Ibn Yunus, full name, Abu'l-Hasan 'Ali Ibn 'Abd al-Rahman Ibn Ahmad Ibn Yunus al-Sadafi) (950-1009) was an important Arab astronomer/astrologer, whose astronomical works are noted for being ahead of their time, having been based on almost modern-like meticulous calculations and attention to detail. His full name was Abu'l-Hasan 'Ali Ibn 'Abd al-Rahman Ibn Ahmad Ibn Yunus al-Sadafi.
He demonstrated the formula:
cos(a)cos(b) = 1 / 2[cos(a + b) + cos(a − b)]
He was born in Egypt, though the date of birth is uncertain, as is information regarding his early life and education. He came from a respected family in Fustat: his father was a historian and scholar of hadith, and his great grandfather had been an associate of the noted legal scholar al-Sahfi.
Early in his life, the Fatimid dynasty come 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 to the latter, al-Zij al-Hakimi al-kabir. This handbook of astronomical tables contained very accurate observations, many of which may have been obtained with very large astronomical instruments.
One remarkable aspect of his turn of the millennium calculations is that he took atmospheric refraction of the Sun's rays at the horizon into account in his observations. His figure of forty minutes of arc between the "true" horizon and the observed horizon is one of the oldest recorded values for this quantity. In the nineteenth century, Simon Newcomb found his observations reliable enough to use them in determining the secular acceleration of the moon.
Ibn Yunus is also thought to have been a poet, and to have used very large instruments in making his observations, though neither assertion is certain. Two of the instruments said to have been used by him include an armillary sphere having nine rings, each of which was said to have weighed 2,000 pounds, and large enough for a horse and rider to pass through; and a copper astrolabe three cubits across.
He was also an astrologer, noted for making predictions and having written the Kitab bulugh al-umniyya ("On the Attainment of Desire"), a work concerning the heliacal risings of Sirius, and on predictions concerning what day of the week the Coptic year will start on.
It is alleged that he predicted his own death, seven days prior to the event, and without any outward sign of ill health. He also invented the pendulum.