Sijzī: Abū
Saʿīd
Aḥmad
ibn Muḥammad ibn ʿAbd al‐Jalīl
al‐Sijzī

Glen van Brummelen

*Born* **Sijistān,
(Iran)**, *circa *945

*Died* *circa*
1020

## Sijzī,
well known for his contributions to geometry, was also a prolific astrologer
and astronomer. We possess few details of his life; his name suggests that
he was born in Sijistān. His father, Abū al‐Ḥūsayn Muḥammad ibn ʿAbd al‐Jalīl, was also a mathematician and astronomer. Parts
of Sijzī's life were spent in Sijistān and Khurāsān.
In Shīrāz in 969/970, he was present (with **Kūhī**,
**Būzjānī**, and others)
for the famous observations of meridian transits of the Sun conducted by
**ʿAbd
al‐Raḥmān
al‐Ṣūfī**. Later in life he became
a friend of **Bīrūnī**, who
often quoted Sijzī's results in his own works.

Of approximately 20 astrological and astronomical treatises composed
by Sijzī, many were compilations and summaries of the works of others,
enhanced and systematized by the addition of tables and commentary. His
*Jāmi **ʿ al‐Shāhī* contains 13 astrological
works, three of which are summaries of treatises by **Abū
Maʿshar**.
One of these, the *Muntakhab Kitāb al‐ulūf*, is an
important source of information on Abū Maʿshar's
*Book of Thousands*. Another of Sijzī's works, the *Kitāb
al‐qirānāt* (Book of Conjunctions), may be thought of
as a supplement to the *Kitāb al‐ulūf*. This material
likely originated in Sasanian sources and deals with various topics, including
astrological world history. Other astrological contributions include the
*Kitāb Zarādusht **ṣuwar darajāt al‐falak* (The book of Zoroaster on the pictures
of the degrees of the zodiac) and *Zāʾirjāt li‐istikhrāj
al‐haylāj wa‐ʾl‐kadkhudāh*, a book of
horoscopes with tables based on Hermes, **Ptolemy**,
Dorotheus, and “the moderns.”

Sijzī seems to have had more than a passing
interest in astronomical instruments. He wrote a treatise on the astrolabe
that contains the geometric “method of the artisans” for drawing azimuth
circles on an astrolabe, as well as descriptions of variations in the retes
on astrolabes known to him. Bīrūnī describes three astrolabe
variants invented by Sijzī, and in the *Exhaustive Treatise on Shadows*
he discusses several of Sijzī's contributions to the theory and use
of a gnomon. Sijzī's treatise *On [the Fact that] All Figures are
Derived from the Circle* contains a geometric description of an instrument
that could be used to find the direction of Mecca (the *qibla*). Finally,
in his *Introduction to Geometry* he says:

I
made in Sijistān a great and important instrument, a model of the whole
world, composed of the celestial spheres, the celestial bodies, the orbs
of their motions with their sizes, their distances and their bodies, and
the form of the earth, the places, towns, mountains, seas and deserts, inside
a hollow sphere provided with a grid. I called it “the configuration of
the universe.”

Most of Sijzī's 40 mathematical works, including a unique medieval
treatise on problem‐solving strategies, focus on geometry in the Euclidean
style. One of these treatises contains a systematic mathematical approach
to establishing the 12 relations that emerge from the transversal figure
in spherical trigonometry (the theorem of Menelaus). Although the work is
strictly mathematical, Sijzī is explicitly aware of its fundamental
importance to mathematical astronomy.

## Selected References

Berggren, J. L. (1981). “Al‐Sijzī on the Transversal
Figure.” *Journal for the History of Arabic Science* 5: 23–36.

——— (1991). “Medieval Islamic Methods for Drawing Azimuth Circles
on the Astrolabe.” *Centaurus* 34: 309–344.

Dold‐Samplonius, Yvonne (1997). “Al‐Sijzī.”
In *Encyclopaedia of the History of Science, Technology, and Medicine in
Non‐Western Cultures*, edited by Helaine Selin, pp. 898–900. Dordrecht:
Kluwer Academic Publishers.

Frank, Josef (1918/1919).
“Zur Geschichte des Astrolabs.” *Sitzungsberichte der Physikalisch‐Medizinischen
Sozietät in Erlangen* 50–51: 275–305.

Hogendijk, Jan P. (English trans. and annot.) and Mohammad Bagheri
(Arabic ed. and Persian trans.) (1996). *Al‐Sijzī's Treatise
on Geometrical Problem Solving*. Tehran: Fatemi.

Kennedy, E. S. (1976).
*The Exhaustive Treatise on Shadows by Abū al‐Rayḥān
Muḥammad b. Aḥmad al‐Bīrūnī*. Translation
and commentary. 2 Vols. Aleppo: Institute for the History of Arabic Science.

Kennedy, E. S. and B. L. van der Waerden (1963). “The World‐Year
of the Persians.” *Journal of the American Oriental Society* 83: 315–327.

Pingree, David (1968). *The Thousands of Abu Maʿshar.*
London: Warburg Institute.