From Theory to Visualization

In order to better understand the specifics of the book “The theory of Perspective demonstrated” by John Lodge Cowley, which dates from the second half of the 18th century, I have read individual sections of the text as well as tried to establish an overall context over both books. I was interested in the way of describing the theoretical principles and the relationship between the two books.

The work consists of 2 books, where the first book is again divided into 2 parts. As a scientific mathematician, Cowley describes his theory very abstractly and in mathematically clear, precise and short explanations. In Part I, he describes in 16 theorems geometric principles about points and lines to derive a perspective drawing. For example, in Theorem II he describes, “Two lines, which cut one another, are in one plane, and three lines, which meet one another, are in one plane.” The descriptions remain on a two-dimensional plane. In Part II, on the other hand, he describes in 19 theorems the geometrical principles concerning planes in space for deriving a perspective drawing. e.g. Theorem II: “the vertical plane is perpendicular to the picture, the vanishing, directing and original planes, and also to the parallel of the eye, the interfecting, vanishing, and directing lines of that same original plane.”

His explanations are each carried out in theorems and following demonstrations and corollars to clarify his thoughts. The theorems are each coordinated and teach the ideas to the reader step by step. In general, the principles in book 1 are described only in text form.

In contrast, the second book consists only of illustrations, which contain construction drawings. To each illustration, as far as it was recognizable, a kind of spatial figure is added. While the construction drawings lead to a first visualization of the guiding principles in the second dimension, the spatial figures finally allow to produce the chosen spatial figures even three-dimensionally by unfolding the sheets and to understand them better. Only the parallel consideration of the two books makes it possible to verify the abstract guiding principles by visual examples of application in a meaningful way.

All in all, in the book “The theory of Perspective demonstrated” it is the aspect of illustration that seems particularly interesting to me. Cowley as a mathematician first describes a very mathematical and abstract derivation of the principles of perspective. These are then translated and illustrated in the second book by construction drawings into the second dimension and then even into a third dimension by spatial figures. The clear mental explanations, but also the application-oriented illustrations of the principles of perspective seem to me unique and convincing. One understands his enthusiasm for his theory and the will to convey it to the user.

Theory – Visualization – Dimensionality