex Madrid I, f. 149 v, ca. 1495 75

3.9 Scheme of a square base container, with side length a and face height h. The push (hydrostatic force) exerted by water on one face is SV , the weight of the whole fluid is p 76

3.10 “Approaching the bottom, water presses its banks with increasing force. You can measure the inequality of its power with a container.” Codex Leicester, f. 6 r, ca. 1508  78

3.11 An object of weight P on an inclined plane 79

3.12 A container with a square base and sloping faces 81

3.13 Parabolic trajectory of a weight or a jet of water, net of air resistance, which is launched from the height a with an initial velocity v0, and an inclination θ to the horizontal 86

3.14 Efflux from orifices made in the wall of a container 88

4.1 Whale skeleton, Certosa di Pisa museum, Calci, Italy 93

4.2 Whale fossil excavation in Tuscany at Orciano Pisano 94

4.3 Gustav Utens, Castello Mediceo di Cafaggiolo, 1599 95

4.4 Jawbone of a whale in Cafaggiolo 96

4.5 Drawings from Codex Madrid I, f. 25 r, shells and a hexagonal pattern 98

4.6 Leonardo da Vinci, A Rocky Ravine, ca. 1475–80 101

4.7 Leonardo da Vinci, The Burlington House Cartoon of the Virgin and Child with St. Ann, 1499–1500. National Gallery, London 103

4.8 Leonardo da Vinci, Map of the Valdichiana, ca. 1503–4 104

5.1 Leonardo da Vinci, Strata of the Earth 120

5.2 Leonardo da Vinci, Deluge 121

6.1 Leonardo da Vinci, Leda and the Swan, ca. 1505–07, pen & brown ink over black chalk on paper. Collection of the Duke of Devonshire, Chatsworth House, UK 126

6.2 Leonardo da Vinci, Studies of Brambles (Rubus fruticosus), ca. 1505–10, red chalk with white heightening. Windsor, RL 12419; RCIN 912419 127

6.3 Peter Paul Rubens, Study of Blackthorn with Brambles and other Plants, ca. 1615–20, black, red, and white chalks and yellow watercolor on light brown paper. London, Courtauld Institute Galleries, Princes Gate Collection 127

6.4 Peter Paul Rubens, Landscape with Het Steen, after 1635, oil on panel. London, National Gallery 129

6.5 Leonardo da Vinci, Copse of Trees, ca. 1500–10, red chalk. Windsor, RL 12431; RCIN 912431 r 135

6.6 Leonardo da Vinci, Sheet of Studies (with Leaves and Fruits), pen and ink. Milan, Veneranda Biblioteca Ambrosiana, Codex Atlanticus, f. 264 r-b [713 r], ca. 1500 135

6.7 Leonardo da Vinci, Prophecy (Walnut and Envy). Paris, Bibliothèque de l’Institut de France, Manuscript G, f. 88 v (Ms. 2178), 1500–16 138

6.8 Leonardo da Vinci, The Veins of the Arm, ca. 1508, pen and ink over traces of black chalk. Windsor, RL 19027; RCIN 919027 r 138

6.9 Leonardo da Vinci, Drawing of Knots and Branch, red chalk. Paris, Bibliothèque de l’Institut de France, Manuscript H, f. 32 v, ca. 1493–94 143

6.10 Leonardo da Vinci, Study of Old Vine, Knot, and Cannon, pen and ink. Milan, Veneranda Biblioteca Ambrosiana, Codex Atlanticus, f. 18 r-b [59 b-r], ca. 1490 143

6.11 Leonardo da Vinci, Study of Blackberry (Rubus fruticosus), ca. 1505–10, red chalk on pale red prepared paper. Windsor, RL 12420 r; RCIN 912420 144

6.12 Attributed to Peter Paul Rubens, Fallen Tree with Brambles, ca. 1615–17, red, blue, and black chalk, pen and brown ink, and touches of bluish and yellow watercolor. Chatsworth, Collection of the Duke of Devonshire, Chatsworth House, UK 154

6.13 Peter Paul Rubens, Trees Reflected in Water at Sunset, ca. 1635, black, red, and white chalk. London, British Museum (inv. Gg. 2–229) 167

7.1 Leonardo da Vinci, Sala delle Asse, ca. 1498. Fresco. Milan, Castello Sforzesco 169

7.2 Leonardo da Vinci, Sala delle Asse (northeast corner), ca. 1498. Milan, Castello Sforzesco 171

7.3 Leonardo da Vinci, Sala delle Asse (detail of rocky base), ca. 1498. Milan, Castello Sforzesco 172

7.4 Leonardo da Vinci, Sala delle Asse (details), ca. 1498. Milan, Castello Sforzesco 173

7.5 Leonardo da Vinci, Sala delle Asse (detail of central heraldic shield), ca. 1498. Milan, Castello Sforzesco 173

7.6 Leonardo da Vinci, Sala delle Asse (detail of golden cords), ca. 1498. Milan, Castello Sforzesco 174

7.7 Leonardo da Vinci. Sala delle Asse (detail of overpainting in Sala delle Asse by Ernesto Rusca). Fresco. Milan, Castello Sforzesco 177

7.8 Giovan Pietro Birago, Frontispiece to Giovanni Simonetta’s Sforziada, 1490. Paris, Bibliothéque Nationale de France 187

7.9 Donato Bramante, Column in the form of a tree trunk, ca. 1492. Milan, Canonica di Sant’Ambrogio 188

8.1 Leonardo da Vinci, Perspective view of a church. Venice, Gallerie dell’Accademia, Gabinetto dei disegni e delle stampe, f. 238 196

8.2 Rome, Church of S. Spirito in Saxia. Photo by M. Carpiceci, 2016 196

8.3 Rome, Church of S. Caterina dei Funari. Photo by M. Carpiceci, 2016 197

8.4 Rome, Church of S. Girolamo degli Schiavoni. Photo by M. Carpiceci, 2016 198

8.5 Leonardo da Vinci, St. Jerome in the Wilderness. Rome, Pinacoteca Vaticana 199

8.6 Leonardo da Vinci, St. Jerome in the Wilderness, detail of the church design. Rome, Pinacoteca Vaticana 206

8.7 Reconstruction after Leonardo da Vinci’s design for a church. Florence, Gallerie dell’Accademia, Gabinetto dei disegni e delle stampe, 238 r. Drawing by A. Carpiceci 207

8.8 Reconstruction after Leonardo da Vinci’s church in St. Jerome in the Wilderness. Rome, Pinacoteca Vaticana. Drawing by A. Carpiceci 207

8.9 Comparison between the church built by Martino Longhi the Elder and Alberto Carpiceci’s reconstruction after Leonardo’s design in f. 238. Photomontage by M. Carpiceci 217

9.1 Leon Battista Alberti, Palazzo Rucellai, Florence, façade, detail 224

9.2 Leonardo da Vinci, Royal Palace at Romorantin, ca. 1508-10. Windsor, RL 12585 v. 226

9.3 Leonardo da Vinci, Studies for a private house, ca. 1505-1507. Codex Atlanticus, f. 220 r-c [592 r]. Milan, Veneranda Biblioteca Ambrosiana 227

9.4 Leonardo da Vinci, Studies for Romorantin Palace. Milan, Veneranda Biblioteca Ambrosiana. Codex Atlanticus, f. 217 v-b [583 r] 227

9.5 Michelangelo Buonarotti. Florence, San Lorenzo Library, Ricetto 230

9.6 Alzato di Ferrara. Published by Andrea Bolzoni, 1747 235

9.7 Palazzo Contrari, battlements, Ferrara 237

9.8 Palazzo Contrari, Portal, Ferrara 237

9.9 Palazzo Contrari, plan, ca. seventeenth century, Ferrara. Archivio di Stato, Bologna, Archivio Pepoli, Map XIII, c. 2, f. 2, sf 3 238

9.10 Convent di Santa Maria della Misericordia, plan, ca. 1519, Reggio Emilia. Archivio di Stato, Reggio Emilia, Raccolte Mappe Archivio dei Monasteri Soppressi, Dallari 120/10.10, Convento di Santa Maria della Misericordia 241

9.11 Convent of Santa Maria della Misericordia, detail, ca. 1519, Reggio Emilia. Archivio di Stato, Reggio Emilia 241

10.1 Antonio di Vincenzo, Plan of the Milanese Cathedral, 1390. Bologna, Museo di San Petronio 255

10.2 Antonio Averulino, known as Filarete, Sforzinda Project of View of the Ospedale Maggiore of Milan, 1460–1464. Florence, Biblioteca Nazionale Centrale, Man. II.I.140, f. 58 256

10.3 Payment to Leonardo da Vinci for the execution of the model for the tiburio, dated August 8th 1487. Milan, Archivio Veneranda Fabbrica del Duomo, Reg. 263 f. 81 v 265

10.4 Leonardo da Vinci, Study for the tiburio. Codex Atlanticus, f. 310 r-b [850 r]. Milan, Veneranda Biblioteca Ambrosiana 266

10.5 Leonardo da Vinci, Study for the tiburio. Milan, Veneranda Biblioteca Ambrosiana, Codex Atlanticus, f. 310 r-b [851 r] 267

10.6 Cesare Cesariano, View of the Duomo with square tiburio, ca. XV r. From De Architectura di Vitruvio. Como, 1521 269

10.7 Arnaldo Bruschi, Proportions between Duomo and its tiburio according to Bramante’s Opinio 270

10.8 Carlo Ferrari da Passano, Ernesto Brivio, Section view of the tiburio. Archivio Veneranda Fabbrica del Duomo, Milan 275

10.9 Leonardo da Vinci, Plan of the Duomo, 1493. Victoria and Albert Museum, London, Codex Forster III, f. 55v 277

10.10 Leonardo da Vinci, View of Milan, 1507, Codex Atlanticus, f. 73 r-v [199 v]. Milan, Veneranda Biblioteca Ambrosiana 278

11.1 Giuseppe Bossi, Copy from the Vitruvian Man for the print reproduction in Del Cenacolo, 1810. Busto Arsizio, Carnaghi Collection 281

11.2 Giuseppe Bossi, Copy from f. 8 r of the Codex Trivulzianus by Leonardo. Milan, Veneranda Biblioteca Ambrosiana 285

11.3 Carlo Giuseppe Gerli, Plate XV from the Drawings by Leonardo da Vinci, 1784 288

11.4 Giuseppe Bossi, Copy from f. 22 r of the Codex Trivulzianus of Leonardo. Milan, Veneranda Biblioteca Ambrosiana 289

11.5 Urban reconstruction of the district of Porta Vercellina 294

12.1 Giotto, Confirmation of the Rule, Bardi Chapel, S. Croce, Florence 303

12.2 Francesco d’Antonio, Christ Healing a Lunatic and Judas Receiving Thirty Pieces of Silver, ca. 1425–1426. Philadelphia Museum of Art 304

12.3 Unknown author, Plaquette of Christ Freeing a Man from the Devil. Paris, Musée du Louvre 306

12.4 Leonardo da Vinci, ‘padiglione del zardino della duchessa,’ detail. Manuscript B, f. 12 r. Paris, Bibliothèque de l’Institut de France 315

12.5 Leonardo da Vinci, Plans of S. Spirito and S. Maria degli Angeli, detail. Manuscript B, f. 11 v. Paris, Bibliothèque de l’Institut de France 316

12.6 Milan, S. Maria presso S. Satiro, the facade on the Via Falcone. Graphic work by Elisabetta Selva 318

12.7 Milan, S. Maria presso S. Satiro, hypothetical reconstructions of an unexecuted façade project by Bramante including the serliana facing Via Torino. Graphic work by Elisabetta Selva 318

12.8 Leonardo da Vinci, Plans of churches, detail. Manuscript B, f. 17 v. Paris, Bibliothèque de l’Institut de France 323

12.9 Leonardo da Vinci, Elevations of the same churches, detail. Manuscript B, f. 18 r. Paris, Bibliothèque de l’Institut de France 324

12.10 Leonardo da Vinci, Plans with the interior and exterior elevations of an octagonal church, detail. Manuscript B, f. 21 v. Paris, Bibliothèque de l’Institut de France 325

12.11 Bramante, Project for new S. Peter’s in Rome. Florence, Galleria degli Uffizi UA 1 327

13.1 Anonymus, Technological studies, Sixteenth century. Florence, GDSU, inv. 4085A 336

13.2 Drawings of a hydraulic pump, of a prospectographer and of decorative interlaces, ca. 1480–1482. Milan, Biblioteca Ambrosiana, Codex Atlanticus, f. 1 bis r-a [5 r] 337

13.3 Studies of a pump shown in its architectural setting with two notes badly touched up by restorers “primo solaro” and “secondo solaro,” ca. 1487–1490. Milan, Biblioteca Ambrosiana, Codex Atlanticus, f. 63 v-a [179 v] 340

13.4 Two drawings of plunging pumps operated by a water wheel, the first one showing the mechanism in its architectural setting with a loggia and a Neptune fountain at the center of it, ca. 1483–1485. Milan, Biblioteca Ambrosiana, Codex Atlanticus, f. 395 v [1099 r] 341

13.5 Cosimo Bartoli, Raccolta di varie machine, 1562–1572. Florence, Biblioteca Nazionale Centrale di Firenze, Palatino E.B.16.5 (II) (ex 1417), c. 4 v 342

15.1 Equestrian portrait of Muzio Attendolo-Sforza, Miniature, A. Minuti, Compendio di gesti del magnanimo et gloriosissimo signore Sforza. Paris, Bibliothèque nationale de France 357

15.2 Map of the city of Cotignola, ca. 1830. Ravenna, Archivio di Stato, Catasto Napoleonico 364

15.3 Rectangle double square, quadrilungo, or 2 x 1 rectangle 366

15.4 Golden rectangle in Cotignola’s castle and golden sections 373

15.5 Rectangle quadrilungo in Cotignola’s square 380

15.6 Unknown romagnolo painter, Cotignola’s square (detail of Graziani House), eighteenth century, oil on canvas. Faenza, Private collection 381

15.6a Edifice with portico. Detail from Codex Atlanticus, f. 220 r-c [592 r]. Milan, Biblioteca Ambrosiana 381

15.7 Sections of a fortress. Manuscript B, f. 69 r. Paris. Institut de France 383