January, by Jean and Paul Limbourg

Towards the 14th century the artists take greater strides in fine-tuning linear perspective rules in their art. The paintings of this period gradually appear to be more and more accurate in representing perspective-- perhaps the lack of mathematical understanding for perspective in Pre-Renaissance art forced the artist to improvise in their attempts to copying three-dimensional reality onto the two-dimensional canvas. This period of transition is well exemplified by Lorenzetti Ambrogio's " Annunciation of the Pinacotheque of Sienna".

The Annunciation of the Pinacotheque of Sienna", 1344, Lorenzetti Ambrogio

The floor is well constructed according to the rules of perspective-- the depth lines (= lines perpendicular to the picture plane) on the floor tiles are converging to the vanishing point. However, since Ambrogio did not understand all of the fundamentals of perspective, he was indecisive about the localization of the vanishing point. He cleverly avoided the difficult task of showing this area of confusion by hiding it behind a column. The column corresponds to the axis of symmetry in the painting which absorbs the tension and stabilizes the picture. Like his contemporaries, he uses little tricks to give a stable sense of space. Still, the accurate construction of the checkerboard floor reveals an amazing intuition in the representation of lines perpendicular to the picture plane. Panofsky even says about the brothers Lorrenzetti:

Die Entdeckung des Fluchtpunkts, als des "Bildes der unendlichen fernen Punkte saemtlicher Tiefenlinien", ist gleichsam das konkrete Symbol fuer die Entdeckung des Unendlichen selbst. [...] Es sind vorallem Dingen die Brueder Lorenzetti, die diesen wichtigen Schritt getan haben[...]. Hier die sichtbaren orthogonalen der Grundebene zum ersten Mal saemtlich, und ohne Zweifel mit vollem mathematischen Bewusztsein, nach einem Punkte orientiert sind.

The discovery of the vanishing point, as the "image of points, infinitely far way, of all the depth lines", is similarly the concrete symbol of the discovery of infinity [...] It is especially the brother Lorrenzetti who made this major step. [...] Here one sees all the perpendicular lines on the ground level for the first time, without any doubts with complete mathematical consciousness, oriented towards one point.

In this sense linear perspective and perhaps even projective geometry finds its origins in artistic efforts.. Go on to next section: III. Renaissance

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