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the first commissioned perspective painting executed later the same year by Brunelleschi’s young friend Masaccio. The painting still stands on the wall of the church of S. Maria Novella, in Florence. It is called The Trinity, and it is the first example of the new art. The view is as if seen through a window into a chapel. The barrel vaults and coffered ceilings are mathematically exact, as though they were blueprints for construction. The perspective is enhanced by the introduction of figures at different stages ‘into’ the painting. And the lines Masaccio scratched on the wall as his perspective ‘plan’ are still to be seen today. The centric point of the painting is at 5 foot 3 inches from the floor, the average height of Masaccio’s Florentine spectator. The subject of the Holy Trinity, imbued as it was with geometric symbolism, may be evidence of the new feeling, expressed elsewhere, that mathematics would become the tool with which to explain the universe and find the way to God.

As has been said, Brunelleschi was a semi-literate craftsman. He was more at home setting up the canteen for his staff, arguing with their union about terms and conditions, hiring and firing, than he was at making his revolutionary technique interesting to the scholars and intellectuals who anyway held his position as an architect in little esteem.

His academic champion turned out to be the architect and mathematician Alberti, an ex-scribe to the Pope. Alberti took Brunelleschi’s perspective geometry, dressed it up in Latin with appropriate classical references, and made it thoroughly acceptable. He also made the geometry easy enough for any painter or architect to follow. He began with a fine cotton veil, in which criss-cross threads formed a kind of grid. When this grid was held up between the painter and the scene, each object would be seen to occupy more or less grid space according to its relative size and distance from the eye. Painting by grids would ensure correct relative proportion in the end result.

Alberti then moved to the technique for painting a scene from the imagination, using perspective geometry to place everything in correct proportion according to its position in the scene. Initially this was demonstrated by placing a series of gridded veils between the painter and a scene. Figurines of the same size, placed at varying distances from the eye, were connected to the front grid by threads. From the painter’s viewpoint, these threads appeared to converge at a single point to the rear of the scene. This was Al Hazen’s ‘centric point’. Alberti called it the ‘vanishing point’.

To reproduce the necessary guidelines on the wall to be painted, a geometric design had first to be drawn along these lines. A frame was chosen, with the horizon line drawn across the rectangle of the frame at the height of the viewer’s eye. The base was divided into an equal number of spaces. Lines were then drawn from these points to the mid-point of the horizon line. The same was done at the upper edge of the frame. These lines radiating from the centric point provided a framework on which all objects could be drawn, correctly positioned and in proportion to their distance from the front of the scene.

The use of a ‘pavement’ on the floor of the scene, to enhance the feeling of perspective, was achieved with further geometry. The base of the frame was extended to one side by the distance of the viewer’s eye in front of the painting. A vertical line was then drawn from the outer end of the line to a point level with the horizon line, and this point was joined by lines radiating out across to the division points on the base of the frame. The same was done on the other side. When all these lateral lines crossed the lines running from the base to the centric point, they formed rectangles shaped strictly according to the perspective required by the viewer to achieve the full illusion of depth.

Masaccio’s Trinity, painted on the wall of S. Maria Novella, Florence. The coffered ceiling was an element of classical Roman architecture. The rich merchant and