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A Dürer woodcut showing a painter studying the first stages in the technique of reproducing a foreshortened view -in this case of a lute - which he has achieved by attaching the ‘sighting’ thread to various points of the object and tracing the points on a screen.

While Alberti still did not know enough about optics to say more than that the outer rays from the objects gave their shape, and the inner ones their colour, he saw that the plane where the observer placed the grid was on a plane intersecting the visual pyramid Al Hazen had described.

What had been achieved was a revolution in the way people looked at the world, not just in terms of visual representation but from a philosophical point of view. Following the discovery of perspective geometry, the position of man in the cosmos altered. The new technique permitted the world to be measured through proportional comparison. With the aid of the new geometry the relative sizes of different objects could be assessed at a distance for the first time. Distant objects could be reproduced with fidelity, or created to exact specifications in any position in space and then manipulated mathematically. The implications were tremendous. Aristotelian thought had endowed all objects with ‘essence’, an indivisible, incomparable uniqueness. The position of these objects was, therefore, not to be compared with that of other objects, but only with God, who stood at the centre of the universe. Now, at a stroke, the special relationship between God and every separate object was removed, to be replaced by direct human control over objects existing in the same, measurable space.

This control over distance included objects in the sky, where the planets were supposed to roll, intangible and eternal, on their Aristotelian crystal spheres. Now they too might be measured, or even controlled at a distance. Man, with his new geometrical tool, was the measure of all things. The world was now available to standardisation. Everything could be related to the same scale and described in terms of mathematical function instead of merely its philosophical quality. Its activity could also be measured by a common standard, and perhaps be seen to conform to rules other than those of its positional relationship with the rest of nature. There might even be common, standard, measurable laws that governed nature.

Meanwhile, the confidence that the discovery must have raised in the Florentines began to make itself evident. If man were the measure of all things, then all things must surely relate to the measure of man: his experiences, his observations, his points of view.

The church of S. Lorenzo, Florence, built in 1423 to a design by Brunelleschi which was made strictly according to the principles of perspective. The vanishing point and focal centre of the building as viewed from the entrance is the holy tabernacle on the altar.

Masaccio’s fresco, The Expulsion of Adam and Eve (c. 1424-8), in the Brancacci Chapel, Florence.

Painting became more realistic in subject-matter and style. The desires of the middle-class patrons of art had now been sanctified by the new philosophy. As the number and wealth of the patrons grew, so did the independence of the artist. Now it was said, ‘Pigliare buna maniera propria per te’ (paint in your own personal style). Hitherto this would have been meaningless advice. Individual, subjective views of the world had been irrelevant, even theologically risky, but with the rules of perspective established they were on safer ground.

In 1420 about 5 per cent of paintings were of non-religious subjects. A century later the proportion had risen to about 20 per cent. Subjects now were taken from the classics rather than the Bible. The figures of saints became smaller, while the background became more important. There was an increasing amount of portraiture, as mirrors and the new realism encouraged the merchant to enhance his own importance with paintings of himself and his family.