106 A History ofMathematics
3. Two texts
No curiosity that occurs, no strange method unheard of, no nice idea that is liked by them who hear it will be
left out. These will be given and clearly explained, so that this book will contain everything the people enquire
about. For indeed this arithmetic is often debated by people who enquire about its whys and hows. (Al-Uql ̄idis ̄i 1978,
p. 36)
It is a characteristic of geometers that when you ask them a question on the division of figures or the multiplication of
lines, they fall into confusion and need a long time to resolve it. (Ab ̄u-l-Waf ̄a 1966, p. 115)As an introduction to the nature and variety of Islamic mathematics, let us consider two texts
from around the same date (tenth centuryce). Both illustrate the problem of ‘practical math-
ematics’, which is raised by the two quotes above. For symmetry, one is a book, in print in an
English translation, by an almost unknown writer; the other an untranslated book by an author
of whom a fair amount is known. The first, which is relatively easy to find, is the arithmetic, or
Kit ̄ab al-Fus.ul f ̄ ̄i al-H.is ̄ab al-Hind ̄i(Book of chapters on Hindu reckoning), written by al-Uql ̄idis ̄i
in Damascus in 951ce(al-Uql ̄idis ̄i 1978). The book is one of the best sources on early arithmetic
using the decimal ‘Hindu’ system, particularly since the earlier (earliest?) one written by the famous
al-Khw ̄arizm ̄i has not survived in Arabic, and the various Latin translations seem all to have added
and subtracted in different ways (see al-Khw ̄arizm ̄i 1992). On the other hand, while al-Khw ̄arizm ̄i
was a notable scholar, nothing is known of al-Uql ̄idis ̄i’s life at all. The name, which means ‘The
Euclidean’ may indicate learning, but apparently people got this nickname for writing copies of
The Elementsfor sale. (Tenth-century Damascus must surely have been unique as a place where
copying the text of Euclid could earn you a living.) However, Greek learning makes no appearance in
al-Uql ̄idis ̄i’s text. It is long, detailed, and careful, and its world is that of street-corner calculators in
Damascus who needed to work quickly and accurately, and who found that the new number system
was ideal for their purposes. It was a competitive world—again this may appear strange—and one
in which the partisans of one method of calculation would attack another. So al-Uql ̄idis ̄i defends his
method, in phrases which are often quoted, as making it possible to carry out calculations among
the distractions of street life:Most scribes will have to use it because it is easy, quick and needs little precaution, little time to get the answer, and
little keeping of the heart busy with the working that he [the scribe] has to see between his hands, to the extent that
if he talks, he will not spoil his work; and if he leaves it and busies himself with something else, when he turns back
to it he will find the same and thus proceed, saving the trouble of memorizing it and keeping his heart busy with it.
(Al-Uql ̄idis ̄i 1978, p. 35)The book is outstanding in its immediacy, and in the sense that al-Uql ̄idis ̄i has of his audience
and what they need. Every rule is explained in great detail:
For example, we try to find the root of 576. We start from the six saying ‘Is, is not, is’, which falls under the five. We
seek a number to draw under the five so that if we multiply it by its like, it exhausts most of the five. We find it 2. We
insert it under the five, multiply it by its like and cast that out of the five. There remains one in place of five. We double
the two in its place, shift the four under the seven, and seek a number to draw under the six so that if we multiply it by
the four and by itself it will exhaust what is above it. We find it four. We multiply four by four, get 16, cast that out from
above. We multiply 4 by itself and drop that from above; nothing remains. We halve the four which we have doubled.
The result is 24. (Al-Uql ̄idis ̄i 1978, p. 76)
Clearly from the above, intelligence, numerical ability, and skill in following instructions are
assumed; and there is no concession to a literary style once the initial points in defence of the book