Jochen Brüning

The tension between image, script and number is clearly of immense importance to cultural history, even if it appears to be as difficult to define the concept precisely as it is to formulate general laws for their interaction. A promising field of study must therefore be delimited sufficiently clearly and present a sufficiently long and significant development in which all three of the media under examination played an important role.

Euclid’s »Elements« and the history of its reception meet these criteria exceptionally well. Given the text’s age and the extent to which it is known, it is clear that only a few others could rival it; its technical nature, however, considerably limits its field of influence, at least on initial examination. The first parts of the work are formed of script and numbers, both of which are written in the same character set. They are joined by the image as the indispensable support in the abstract reflections, but from the outset, as befits the programme set out in the title, the images are composed of »elements«: the »point«, »straight line«, »triangle«, etc. Image, script and number are therefore similarly essential in constituting and communicating the work’s substantive content, yet their individual roles have been subject to diverse changes over the course of time. The large number of »proofs« supplied by the various editors can be seen as a special index of this interaction. To date, they have received scarcely any attention.

In order to analyse this cultural historical process, it is very helpful that the corpus of the »Elements« has remained largely stable over the course of its more than two-thousand-year history so that differences in the value placed on its constituent parts and their organisation are relatively easily identifiable. The proposed project seeks to explore the specific interactions of image, script and number in the presentation, reception and influence of Euclid’s »Elements«. We are particularly interested in the extent to which demonstrable phenomena are characteristic for the overall development of mathematics as this is the field where the most direct influences are to be expected, given the nature of the »Elements«. With this as our starting point, the study can be expanded to include cultural historical developments of a more general character.