The theory of permanent Muslim-Christian enmity, though it flourishes in the caves of Tora Bora and parts of the American academy, was long ago exploded by the historians. In this clear and well-written book, Jonathan Lyons delves into all sorts of musty corners to show how Arabic science percolated into the Latin world in the middle ages and helped civilise a rude society.

He tells how Arab advances in astronomy, mathematics, engineering, navigation, geography, medicine, architecture, chemistry, gardening, finance and verse passed into Europe by way of the Crusader kingdoms, Sicily and Spain and prepared the ground for both the Renaissance and the scientific advances of the 16th and 17th centuries. This infiltration of ideas has left traces in our language, from alcohol, algebra and algorithm to the Arabic names of the bright stars Betelgeuse and Aldebaran.

With the fall of the Roman empire in the west, Europe lost touch with much of its classical inheritance and was isolated by the Arab invasions from the Byzantine empire where some ancient learning survived. Lyons recounts how early medieval Christendom was unable accurately to measure the time of day for monastic offices, or fix the date of Easter, while dogmatic schemes of scripture and hierarchy left little scope for natural science. Aristotle's influence was confined to the logic and rhetoric of the schools. Bishop Isidore of Seville promulgated the idea that the Earth was flat.

In contrast, when the Arabs conquered Iraq in the first half of the seventh century AD, they came upon living schools of Hellenistic learning in natural science and medicine, along with Indian mathematics and astronomy that had come by way of Iran. Systematic reasoning, driven out of Muslim jurisprudence in favour of precedents from the Prophet's life and conduct, found a new field of inquiry in ancient geography and cosmology. After the founding of Baghdad in AD762, the Abbasid caliphs established a library and a team of translators at the Beit al-Hikma, the "House of Wisdom" of Lyons's title.

A famous early catalogue of Arabic books known as the Fihrist lists as many as 80 Greek authors in Arabic translation, chief among them Aristotle, the mathematician Euclid and the medical philosophers Hippocrates and Galen. For this natural philosophy, the Arabs coined the word falsafa, and called its practitioners falasifa. The great Arabic philosophers such as Ibn Sina in Iran (known in Latin Europe as Avicenna, who died in 1037) and Ibn Rushd in Spain (Averroes, who died in 1198) found ways of inserting Aristotelian natural philosophy and Ptolemaic cosmology into a scriptural monotheism, which was precisely what the Latins needed. As Lyons writes, "Arabic replaced Greek as the universal language of scientific inquiry".

He begins with a vivid contrast. In 1109, 10 years after the Crusaders sacked Jerusalem and put Muslims, Jews and eastern Christians to the sword, Adelard of Bath, a well-born scholar, set off for Antioch not to kill Muslims but, as he put it, "to investigate the studies of the Arabs" (studia arabum). As so often in medieval biography, a few "facts" are made to work hard, and some scholars (though not Lyons) doubt Adelard ever mastered Arabic. Nonetheless, he is thought to have taken part in translations from Arabic of Euclid's geometric system, the elements, and the astronomical tables of al-Khwarizmi, and composed such original works as On the Use of the Astrolabe. For Lyons, Adelard is the "first man of science". Such was the prestige of Arabic learning in England, according to a startling passage here, that partisans of King Henry II, during the quarrel with Rome over Thomas Becket, threatened the king would convert to Islam.

The new learning spread. By the middle of the 12th century, Euclid and Pythagoras are arrayed with the Virgin on the west front of Chartres cathedral. Lyons summons up a world of itinerant scholars such as Michael Scot, who (in the words of one monk) "in Paris seek liberal arts, in Orléans classics, at Salerno medicine, at Toledo magic, but nowhere manners and morals". Scot found his way to the Arabising court of one of the "baptised Sultans", the Emperor Frederick II, where he translated Arabic commentaries on Aristotle and helped promote the great mathematician Leonardo of Pisa. Leonardo, generally known as Fibonacci, gave a systematic account of the Arab/Indian numerical system and "the sign 0, which the Arabs call zephyr", or rather sifr - and which we call the zero.

For the orthodox, these men reeked of brimstone, and Dante placed Michael with the wizards in the eighth circle of hell. St Thomas Aquinas brought a measure of peace to the church, but the systems of Aristotle and Ptolemy became rigid and brittle till they shattered in the Copernican revolution of the 16th century.

Why Muslim science and medicine remained in their medieval state in certain regions well into our lifetimes belongs to another book. For all Lyons's wonder and admiration, the falasifa were always out of the mainstream of Muslim thought; they are best understood as a sort of sect, like the Shia, and were just as vulnerable to charges of heresy. The only small blemish in this fine book is that Lyons has printed a beautiful page of al-Biruni's Arabic treatise on mathematics back to front, so the text can only be read in a mirror.

 James Buchan's latest novel is The Gate of Air, published by Maclehose Press.