Mention might be made of about forty mathematicians and astronomers who wrote books on these subjects. The best of them, such as Al-Farghani (Alfraganius) and others, lived at the court of Mamun, who built an astronomical observatory in Baghdad and another near Damascus, on Mount Kasiun. He caused also two degrees of the meridian to be measured on the plain of Sinjar, so as to ascertain the circumference of the earth with more precision. In A.D. 824 there were held philosophical disputations in his presence. Al-Farghani was the author of an introduction to astronomy, which was printed by Golius at Amsterdam in 1669, with notes.

Between the years A.D. 877 and 929 there flourished the famous calculator and astronomer, Muhammad bin Jaber al Battani, Latinized as Albategnius. He was the author of the astronomical work entitled 'The Sabæan Tables,' and adopted nearly the system and the hypothesis of Ptolemy, but rectified them in several points, and made other discoveries, which procured him a distinguished place among the scholars whose labours have enriched astronomical science. Al-Battani approached much nearer to the truth than the ancients as far as the movements of the fixed stars are concerned. He measured the greatness of the eccentricity of the solar orbit, and a more correct result cannot be obtained. To the work containing all his discoveries he gave the name of 'As-Zij-as Sabi,' which was translated into Latin under the title 'De Scientiâ Stellarum.' The first edition of it appeared at Nuremberg in A.D. 1537, but it is believed that the original work is in the library of the Vatican. He was classed by Lalande among the forty-two most celebrated astronomers of the world. He died A.D. 929-930.

Another celebrated astronomer, Ali bin Yunis, was a native of Egypt, and appears to have lived at the court of the demented tyrant of Egypt, Al-Hakim bramrillah, and under his patronage to have composed the celebrated astronomical tables called, after his name, 'The Hakimite Tables.' Ibn Khallikan states that he had seen these tables in four volumes, and that more extensive ones had not come under his notice. These tables were considered in Egypt to be of equal value to those of the astronomer Yabya bin Ali Mansur, who had in A.D. 830, by order of the Khalif Mamun, undertaken astronomical observations both at Baghdad and Damascus. Ibn Yunis spent his life in the preparation of astronomical tables and in casting horoscopes, for it must be remembered that with the Muslims astronomy and astrology were synonymous, and their most learned astronomers were also their most skilful astrologers. His character for honesty was highly esteemed, and he was also well versed in other sciences, and displayed an eminent talent for poetry. He died A.D. 1009, and is not to be confounded with his father, Ibn Yunis, the historian, who died A.D. 958.

Yet another name must be mentioned, viz., the Spanish-Arab astronomer Ibn Abd-ar-Rahman Es-Zerkel, Europeanized as Arzachal. He first resided at Toledo, at the court of its sovereign, Mamun, for whom he made an astrolabe, which he called in his honour the Mamunian. He then went to Seville, where he wrote for Motamid bin Abbad (A.D. 1069-1091) a treatise on the use of certain instruments. During his residence at Toledo he constructed two clepsydras, the waters of which decreased and increased according to the waning and growing of the moon, and these two basins were destroyed only in A.D. 1133 by Alphonse VI., when he took Toledo. Arzachal left a work on eclipses, and on the revolution of years, as well as the tables of the sky, to which the name of Toledan tables have been given. His writings, but especially the last, which must have been consulted by the editors of the Alphonsine tables, were never translated, and exist only in manuscript in libraries where but few scholars can consult them. Arzachal made many observations in connection with the sun, and was also the inventor of the astronomical instrument called after his name, Zerkalla. He died A.D. 1080.

Before leaving this subject it may be mentioned that Makkari, in his great encyclopædia of Spain, enumerates fifteen astronomers of Andalusia, all more or less known in their time. Also that Bedei-ul-Astrolabi and Ibn Abdul-Rayman distinguished themselves as makers of astronomical instruments, and inventors of new ones. While Arzachal was the greatest representative of Arab astronomy in the West, Umar Khayam, the astronomer, mathematician, freethinker, and poet, was its greatest representative in the East, in Persia, where he died A.D. 1123.

A great deal in Arabic literature has been written about grammar, and, until its principles were finally laid down and established, it was always a source of continual controversy between different professors and different schools. Abul Aswad ad-Duwali has been called the father of Arabic grammar. It is said that the Khalif Ali laid down for him this principle: the parts of speech are three, the noun, the verb, and the particle, and told him to form a complete treatise upon it. This was accordingly done; and other works on the subject were also produced, but none of them are apparently now extant. Muhammad bin Ishak has stated that he saw one of them, entitled 'Discourse on the Governing and the Governed Parts of Speech;' and the author of the 'Fihrist' also alludes to this work. Abul-Aswad died at Busra in A.D. 688, aged eighty-five, but some years later his two successors in this branch of literature (viz., Al-Khalil and Sibawaih) far surpassed him in every way.

Al-Khalil bin Ahmad, born A.D. 718, was one of the great masters in the science of grammar, and the discoverer of the rules of prosody, which art owes to him its creation. He laid the foundation of the language by his book 'Al-Ain' (so called from the letter with which it begins), and by the aid he afforded thereby to Sibawaih, whose master he was, in the composition of his celebrated grammatical work known by the name of 'The Book.' In the work called 'Al-Ain,' Khalil first arranged the stock of Arabic words, dealing with the organ of speech and the production of sounds, and then dividing the words into classes, the roots of which consisted of one, two, three, four, or five letters. It is still a matter of dispute whether the book 'Al-Ain' was wholly composed by Khalil himself, or completed in course of time by his pupils. A copy of this celebrated lexicon and work on philology is in the Escurial Library. Khalil also wrote a treatise on prosody, and other works on grammar, and a book on musical intonation. He died A.D. 786, at Busra. 'Poverty,' he said, 'consists not in the want of money, but of soul; and riches are in the mind, not in the purse.'

Sibawaih, the pupil of Khalil, has been called the father of Arabic lexicography, and the lawgiver of Arabic grammar. Ibn Khallikan says that he was a learned grammarian, and surpassed in this science every person of former and later times. As for his 'Kitab,' or 'Book,' composed by him on that subject, it has never had its equal. The great philologist and grammarian, Al-Jahiz, said of the book of Sibawaih, that none like it had ever been written on grammar, and that all writers on this subject who had succeeded him had borrowed from it. When Al-Kisai was tutor to the prince Al-Amin, son of Harun-ar-Rashid, Sibawaih came to Baghdad, and the two great grammarians (Sibawaih, the chief of the school of Busra, and Al-Kisai, chief of the school of Kufa) had a long dispute about a certain expression of Arabic speech, and an Arab of the desert was called in to arbitrate between them. The man first decided in favour of Sibawaih, but when the question was put in another form, the Bedouin asserted that Kisai was right. As Sibawaih considered that he had been unjustly treated in the matter, he left Baghdad for good. The year of his death has been given differently by various authors, the earliest date being A.D. 787, and the latest A.D. 809.

The most celebrated grammarians of the third century of the Hijrah (A.D. 816-913) were Al-Mubarrad, who died A.D. 898, and Thalab, who died A.D. 903. They were also great antagonists to each other. Al-Mubarrad, the author of thirty works, was the chief of the school of Busra, and Thalab of that of Kufa, both founded during the preceding century by Sibawaih and Kisai. Thalab was the first collector of books in Islam, and those left by him were very valuable.

Mention must also be made of Al-Farra, the grammarian, and distinguished by his knowledge of grammar, philology, and various branches of literature. He died A.D. 822, at the age of sixty-three, and preceded both Mubarrad and Thalab, the latter of whom used to say: 'Were it not for Al-Farra, pure Arabic would no longer exist; it was he who disengaged it from the ordinary language and fixed it by writing.' At the request of the Khalif Al-Mamun he drew up in two years a most elaborate work, which contained the principles of grammar, and all the pure Arabic expressions which he had heard. It was entitled 'Al-Hudûd' (the Limits or Chapters), and directly it was finished he commenced another in connection with the Koran, which is spoken of as a most wonderful production. He wrote besides several other works on grammar, and acted as tutor to the two sons of the Khalif Mamun.