Abstract
Perspective, as a system of visual representation, draws its name from the medieval Latin term perspectiva which means ‘optics.’ We owe this linguistic connection to the fact that certain principles of perspective developed from theories of vision. Between the two sets of notions one can find relationships of both continuity and discontinuity. A study of textual parallels has established this continuity. However, there are clear distinctions between perspectiva and perspective. Apart from the close relationship between science and technique that characterized them both, medieval perspectiva was a tripartite science embracing optica, catoptrica and dioptrica, whereas perspective would focus exclusively on direct vision; perspectiva postulated the binocular vision whereas linear perspective would adopt the conditions of monocular vision. These were the two main bifurcations that led to the development of perspectiva artificialis.
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Notes
- 1.
“Comprehensio magnitudinis non est nisi ex comparatione basis piramidis radialis continentis magnitudinem ad angulum piramidis qui est apud centrum visus et longitudinem piramidis, que est remotio magnitudinis rei vise,” Opticae Thesaurus Alhazeni Arabi libri septem, New York, 1972, p. 58; A. Mark Smith, Alhacen’s Theory of Visual Perception, Philadelphia, 2001, vol. I, p. 185.
- 2.
“Non potest esse certificatio magnitudinis rei secundum quantitatem anguli, sed oportet quod consideretur angulus et longitudo pyramidis,” The ‘Opus majus’ of Roger Bacon, ed. A.G. Little, reprint, Frankfurt am Main, 1964, pp. 115–116.
- 3.
“Comprehensionem quantitatis ex comprehensione procedere pyramidis radiose et basis comparatione ad quantitatem anguli et longitudinem distantie,” David C. Lindberg, John Pecham and the Science of Optics, Madison, 1970, p. 146.
- 4.
For example, Emma Simi Varanelli, “Dal Maestro d’Isacco a Giotto. Contributo alla storia della ‘perspectiva communis’ medievale,” Arte medievale 2. Ser. 3 (1989): 115–143; Luca Baggio, “Sperimentazioni prospettiche e ricerche scientifiche a Padova nel secondo Trecento,” Il Santo, 34 (1994): 173–232; Francesca Cecchini, “Artisti, commitenti e perspectiva in Italia alla fine del Duecento,” in La prospettiva. Fondamenti teorici ed esperienze figurative dall’Antichità al mondo moderno, ed. R. Sinisgalli, Fiesole, 1998, pp. 56–74; Eadem, “Ambiti di diffusione del sapere ottico nel Duecento,” in L’Œuvre et l’artiste à l’épreuve de la perspective, eds. M. Dalai Emiliani, M. Cojannot Le Blanc, P. Dubourg Glatigny, Rome, 2006, pp. 19–42.
- 5.
James A. Weisheipl, “Classification of the sciences in medieval thought,” Mediaeval Studies 27 (1965): 54–90; Idem, “The nature, scope, and classification of the sciences,” ed. D.C. Lindberg, Science in the Middle Ages, Chicago, 1978, pp. 461–482; Graziella Federici Vescovini, “L’inserimento della ‘perspectiva’ tra le arti del quadrivio,” Actes du IVe Congrès international de Philosophie médiévale, Montréal/Paris, 1969, pp. 969–974.
- 6.
Henri Hugonnard Roche, “La classification des sciences de Gundissalinus et l’influence d’Avicenne,” in Études sur Avicenne, eds. J. Jolivet and R. Rashed, Paris, 1984, pp. 41–63; Jean Jolivet, “Classification des sciences,” in Histoire des sciences arabes, ed. R. Rashed, Paris, 1997, 3, pp. 255–270.
- 7.
Aristotle rejects the mixing of genres during the course of a demonstration but admits the subordination of the sciences under certain conditions; Aristotle, Posterior Analytics, ed. H. Tredennick, Cambridge, 1966, I, IX, 66–69 and I, XIII, 88–90. He recognized, for example, that optics was subordinate to geometry, I, XIII, 88–90. Later, metaphysical considerations sometimes contributed to emancipate optics from pure mathematics. On subalternation scientiae in the Middle Ages, see Steven J. Livesey, “Science and theology in the fourteenth century: the subalternate sciences in Oxford commentaries on the sentences,” Synthese 83 (1990): 273–292.
- 8.
“It is known that the mathematical sciences are five—namely arithmetic, geometry, music, astronomy and perspective—which differ, as was seen in the first conclusion/Est sciendum quod quinque sunt scientiae mathematicae, scilicet arismetrica, geometria, musica, astrologia et perspectiva quae differunt secundum quod visum in prima conclusione,” Dominicus de Clavasio, Quaestiones perspectivae, Florence, BNCF, San Marco, Conv. Soppr. J X 19, quaest. 1, ff. 44r-v; Graziella Federici Vescovini, Studi sulla prospettiva medievale, Turin, 1964, p. 210.
- 9.
The inclusion of the practical sciences in the overall classification of the sciences seems to have begun with the ancient Greeks. Pappus reports that Heron’s disciples divided mechanics into two parts: (i) the theoretical, which included geometry, arithmetic, astronomy, and physics, and (ii) the manual, which included architecture (οἰκοδομική), ironworks (χαλκευτική), carpentry (τεκτονική), and painting (ζωγραφική), Pappi Alexandrini Collectionis quae supersunt, ed. F. Hultsch, Berlin, 1876–8, pp. 1022.3–1028.3 (VIII, praef. 1–3).
- 10.
Roger Bacon, Communia mathematica Fratris Rogeri, ed. R. Steele, Oxford, 1940 (I, 3, 2).
- 11.
Luca Pacioli, Summa de aritmetica, geometria, proportione et proportionalita, Venice, 1494, fol. 75r.
- 12.
Bernard Vitrac in Euclide, Éléments, vol. 2, pp. 19, 22.
- 13.
Luca Pacioli, Divina proportione, Venice, 1509; Pietro Cataneo, L’Architettura, Venice, 1567; Andrea Palladio, I Quattro Libri de architettura, Venice, Domenico dei Franceschi, 1570. On the devices per numero and per linea, see Samuel Gessner, Les Mathématiques dans les écrits d’architecture italiens, 1545–1570, Paris, 2006, pp. 109–144.
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James A. Weisheipl, “Classification of the sciences in medieval thought,” Mediaeval Studies 27 (1965): 54–90; Graziella Federici Vescovini, “L’inserimento della ‘perspectiva’ tra le arti del quadrivio,” Arts libéraux et philosophie au Moyen Âge, Paris/Montréal, 1969, pp. 969–974; Jean Jolivet, “Classification des sciences” in Histoire des sciences arabes, eds. Roshdi Rashed and Régis Morelon, Paris, 1997, vol. 3, pp. 255–270.
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Euclidis opera omnia, vol. VII: Optica… Catoptrica cum scholiis antiquis, ed. J.L. Heiberg, Leipzig, 1895; Wilfred R. Theisen, “Liber de visu: The Greco-Latin Tradition of Euclid’s Optics,” Mediaeval Studies 41 (1979): 44–105; Heronis Alexandrini opera quae supersunt omnia, vol. II. Mechanica et Catoptrica, eds. L. Nix and W. Schmidt, Stuttgart, 1900; Damianos Schrift über Optik, ed. R. Schöne, Berlin, 1897; Albert Lejeune, L’Optique de Claude Ptolémée dans la version latine d’après l’arabe de l’émir Eugène de Sicile, Leiden, 1989; Euclidis opera omnia, vol. VII: Opticorum recensio Theonis, ed. J.L. Heiberg, Leipzig, 1985.
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- 17.
Ludwig Baur, “Die philosophischen Werke des Robert Grosseteste,” Beiträge zur Geschichte der Philosophie des Mittelalters 9 (1912): 1–778; David C. Lindberg, Roger Bacon and the Origins of Perspectiva in the Middle Ages, Oxford, 1996; Witelo, Opticae Thesaurus; David C. Lindberg, John Pecham and the Science of Optics, Madison, 1970; José-Luís Mancha, “Egidius of Baisiu’s theory of pinhole images,” Archive for History of Exact Sciences, 40 (1989): 1–35; Maria Rita Pagnoni-Sturlese, Rudolf Rehn and Loris Sturlese, Dietrich von Freiberg. Opera Omnia, IV. Schriften zur Naturwissenschaft, Hamburg, 1985; Graziella Federici Vescovini, “Les questions de ‘perspective’ de Dominicus de Clivaxo,” Centaurus 10 (1964): 236–246; Blaise de Parme, Questiones super perspectiva communi, eds. G. Federici Vescovini et al., Paris, 2009.
- 18.
Gérard Simon, Le Regard, l’être et l’apparence dans l’optique de l’Antiquité, Paris, 1988.
- 19.
Alain Besançon, L’Image interdite. Une histoire intellectuelle de l’iconoclasme, Paris, 1994; Emma Simi Varanelli, “Arte della memotecnica e primato dell’imagine negli ordines studentes,” Bisancio e l’Occidente: arte, archeologia, storia, Rome, 1996, pp. 505–525.
- 20.
Robert E. Wolf, “La querelle des sept arts libéraux dans la Renaissance, la Contre-Renaissance et le Baroque,” Renaissance, Maniérisme, Baroque, Paris, 1972, pp. 259–288.
- 21.
Klaus Bergdolt, Der dritte Kommentar Lorenzo Ghibertis. Naturwissenschaften un Medizin in der Kunsttheorie der Frührenaissance, Weinheim, 1998.
- 22.
Leonardo da Vinci, The Notebooks of Leonardo da Vinci, ed. Jean Paul Richter, New York, Dover, 1970, vol. I, p. 24.
- 23.
David C. Lindberg, John Pecham and the Science of Optics, p. 62.
- 24.
For a detailed study of the textual parallels, see Raynaud, L’Hypothèse d’Oxford, Paris, 1998, pp. 163–209; idem, “L’ottica di al-Kindī e la sua eredità latina. Una valutatione critica,” in Lumen, Imago, Pictura, Atti del convegno internazionale di studi (Rome, Bibliotheca Herziana, 12–13 April 2010), eds. S. Ebert-Schifferer, P. Roccasecca and A. Thielemann, Rome (in press); Idem, “An unknown treatise on shadows referred to by Leonardo da Vinci,” in Perspective as Practice. An International Conference on the Circulation of Optical Knowledge in and Outside the Workshop, eds. S. Dupré and J. Peiffer, Max Planck Institut für Wissenschaftsgeschichte (Berlin, 12–13 October 2012), Berlin (in press); Idem, “Application de la méthode des traceurs à l’étude des sources textuelles de la perspective. Auteurs, traités, manuscrits,” in Vision and Image-Making: Constructing the Visible and Seeing as Understanding, Actes du colloque international, Centre d’Études Superieures de la Renaissance et Le Studium CNRS, Orléans (Tours, 13–15 September 2013).
- 25.
David C. Lindberg, A Catalogue of Medieval and Renaissance Optical Manuscripts, Toronto, 1975. With regard to the invention of perspective, links have also been drawn to the abacus, the cartographic projections of Ptolemy, the use of the astrolabe, or a combination of all of these sources, Birgitte Bøggild-Johanssen and Marianne Marcussen, “A critical survey of the theoretical and practical origins of the Renaissance linear perspective,” Acta ad Archaelogiam et Artium Historiam Pertinentia 8 (1981): 191–227. This knowledge probably contributed to the development of the perspective system, but in the Quattrocento their influence remained secondary to that of optics: (1) if perspective had been based on cartography, contemporaries would probably have spoken of “the cartography of painters” rather than “the perspective of painters”; (2) the identification of certain sources appears to be conjectural because they are not supported by a study of parallel texts (Raynaud, L’Hypothèse d’Oxford, pp. 165–167); (3) the notion of a “source” depends on one’s point of view. Simply because knowledge appears to us on logical grounds to be ‘pertinent’ to a subject does not necessarily mean that it would have been utilized.
- 26.
Raynaud, L’Hypothèse d’Oxford, pp. 301–349.
- 27.
See the statistical tables in Raynaud, L’Hypothèse d’Oxford, p. 329.
- 28.
Raynaud, Optics and the Rise of Perspective, Oxford, 2014, chapter 3, especially pp. 64–65.
- 29.
“Otherwise, vision is fundamentally triple, depending upon whether it is made of straight, refracted or reflected rays/Aliter vero triplicatur uisio secundum quod fit recte, fracte et reflexe,” The ‘Opus majus’ of Roger Bacon, ed. Little, p. 162.
- 30.
Alhacen, Opticae Thesaurus, pp. 76–87; Smith, Alhacen’s Theory of Visual Perception, vol. II, p. 562–582; The ‘Opus majus’ of Roger Bacon, pp. 92–99; Lindberg, John Pecham and the Science of Optics, pp. 116–118; Witelo, Opticae Thesaurus… Item Vitellonis Thuringopoloni libri decem, pp. 98–108.
- 31.
Erwin Panofsky, “Die Perspektive als symbolische Form,” Vorträge der Bibliothek Warburg 4 (1924/5): 258–331, Perspective as Symbolic Form, New York, 1991, p. 29.
- 32.
Decio Gioseffi, Perspectiva artificialis, Trieste, 1957, p. 8.
- 33.
Roger Laurent, La Place de J.-H. Lambert (1728–1777) dans l’histoire de la perspective, Paris, 1987, p. 37.
- 34.
Antonio di Tuccio Manetti, The Life of Brunelleschi, by Antonio di Tuccio Manetti/Vita di Filippo di Ser Brunelleschi, eds. H. Saalman and C. Engass, University Park, 1970, p. 43.
- 35.
Gino Arrighi, “Un estratto dal ‘De visu’ di M° Grazia de’ Castellani,” Atti della Fondazione Giorgio Ronchi 22 (1967): 44–58, p. 47; Filippo Camerota, “Misurare ‘per perspectiva’,” La prospettiva. Fondamenti teorici ed esperienze figurative dall’Antichità al mondo moderno, Fiesole, 1998, pp. 293–308.
- 36.
“Verbi gratia, quod quando visus aspexerit parietem remotum a visu remotione mediocri, et certificaverit visus remotionem illius parietis et quantitatem eius, et certificaverit quantitatem latitudinus eius, deinde apposuerit aspiciens manum uni visui inter visum et parietem et clauserit alterum oculum, inveniet tunc quod manus eius cooperiet portionem magnam illius parietis,” Alhacen, Opticae Thesaurus, p. 52; Smith, Alhacen’s Theory of Visual Perception, vol. I, p. 171.
- 37.
“Si monoculus aspiciat aliquem parietem magnum et quantitatem eius certificet deinde oculo suo manum anteponat, ipsa manus uidebitur sub eodem angulo uel sub maiori quam paries uisus est, nec tamen tanta ei apparebit quantus paries apparet quia minus distat,” Lindberg, John Pecham and the Science of Optics, p. 146.
- 38.
“Dico che la parte del dardo quale sta fra C et B entra tante volte nella distanza quale sta fra B e D cioè fra l’occhio vostro e il piè del dardo, quante volte l’altezza della torre entra nella distanza quale è fra l’occhio vostro et il piè della torre,” Alberti, Ex ludis rerum mathematicarum, Cambridge, Mass., MS. Houghton Typ 422.2, fol. 1v.
- 39.
This exercise was included by many authors in their treatises on geometry, from Euclid to Johannes of Muris, and from Dominicus of Clavasio to Cosimo Bartoli; Euclid, Liber de visu, ed. W. Theisen, p. 72; Stephen K. Victor, Practical Geometry in the High Middle Ages, Philadelphia, 1979, p. 295; Hubert L.L. Busard, Johannes de Muris. De Arte mensurandi, Stuttgart, 1998, p. 145; idem, “The Practica Geometriae of Dominicus de Clavasio,” Archive for the History of Exact Sciences 2 (1965): 520–575, p. 539; Cosimo Bartoli, Del modo di misurare le distantie, le superfitie, i corpi, Venezia, 1564, fol. 19v, 24r.
- 40.
Marica Marzinotto, “Filippo Gagliardi e la didattica della prospettiva nell’accademia di San Luca a Roma, tra XVII e XVIII secolo,” L’Œuvre et l’artiste à l’épreuve de la perspective, Rome, 2006, pp. 153–177.
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Raynaud, D. (2016). Perspectiva Naturalis/Artificialis. In: Studies on Binocular Vision. Archimedes, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-42721-8_1
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