Astrology Born from the Eye; the Painter Disputes the Poet
Perspective as daughter of painting; geometry and arithmetic grasp only quantity, not beauty
This leaf of the Trattato closes an attack on a philosopher who tore out his own eyes, calling the act pure madness, then opens chapter [17], 'How the science of astrology is born from the eye.' Leonardo argues that all astrology depends on the visual lines and on perspective, the daughter of painting, and that without such lines the geometer's art is blind. He grants geometry and arithmetic only the knowledge of quantity, reserving quality, the beauty and ornament of the world, for painting, before chapter [18] opens the dispute between painter and poet. Brief marginal notes appear at the lower left that are not part of the transcription.
On this page
Astrology depends on the visual lines of perspective
Chapter [17] argues that no part of astrology functions except through the visual lines and through perspective, which Leonardo calls the daughter of painting. The painter, by the necessity of his art, gave birth to perspective, and within its lines are enclosed all the various figures of the bodies generated by nature, without which the geometer's art is blind.
Geometry and arithmetic know only quantity, not beauty
The geometer reduces every bounded surface to the figure of the square and every body to the cube, and arithmetic does the like with its cube and square roots. Yet these two sciences reach only continuous and discontinuous quantity; they do not concern themselves with quality, which is the beauty of nature's works and the ornament of the world.
The mad philosopher who tore out his eyes
The page opens by ridiculing a philosopher who tore out his own eyes to remove the impediment to his reasoning, calling the act sheer madness since he might merely have shut them until his frenzy passed. This anecdote, on the eye and vision, leads into the chapters that follow.