MATHEMATICAL SCIENCE

T1o Spain then came the small number of foreigners who were tormented by the desire to know. Gerbert (born in Auvergne about 930, elected pope in 999, under the name of Silvester II, died in 1003), so celebrated for his adventures, his learning, and his labours, after going through all the schools of France, Italy, and Germany without being able to satisfy the passion for instruction which possessed him, came finally to Spain to seek that physical and mathematical knowledge which raised such admiration in France, Germany, and Italy, whither he returned to spread them, that the prodigies of his learning could only be explained by the accusation of having delivered himself over to the devil.

2Gerbert is unanimously credited with having been the first to introduce the use of Arabic figures into these countries, and with having added some elementary notions of algebra to the calculations of arithmetic. He also passes as the first constructor of clocks. Whether, as most of his biographers affirm, Gerbert pursued his studies as far as the homes of the Arabs in Cordova and Seville, or whether he only made a long sojourn in Catalonia and associated with the scholars of that country, as is witnessed to by his collection of _Epistles_, addressed in great part to Catalans like Borrell, count of Barcelona, Ayton, Joseph, and Lupit, it is none the less certain that Gerbert learned all he knew from the Arabs, and that that knowledge, so prodigious as to appear supernatural, was, as William of Malmesbury says, “stolen from the Saracens.”

3His example and his success roused other foreigners to come and glean, where he had made so ample a harvest. The German Hermannus-Contractus (who died in 1054), author of the book, _De Compositione Astrolabii_; the English Adelard, who translated the first Arabic _Euclid_ into Latin (about 1130); the Italian Campano of Novara, who published a _Theory of the Planets_; Daniel Morley; Otto of Freising; with Hermann the German; Plato of Tivoli; Gerard of Cremona, who translated at Toledo itself, Alhazen; Avicenna, Rhazes, Albucasis, and even Ptolemy’s _Almagest_, not from the Greek, but from the Arabic--that Gerard of Cremona of whom it was said: “At Toledo he lived, Toledo he raised to the stars”--all went in succession to gather in Spain the elements of mathematics, physics, and astronomy, which they carried thence to their compatriots.

4Montucla[k] not only says that “the Arabs were long the sole depositaries of learning, and that it is to their commerce that we owe the first rays of light which came to chase away the darkness of the eleventh, twelfth, and thirteenth centuries”; he adds that “during this period, all who obtained the greatest reputation in mathematics had been to acquire their knowledge amongst the Arabs.” It is asserted that all the authors who wrote on the exact sciences before the fifteenth century did nothing but copy the Arabs, or, at the most, enlarge upon their lessons. Such were the Italian Leonardo da Pisa, the Polish Vitellio, the Spaniard Raymond Lully, the English Roger Bacon, and finally the French Arnauld de Villeneuve, who is credited with having discovered spirits of wine, oil of turpentine, and other chemical preparations.

5During the same period, the whole of European geography was limited to the _Seven Climates_ of Edrisi, and, in the seventeenth century, when correcting by Abu Ishak Ibrahim ben Yahya certain geographical errors, Abraham Hinckelmann was able to say: “The greatest assistance and illumination for posterity we owe to Arabism.” As to the famous _Astronomical Tables_ of Alfonso X, they, like his book on _Armillaries_ or celebrated spheres, only sum up the discoveries of the Arabs previous to the thirteenth century. It was from their works that all his learning was drawn by that celebrated monarch, who received the surname of the Wise (or learned), and who did indeed effect some advancement in science, between the system of Ptolemy and that of Copernicus. The _Alphonsine Tables_ are borrowed from the various _Ziji_ or tables of the Arab astronomers, and reproduce their form and substance.

6When Louis XIV had a degree of the meridian measured geometrically, in order to determine the size of the earth, he doubtless did not know that five centuries before, the caliph Al-Mamun had ordered the same operation to be performed by his astronomers at Baghdad. In the Middle Ages, according to Bailly,[l] “the first step taken towards the revival of learning was the translation of Alfergan’s _Elements of Astronomy_.” That famous Spanish rabbi, Aben-hezra (or Esdra), who was surnamed the Great, the Wise, the Admirable, on account of his book on _The Sphere_, was born at Toledo, in 1119, and had been a disciple of the Arabs in astronomy. He spread his masters’ lessons throughout Europe.

7It was from Albategnius, more than from Ptolemy, that Sacrobosco (John of Holywood) had drawn the materials for his book _De Sphera Mundi_; it was in Albategnius, too, that the commentator on that great astronomer, Regiomontanus (Johann Müller, of Königsberg, _Regius Mons_), had found the first notion of tangents. It was from Alhazen’s _Twilight_ that the illustrious Kepler took his ideas of atmospheric refraction; and it may be that Newton himself owes to the Arabs, rather than to the apple in his orchard at Woolsthorpe, the first apperception of the system of the universe; for Muhammed ben Musa (quoted in the _Bibliot. arab.

8Philosophorum_) seems, when writing his books on _The Movement of the Celestial Bodies_ and on _The Force of Attraction_, to have had an inkling of the great law of general harmony.