Most medieval Islamic authors who wrote on geometry were trained in the method of Euclid’s Elements, which was available in several good Arabic translations. These authors studied geometry in order to deepen their knowledge in mathematics and astronomy, pointing to the interrelatedness of these disciplines. The polymath Abū al-Wafāʾ Būzjānī (940-998) was no exception, and his book entitled Kitāb fī mā yaḥtaj ilayh al-ṣāniʿ min al-aʿmāl al-handasiyya (A Book on Those Geometric Constructions Which Are Necessary for a Craftsman) is our only known geometric work in the Islamic world specifically addressing the needs of craftsmen and artisans.

In his practical manual on geometry Abū al-Wafāʾ addresses practitioners in various fields of design which required understanding of the methods of geometric constructions. But in proposing different solutions to given problems he was also demonstrating his knowledge as a brilliant theoretical geometrician.

Over the two sessions we will engage in a dialogue with Būzjānī’s text, tracing his general exercises, potentially useful in a workshop environment, to Euclid’s propositions, and look at his discussion of tools, where he adds a set square to Euclid's ruler and compass, as the three basic instruments necessary for geometric constructions. We will compare those to other extant works in this genre which discuss same constructions and describe additional tools, such as plummet, T-square, movable ruler, and perfect compass, needed for angle trisection or dealing with the science of conics, which fall outside Euclid’s Elements.

We will then move on to Abū al-Wafāʾ discussion of the differing methods of craftsmen and geometricians, and how the approximation-methods of the former are contrasted with the more accurate methods of the latter. We will reconstruct a drawing by Abu’l-Wafaʾ based on Euclid’s proposition dealing with congruent areas of squares and rectangles, and see how it developed into a popular motif in Islamic architecture, known as ‘whirling kites’.