This is the first of a series of short articles intended to inform, refresh or inspire further research into specific subjects.
Perspective is the foundation of most painting practice, even those of us who wish to ignore the profound influence of perspective should understand the the principles of its application.

THE ORIGINS AND DEVELOPMENT OF
LINEAR PERSPECTIVE
PART ONE

Linear perspective exists within the geometrical realm of mathematics. Art theorist and historian Margaret Hagen argues that all art, and not just Western art, is governed by these geometrical principles (1) . Of course this is true when you consider that anything painted upon a canvas, or drawn upon a flat sheet of paper, is restricted within two dimensions. All paintings or drawings are two-dimensional illusions of the three-dimensional world, or are abstractions from it. However, even Picasso's strange cubist visions are the subject of mathematical principles. Taking this argument further, even if we remove the picture plane from the equation, everything produced in paint or pencil is also the subject of mathematical rules and formulae. The rules of dimensions, height, length etc, even if they are hardly perceptible, still exist.

The Greeks were the first to explore the ideas of projection and recession of images, through the illusionist paintings of stage scenery, some four hundred years before the birth of Christ. The most significant development, at that time, was Euclid's recording of optical experiments entitled Optica around three hundred B.C. This was the first known written application of laws of geometry to problems of how people see the world around them. He produced definitions of the rectilinear visual ray and the visual cone as geometric constructions (2) .

Later, artists like Leonardo da Vinci also recognised the reliance of art upon the science of mathematics. Many of the artists of the Renaissance were also dedicated mathematicians; curious about the scientific foundations of the world they saw around them (3) .

Filippo Brunelleschi is now generally credited with 'inventing' linear perspective around 1413, although Giotto's works of the previous century bears witness to a sustained, orderly, and deeply considered attention to the representation of figures and space. In 1425 A.D. Masaccio painted frescoes in the Brancacci Chapel in Santa Maria Novella, Florence, which is the first surviving picture constructed according to clear-cut linear perspective rules. Perhaps it is no coincidence that this was the same year in which Brunelleschi is accredited with providing the first demonstrations of his experiments with perspective. Much of the research carried out at this time was centred on the discovery and arrival of Ptolemy's Geographia in Europe around 1500 A.D (4) . And, as is common to the processes of development of such theories, even Ptolemy's work was based on that of others before him.

Around 140 A.D. Ptolemy applied the work of Euclid's Optica to the geometric laws of refraction. It was this foundation, echoed later by similar works by Giotto and Lorenzetti, that paved the way for Brunelleschi to achieve, what in popular terms is called scientific accuracy. While it is impossible for us to know how far Brunelleschi intellectualised his system mathematically, it was not long before Alberti's expansion of these ideas, in around 1435, that paved the way for what was to come.

IN THE NEXT INSTALLMENT:
The system of linear perspective.
© Nigel Williams 2001

REFERENCES
(1) Kemp M., 'The Science of Art' chpt 1 p.9.
(2) Edgerton S.Y.Jr., 'The Renaissance Rediscovery of Linear Perspective' p.XV.
(3) Kemp M., 'The Science of Art' p.9.para 5.
(4) Edgerton S.Y.Jr., 'The Renaissance Rediscovery of Linear Perspective' p.XV.