(Essay submitted to complete requirements for the class HIS189: Muslim Spain: Philosophy and Culture., Fall 2020, Stanford Continuing Studies)
Manish S. Vaidya
Prof. Vincent Barletta
8 November 2020
Al-Zarqali and the Astrolabe in al-Andalus
Muslim rule began in the Iberian Peninsula at the start of the eighth century CE. After a period of conquest and subsequent consolidation over the next two centuries, al-Andalus entered a period of unprecedented cultural growth. While the Golden Age arrived in al-Andalus in the mid-tenth century under the reign of Abd al-Raḥmān III, a creative and scientific revolution had already been occurring for almost 200 years prior in the eastern Islamic capitals. In cities like Baghdad and Damascus, Muslims absorbed Indian, Mesopotamian, Persian, Greek, and Roman knowledge of astronomy. Scientific thinkers in Al-Andalus were open to knowledge from these lands and embarked on a cultural evolution that involved significant advances in this field. Of particular interest is the universal astrolabe developed in eleventh-century al-Andalus by Abū Ishāq Ibrāhīm al-Zarqālī (1029-1087).
Early Development of the Astrolabe
The astrolabe gets its name from the Greek astrolabos, or “star-taking.” It is used primarily to make astronomical measurements, typically of the altitudes of celestial bodies, but it also has many other practical applications.
The earliest references to basic principles of the astrolabe can be found in the works of the Greek mathematician Hipparchus who lived in Nicaea from 190 BCE to 120 BCE. Hipparchus is credited with discovering stereographic projection, the mathematical means of representing the three-dimensional sky onto a two-dimensional surface. The first significant writer on the description and construction of astrolabes was the Ptolemy, who lived in the second century CE. He offers enormous detail about the earliest uses of the instrument in his Planisphaerium. In this work, Ptolemy details the practical workings of the device by combining his own work on the instrument with theories of stereographic projection.
Theon (335-405 CE) was a Greek scholar and mathematician who lived in Alexandria, Egypt. He primarily worked to compile Euclid’s expositions on geometry, and he wrote a short text titled, “On the Little Astrolabe,” which is one of earliest surviving texts describing the construction and use of the device. Theon did not actually build an astrolabe, but historians think he did provide a full blueprint. Synesius (370-415 CE) was a member of a well-known and rich family of Cyrene (present day Libya). Synesius wrote a treatise titled, “On an Astrolabe,” which he sent to Pylaemenes, an important military leader whom Synesius had met in Constantinople. This treatise was sent along with a silver planisphere (two circular plates with markings to represent the sky), which appears to have been a prototype for an astrolabe. The Byzantine scholar Ammonius (d. ca. 517 CE) also wrote a treatise on the construction and use of the astrolabe. He incorporated the astrolabe into his teachings, thus introducing a number of people to the instrument. His most famous pupil, the mathematician and philosopher John Philoponus (490-574 CE), wrote a book in 530 CE on the astrolabe titled, “On the Use and Construction of the Astrolabe and the Lines Engraved on it.”. That Ammonius also wrote on this topic is mentioned by Philoponus at the start of this book.
Severus Sebokht, also Seboukt of Nisibis (575-667 CE), was a Syrian scholar and bishop who wrote a description of the astrolabe in Syriac. Sebokht’s analysis is similar to the one adopted by Theon. Instead of focusing on theoretical issues, he concentrated on practical description and application. He greatly expanded the standard list of uses. Knowledge and production of the astrolabe spread from the Byzantine east through Syria and eventually into the Abbasid capital of Baghdad.
Al-zarqali’s Work On The Astrolabe
Abū Ishāq Ibrāhīm al-Zarqālī (1029-1087 CE) was born in Cordoba. He came from a family of craftsmen who made several mechanical devices. Having inherited his family skill, al-Zarqali then moved to Toledo, where he entered the service of Sultan al-Ma’mun. His job was to make instruments for the astronomers of al-Ma’mun, who were then engaged in a major research project on astronomy. With hard work and by virtue of being highly talented, he soon became the director of the project. He spent a long fruitful year in Toledo, where he conducted extensive observations, made mechanical devices and astronomical instruments, and wrote a number of books. His water clock attracted a good deal of attention, and Jewish scholar Moses ben Ezra even wrote a poem about it. Leaving Toledo in 1078 CE during Alfonso VI’s repeated attacks on the city, al-Zarqali went back to Cordoba to continue his research.
By the time of al-Zarqali, the astrolabe had become very valuable to Muslims. It helped determine the five daily astronomically defined prayer times, and it was an aid in finding the direction to Mecca—Islam’s holiest city and a required direction during prayer. Al-Zarqali perfected his device, thus inventing the first universal astrolabe. He called it al-safiha (asaphea in Latin), and unlike its predecessors, this astrolabe could be used at any location around the world instead of only at a specific latitude. His works inspired a generation of Islamic astronomers in Al-Andalus, and they later went on to be very influential in the rest of Europe. Copernicus, for example, mentions Arzachel and quotes him in his book on the movement of celestial bodies. The crater Arzachel (the Latinized version of “al-Zarqali”) on the earth’s moon is named after him.
In various recorded instances we can find evidence of the importance of contributions by al-Zarqali. In his Jāmiʿ al‐mabādiʾ wa‐ʾl‐ghāyāt fī ʿilm al‐mīqāt, an encyclopedic work on astronomy, Abū al‐Hassan ʿAlī al‐Marrākushī (a Moroccan astronomer and mathematician who lived in the thirteenth century) credits al-Zarqālī with detailed astronomical observations in Toledo in 1061 (which were collectively referred to as the “Toledo tables”). This testimony is confirmed by Ibn al‐Hāʾim al‐Ishbīlī (a twelfth-century astronomer and mathematician from Seville) in his work Al‐zīj al‐kāmil fī al‐taʿālīm, where he credits al-Zarqali with over 30 years of observations of the movement of the sun and the moon.
Al-Zarqali wrote two treatises on the universal astrolabe. The first is Al‐ṣaf īḥa al‐mushtaraka li‐jamīʿ al‐ʿurūḍ (Collection of plates held together by a staff) and a 100-chapter book on the use of the ṣaf īḥa (plate), called the Zarqāliyya. His pivotal contribution to the development of the astrolabe was to replace the standard equatorial projection (flattening the globe at the equator) with a combination of the stereographic (3D to 2D) projection of the meridian projection (earth flattened at the central meridian) onto the plane of a solistial colure (the great circle of the celestial sphere, which passes through the poles and the two solstices: the first point of Cancer and the first point of Capricorn). This allowed for the multiple overlay of projections by placing the celestial sphere over the local sky and pivoting it on the celestial pole.
Working of the Astrolabe
An astrolabe consists of several independently rotating discs held together at the center. On the top and bottom are two rotating bars. The core principle that makes an astrolabe work is called stereographic projection. The idea is to represent the three-dimensional image of the night sky that surrounds us onto a flat, two-dimensional surface. If we imagine that the Earth is at the center of the universe, and surrounding it is the sky projected onto a sphere each point on the sphere (both celestial and earth itself) can then be mapped on to a flat surface, along with mapping the orbits.
An important characteristic of the stereographic projection is the fact that it maps circles to circles and preserves angles. This made it possible to tackle problems involving spherical triangles, for instance, using planar trigonometry, which simplified matters considerably. In thus way, the North Star corresponds to the center of the device.
The primary use of the astrolabe is to find the angular height of an object in the sky. To determine the height of an object, the astrolabe is raised to eye level, holding it by the ring, and pointing the alidade on the back of the astrolabe in the direction of the object. Then applying the similarity property of triangles, the height can be calculated.
We can apply similarity of triangles to lay out the equation x/n = h/d , which gives us the height h of the object h = xd*n.
The astrolabe is also useful for mapping a projection radius to allow for measurements along known lines on the celestial sphere. In the figure below, point p lies on the Tropic of Cancer and a line can be drawn to connect this to the south pole.
The stereographic projection of the Tropic of Cancer is given by the intersection of this line with the equatorial plane (imaginary flat surface passing through the equator) at point q. The radius of projection is then denoted by x. Then, we draw a line from the center of the Earth to p. The length of this line will be the same as radius r (property of a sphere). We then draw the radius of the Tropic of Cancer and intersect it with a straight line going through the south pole and the origin. This creates the triangles shown in the figure. We can then solve for x by using similarity property of triangles
which can be cross-multiplied to give
which can be further simplified to
and this gives us the radius of the circle x which can represent the tropic of cancer on the astrolabe.
For Muslims, finding the time of the day is critical as it allows for identification of the right time for prayer. Religious practice requires praying five times a day (Fajr, Dhuhr, Asr, Maghrib, Isha). Astrolabes were very important tools for believers who were not within hearing distance of a mosque and could not rely on the call of the mufti to figure out prayer times. Using the astrolabe, the time of day could be found through one of the three following methods:
- The altitude of the Sun or a bright star was determined using the back of the instrument. The astrolabe was held above eye level using the ring above the crown. The alidade was then rotated until the Sun’s shadow or the star itself was visible through the sights on the alidade. This gave the altitude of the star in question.
- Using the Sun’s altitude, its position on the ecliptic was found by setting the alidade to align with the date and reading the longitude on the zodiac scale. On the front of the astrolabe, the rule was rotated until it crossed the ecliptic at the Sun’s current longitude. The point where the rule crossed the ecliptic was the Sun’s current position.
- The rete and rule were then rotated together until the Sun or star pointer was at the measured altitude. This resulted in the the rule pointing to the solar time on the limb.
The arc of discovery in the field of nautical astronomy extends from the earliest mathematical calculations in India to the studies in Haroon al-Rashid’s Baghdad, and finally to work in al-Andalus. A combination of the study of astronomy with practical tool-building craft led to the development of the Mariner’s astrolabe. This device was perfected by the innovators in muslim al-Andalus in the 10th century CE by astronomer artisans like Abū Ishāq Ibrāhīm al-Zarqālī. The astrolabe not only allowed for time and direction readings, but in a sense allowed people to hold the heavens in their hand. This notion of capturing nature in a device also led to thinking around humans beginning to crack the mysteries of nature. The universe was not after all a mystic, unknowable creation, but a system bounded by rules. Studying and analyzing the rules allowed for ways to map the universe itself
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