Sharaf al‐Dīn
al‐Ṭūsī

Glen van Brummelen

*Born* **Ṭūs, (Iran)**, *circa *1135

*Died* **(Iran), 1213**

Although Sharaf al‐Dīn al‐Ṭūsī is known especially for
his mathematics (in particular his novel work on the solutions of cubic
equations), he was also the inventor of the linear astrolabe, a tool that
derives from the planispheric astrolabe but is more easily constructed.
From his name we may infer that Sharaf al‐Dīn was born in the
region of Ṭūs, in northeastern Iran.
He spent a major part of his early career as a teacher of the sciences,
including astronomy and astrology, in Damascus and Aleppo; he also taught
in Mosul. Among his students was Kamāl al‐Dīn ibn Yūnus,
who would eventually teach Sharaf's namesake, the great **Naṣīr al‐Dīn al‐****Ṭūsī**.

Sharaf
al‐Dīn al‐Ṭūsī
devoted several treatises to the linear astrolabe, sometimes called the
staff of al‐Ṭūsī. Its principle is
simple – many of the important circles on the planispheric astrolabe, especially
the almucantars (altitude circles) and the circles of declination, are centered
on the meridian line. The main rod of the linear astrolabe is equivalent
to the meridian line and contains markings to indicate the centers of these
circles and their intersections with the meridian. The ecliptic (which appears
on the movable rete of a standard astrolabe) is represented by the intersections
of the beginnings of the zodiacal signs with the meridian when the rete
is rotated. Many typical operations on a traditional astrolabe require the
locations of points of intersection of these various circles. By attaching
ropes to the appropriate points on the staff to act as radii, the circles
and their intersections can be reconstructed and the astronomical problem
solved. A scale giving chord lengths in the meridian circle extended the
linear astrolabe's range of applications. Attached to a plumb line, it was
also used to take observations of solar altitude. Additional markings allowed
the determination of the *qibla* (the direction of Mecca) and solutions
of astrological problems.

The
simplicity of the linear astrolabe made it easy to construct, but its less
than artful appearance rendered it unattractive to collectors. It was neither
as durable nor as accurate as a planispheric astrolabe, and its operations
were less intuitive. None have survived.

## Selected References

Al‐Ṭūsī,
Sharaf al‐Dīn (1986). *Oeuvres mathématiques: Algèbre et géométrie au XIIe siècle*, edited and translated by Roshdi Rashed. 2
Vols. Paris: Les Belles Lettres.

Carra
de Vaux, R. (1895). “L'astrolabe linéaire ou bâton d'al‐Tousi.” *Journal
asiatique*, 9th ser., 5: 464–516.

Michel,
Henri (1943). “L'astrolabe linéaire d'al‐Tusi.” *Ciel
et terre* 59:
101–107.

———
(1947). *Traité de l'astrolabe*. Paris: Gauthier‐Villars.