Geometric and Arithmetical Methods in Early Medieval Perspective

Dominique Raynaud (1, 2)

1 PLC - Philosophie, Langages et Cognition
2 GEMAS - Groupe d'étude des méthodes de l'analyse sociologique

This paper examines the hypothesis that early perspective paintings were drawn arithmetically, without vanishing points. The best argument for this hypothesis is that the division of two parallel lines by straight lines intersecting each other at the vanishing point (geometrical method) is equivalent to the division of those parallel lines in proportional parts (arithmetical method). If arithmetical method had been used, then the vanishing points exhibited ex post should be purely fortuitous. But the lack of multiples and submultiples of measurement units, the absence of proportionality ratios, the length of the operating series, and the correspondence of vanishing points to visible loci of the picture offer sound objections for this hypothesis. The use of optics and geometrical method is more probative—though it does not mean that painters were using concepts of linear perspective, which would be an anachronism.

Mots clés: geometry; Middle Ages; perspective; painting; arithmetic; geometry.

Domaines: Histoire, Philosophie et Sociologie des sciences

Dominique Raynaud. Geometric and Arithmetical Methods in Early Medieval Perspective. Physis; rivista internazionale di storia della scienza, 2008, 45, pp.29-55. ⟨halshs-00479819⟩