Practical Arabic Mathematics: Measuring the Muqarnas by al-K¯ash¯i

The subject of the present paper’ is al-Kishi’s calculations on the muqarnas (fig. l) , contained in his Key of Arithmetic [Miftih alHisib]. The treatise forms the third and last section’ of chapter nine, Measuring Structures and Buildings, the last chapter of Book IV, On Measurements. At the beginning of this chapter al-KZshi explains why he discusses the subject: “The specialists merely spoke about this (i.e. measuring) for the arch (faq) and the vault ( i za j ) and besides that it was not thought necessary. But I present it among the necessities together with the rest, because it is more often required in measuring buildings than in the rest.” Hence it is written for practical purposes, like the whole Key of Arithmetic. This work is a kind of encyclopaedia of elementary mathematics intended for everyone. According to its title, arithmetic is seen as the key. to solving all problems which can be reduced to calculations. In the very beginning of the work al-Kishi defines: “Arithmetic is the science consisting of basic rules to find numerical unknowns from relevant known quantities.” The necessity of measuring surface areas and volumes of buildings lies in the possible application. In medieval Italy it was common practice to pay the artisans according to the surface area they had