Ibn Yunus

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Abu al-Hasan ‘Ali ibn ‘Abd al-Rahman ibn Ahmad ibn Yunus al-Sadafi al-Misri (Arabic: ابن يونس; c. 950 – 1009) was an important Egyptian Muslim astronomer and mathematician,[1][2][3][4] whose works are noted for being ahead of their time, having been based on meticulous calculations and attention to detail.

The crater Ibn Yunus on the Moon is named after him.


Information regarding his early life and education is uncertain. He was born in Egypt between 950 and 952 and came from a respected family in Fustat. His father was a historian, biographer, and scholar of hadith, who wrote two volumes about the history of Egypt—one about the Egyptians and one based on traveller commentary on Egypt.[5] A prolific writer, Ibn Yunus’ father has been described as “Egypt’s most celebrated early historian and first known compiler of a biographical dictionary devoted exclusively to Egyptians”.[6] His great-grandfather had been an associate of the noted legal scholar Imam Shafi.

Early in the life of Ibn Yunus, the Fatimid dynasty came to power and the new city of Cairo was founded. In Cairo, he worked as an astronomer for the Fatimid dynasty for twenty-six years, first for the Caliph al-Aziz and then for al-Hakim. Ibn Yunus dedicated his most famous astronomical work, al-Zij al-Kabir al-Hakimi, to the latter.

As well as for his mathematics, Ibn Yunus was also known as an eccentric and a poet.[7]



In astrology, noted for making predictions and having written the Kitab bulugh al-umniyya (“On the Attainment of Desire”), a work concerning the heliacal risingsof Sirius, and on predictions concerning what day of the week the Coptic year will start on.


Ibn Yunus’ most famous work in Islamic astronomy, al-Zij al-Kabir al-Hakimi (c. 1000), was a handbook of astronomical tables which contained very accurate observations, many of which may have been obtained with very large astronomical instruments. According to N. M. Swerdlow, the Zij al-Kabir al-Hakimi is “a work of outstanding originality of which just over half survives”.[8]

Yunus expressed the solutions in his zij without mathematical symbols,[9] but Delambre noted in his 1819 translation of the Hakemite tables that two of Ibn Yunus’ methods for determining the time from solar or stellar altitude were equivalent to the trigonometric identity {\displaystyle 2\cos(a)\cos(b)=\cos(a+b)+\cos(a-b)}[10] identified in Johannes Werner’s 16th-century manuscript on conic sections. Now recognized as one of Werner’s formulas, it was essential for the development of prosthaphaeresis and logarithms decades later.

Ibn Yunus described 40 planetary conjunctions and 30 lunar eclipses. For example, he accurately describes the planetary conjunction that occurred in the year 1000 as follows:

A conjunction of Venus and Mercury in Gemini, observed in the western sky: The two planets were in conjunction after sunset on the night [of Sunday 19 May 1000]. The time was approximately eight equinoctial hours after midday on Sunday … . Mercury was north of Venus and their latitude difference was a third of a degree.[11]

Modern knowledge of the positions of the planets confirms that his description and his calculation of the distance being one-third of a degree is exactly correct. Ibn Yunus’s observations on conjunctions and eclipses were used in Richard Dunthorne and Simon Newcombs’ respective calculations of the secular acceleration of the moon.[11][12]


Recent encyclopaedias[13] and popular accounts[14] claim that the tenth century astronomer Ibn Yunus used a pendulum for time measurement, despite the fact that it has been known for nearly a hundred years that this is based on nothing more than an error made in 1684 by the Savilian Professor of Astronomy at Oxford Edward Bernard.[15]

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Died  (Egypt), 1009

Ibn Yūnus was one of the greatest astronomers of medieval Islam and the most important astronomer of medieval Egypt. Unfortunately, nothing of consequence is known about his early life or education. As a young man he witnessed the Fatimid conquest of Egypt and the founding of the new city of Cairo in 969. In the period up to the reign of Caliph al‐ʿAzīz (975–996), he made astronomical observations that were renewed by order of Caliph al‐Ḥākim, who succeeded al‐ʿAzīz in 996 at the age of 11 and was much interested in astrology. Ibn Yūnus’s recorded observations continued until 1003.

Ibn Yūnus’s major work was a monumental zīj or astronomical handbook with tables. Three substantial fragments of it survive in three manuscripts in Leiden, Oxford, and Paris. The Ḥākimī Zīj, dedicated to the caliph, is distinguished from all other extant zījes by beginning with a list of observations made by Ibn Yūnus and others made by some of his predecessors. Despite his critical attitude toward these earlier scholars and his careful recording of their observations and some of his own, he completely neglects to describe the observations that he used in establishing his own planetary parameters; nor does he indicate whether he used any instruments for these observations. In view of the paucity of this information, it is remarkable that the statement that Ibn Yūnus worked in a “well‐equipped observatory” is often found in popular accounts of Islamic astronomy. A. Sayılı has shown how this notion gained acceptance in Western literature.

Ibn Yūnus’s Zīj was intended to replace the Mumtaḥan Zīj of Yaḥyā ibn Abī Manṣūr, prepared for the ʿAbbāsid Caliph Maʾmūn in Baghdad almost 200 years earlier. When reporting his own observations, Ibn Yūnus often compared what he observed with what he had computed using the Mumtaḥan tables.

The observations Ibn Yūnus described are of conjunctions of planets with each other and with Regulus, solar and lunar eclipses, and equinoxes; he also records measurements of the obliquity of the ecliptic (Chapter 11) and of the maximum lunar latitude (Chapter 38).

In spherical astronomy (Chapters 12–54), Ibn Yūnus reached a very high level of sophistication. Although none of the several hundred formulae that he presents is explained, it seems probable that most of them were derived by means of orthogonal projections and analemma constructions, rather than by the application of the rules of spherical trigonometry that were developed by Muslim scholars in Iraq and Iran during the 10th century.

The chapters of the Zīj dealing with astrological calculations (77–81), although partially extant in an anonymous abridgment of the work preserved in Paris, have never been studied. Ibn Yūnus was famous as an astrologer and, according to his biographers, devoted much time to making astrological predictions.

Ibn Yūnus’s second major work was part of the corpus of spherical astronomical tables for timekeeping used in Cairo until the 19th century. It is difficult to ascertain precisely how many tables in this corpus were actually computed by Ibn Yūnus. Some appear to have been added in the 13th and 14th centuries. The corpus exists in numerous manuscript sources, each containing different arrangements of the tables or only selected sets of tables. The best copies are two manuscripts now in Dublin and Cairo. In its entirety the corpus consists of about 200 pages of tables, most of which contain 180 entries each. The tables are generally rather accurately computed and are all based on Ibn Yūnus’s values of 30° 0′ for the latitude of Cairo and 23° 35′ for the obliquity of the ecliptic. The main tables in the corpus display the time since sunrise, the time remaining to midday, and the solar azimuth as functions of the solar altitude and solar longitude; entries are given for each degree of both arguments, and each of the three sets contains over 10,000 entries. The remaining tables in the corpus are of spherical astronomical functions, some of which relate to the determination of the five daily prayers of Islam. The impressive developments in astronomical timekeeping in 14th‐century Yemen and Syria, particularly the tables of Abū al‐ʿUqūl for Taiz and Khalīlī for Damascus, also owe their inspiration to the main Cairo corpus.

It is clear from a contemporaneous biography of Ibn Yūnus that he was an eccentric, careless, and absent‐minded man who dressed shabbily and had a comic appearance. One day in the year 1009, when he was in good health, he predicted his own death in 7 days. He attended to his personal business, locked himself in his house, and washed the ink off his manuscripts. He then recited the Quran until he died – on the day he had predicted. According to his biographer, Ibn Yūnus’s son was so stupid that he sold his father’s papers by the pound in the soap market.