One of the many important considerations in creating a handmade book is what will be its shape? What scale and proportion of the book will make the story feel right in the hand? You may prefer to use your own intuitive sense of design in creating a page shape but you may want to explore historical forms and the application of systematic principles of proportion developed by mathematicians, artist/designers, and architects.
“. . . In pre-modern science, observations of humankind, of our world, and of the universe were understood as relationships expressed in proportional degree rather than in today’s finite mathematical terms. . . .Geometry provided a formal means for understanding the nature of relationships, whether expressed ultimately in numerical (arithmetic), tonal (music), organic (medicine) or spacial terms (mechanics, architecture, and astronomy).” (Zenner, 2004)
In Robert D. Stevick’s, The earliest Irish and English Bookart, Visual and Poetic Forms Before A.D. 1000, the author looks at mathematical influences used in early poetry and manuscript design. Between 600 and 1000 A.D. hand lettered and painted Gospel Books were produced in small monastic communities in Ireland and Northumbria. The Irish adapted their own style of manuscript decoration from central European designs found on metalwork. These illuminations were characterized by complex interlacing designs. Stevick points out that similar geometrical patterns of decoration were produced in manuscripts over time, suggesting that a methodology of drawing these forms had been established.
Much of design in the Middle Ages was based on proportion rather than accurate numbered measure. The early Gospel page illuminations are symmetrical rectangular designs, which begin as a square. Using measurements from inside the form the square may be enlarged. In this way, individual parts of the form are repeated throughout the whole geometrical construct, creating a spatial pattern, which produces a visual harmony. It is possible to create a wide variety of interesting forms using only a few geometric concepts and a compass and straight edge.
According to Stevick “The two true measures of geometry” are the √2:1 rectangle and the golden rectangle Phi:1. Both forms are systematically derived from a square with lines and arcs. (Left: squaring the circle)
Dividing a square in half diagonally produces a √2 rectangle and an arc is scribed from the arc of the diagonal. The √2 rectangle is the proportion of standardized paper sizes in Europe. (Right: √2 rectangle)
A Golden Rectangle Phi:1 is derived from a square after first being equally divided into two rectan-gles with an arc drawn from one corner to the opposite side. Each of these structures gives a slightly different proportioned rectangle. (Left: Golden rectangle)
Interesting results may be achieved in exploring these forms without knowing their mathematical numbers and equations. With rudimentary knowledge of the use of a compass and straight edge one may create interesting design forms.
Stevick, R. (1994). The Earliest Irish and English Bookart, Visual and Poetic Forms Before A.D. 1000. Philadelphia: University of Pennsylvania Press. This is a fascinating and deep discussion of the mathematical proportions of early bookarts and poetry. Especially illuminating are the illustrated geometrical constructs with detailed but easy to follow derivations.
Zenner, M., ed. (2004). Villard’s Legacy, Studies in medieval technology, science and art in memory of Jean Gimpel, Volume 2. Burlington, VT: Ashgate Publishing Company. This is a book of interesting inter-disciplinary essays on the history of medieval science and technology.
All of these geometrical constructs were completed by the artist with compass, straight edge, pencil, ink, and gouache. Thanks for reading this blog.