Mathematics and Astronomy

 Mathematics:

Research into mathematics, especially algebra, expanded among the Arabs, and the discovery of algebra is attributed to the Arabs. However, its origins had been known for a long time. Nevertheless, the Arabs completely transformed algebra, and they are credited with its application to geometry.

Algebra became so widespread among the Arabs that Muhammad ibn Musa wrote a comprehensive book on it at the behest of al-Ma’mun in the early ninth century AD. It was from this translation that Europeans acquired their first knowledge of algebra, a long time later.

I will limit myself to mentioning the most important mathematical works of the Arabs briefly, because explaining them in detail would involve entering into technical details. I say that the Arabs were the ones who introduced the tangent into trigonometry, established sines in place of chords, applied algebra to geometry, solved cubic equations, delved deeply into the study of conics, and transformed spherical trigonometry by reducing the solution of equilateral triangles to a few basic theorems that would form its basis.

The introduction of the tangent into trigonometry is of great importance. Listen to what Monsieur Challe said in his book: “A Summary of the History of the Principles of Geometry”.

This blessed scientific revolution, which led to the introduction of those heavy, complex methods in the sine and the full sine, did not affect the scientists of the modern centuries until five hundred years had passed, with the call of Reggio Montanus, even though Copernicus, who appeared about a century later, was ignorant of that revolution.

 Astronomy among the Arabs:

Astronomy was one of the first subjects studied in Baghdad, and not only the Arabs studied its issues, but their heirs also followed their path, especially the grandson of Timurlane, Ulugh Beg, famous for his Ziyāj, who can be considered the last example of the Baghdad school, whose prosperity lasted for seven centuries (750 AD – 1450 AD) .

Baghdad was an important center for astronomical research, but it was not the only center for these researches. There were many observatories in the countries extending from Central Asia to the Atlantic Ocean, including those in Damascus, Samarkand, Cairo, Fez, Toledo, Cordoba, etc.

The most important schools of astronomy were those in Baghdad, Cairo, and Andalusia. Let us say a word about each one of them: The Abbasid Caliphs, since they made Baghdad, which was established in 762 AD, the capital of their state, encouraged the study of astronomy and mathematics, and the translation of what Euclid, Archimedes, and Ptolemy wrote, and the translation of all the Greek books on those sciences, and they summoned scholars who were somewhat famous to their court.

The Baghdad Astronomical School, during the time of Harun al-Rashid, and especially during the time of his son al-Ma’mun (814-833 AD) , carried out important work. The collection of observations made in the observatories of Baghdad and Damascus was combined in the book “Al-Zij al-Musahah”, the loss of which we regret. However, we can know the accuracy of the observations contained in this book from the great accuracy with which the deviation of the sun’s azimuth was determined at that time. The declination figure, as verified in it, was 23 degrees, 33 minutes, and 52 seconds, that is, equal to the present figure.

The observation of the equinox by the Arabs led to their exact determination of the length of the year. The Arabs proceeded to measure the meridian, which was not achieved until a thousand years later. They achieved this measurement by calculating the distance between the starting point from which the observers set out and the ending point, where a difference of one degree in the elevation of the pole appeared. We do not know the result because we do not know the correct measure of the unit of length they agreed upon. However, we rule out the possibility that the number they arrived at was completely correct after considering the shortness of that line. We mention among the other works of the astronomers of the Baghdad School the calendars they established for the positions of the planets and their exact determination of the precession of the equinoxes.

The names of some of the astronomers of that time have come down to us, the most famous of whom is Al-Battani, who lived in the ninth century and died in 929 AD. He was as important among the Arabs as Ptolemy was among the Greeks. His book, “Zij al-Sabi,” contained the astronomical knowledge of his time, just as Ptolemy’s book did. The original text of his Zodiacs has not come down to us, and Europe only knew it in its unfortunately distorted Latin translation. The famous Lalande placed Al-Battani among the twenty astronomers who were considered the most famous astronomers in the world.

Amagor and his son, who made observations between 883 and 933 AD, compiled phases. The latter went so far as to shift the boundaries of the largest circle of lunar latitude, contrary to the astronomers who preceded him, especially Ptolemy. The study of this anomaly in the lunar latitude led to the discovery of a third lunar variation.

The three sons of Musa ibn Shakir, who lived in the ninth century AD, were also famous as astronomers. They determined the precession of the equinoxes with an accuracy unknown before them, and they created calendars for the positions of the wandering stars. They measured the latitude of Baghdad in the year 959 AD, recording it at 33 degrees and 20 minutes, a number that is correct to within approximately ten seconds.

The most famous of the many astronomers who appeared after them was Abu al-Wafa, who died in Baghdad in 998 AD. Among the things that this astronomer knew was the third lunar paradox to which we referred earlier, as it appeared from his important Arabic manuscript that Sidillo found a few years ago. He was struck by the deficiency in Ptolemy’s theory regarding the moon, so he investigated its causes and saw a third paradox, other than the central equation and the periodic paradox, which is known today as the paradox.

In fact, this discovery, which was attributed to Tycho Brahe six hundred years after Abu al-Wafa, is extremely important. Monsieur Sedillot used it as evidence that the Baghdad School had reached, at the end of the tenth century, the furthest point that astronomy could reach without spectacles and an observer.

Abu al-Wafa was equipped with sophisticated instruments. He observed the deviation of the sun’s azimuth in a quarter of a circle with a radius of twenty-one feet, which is a width that would be considered large in modern observatories.

The events that led, since the end of the tenth century, to the decline of the political authority of the caliphs in Baghdad caused a lull in studies, and arose from the division of the state and the conquests of, The Seljuks, the Crusades, the Mongol raids – the country was in turmoil, and Cairo and the great Arab universities of Andalusia took Baghdad’s place as the scientific leader of Islam.

However, Baghdad did not stop practicing science, and the Arabs’ love for science was so strong that wars, civil strife, and foreign raids did not prevent them from taking an interest in it. The Arabs attained such a breadth of knowledge that they greatly influenced their conquerors, and these conquerors immediately became their protectors.

Nothing creates more wonder than the victory of Arab civilization over the barbarism of all invaders, and the immediate graduation of these invaders from the school of the defeated Arabs. The work of the Arabs in the field of civilization continued long after the demise of their political power, and thanks to that, Baghdad’s scientific progress continued after it became the grip of foreigners. The Baghdad astronomical school continued to flourish until the middle of the fifteenth century AD, and did not stop publishing important treatises on astronomy. Among these was the publication of Al-Biruni, who was an advisor to Sultan Mahmud of Ghazna (1030 AD) , his article on “Correction of the Longitude and Latitude of the Inhabited Lands.” This Al-Biruni visited India and taught the Hindus what the Baghdad school had concluded. Among these was the order of Sultan Malik Shah the Seljuk, in 1079 AD, to carry out observations that resulted in the correction of the annual calendar to something better than the Gregorian calendar, which was made six hundred years later. This is because the Gregorian calendar leads to an error of three days every ten thousand years, although the calendar Arabic only leads to two days error in such a time.

The Mongols were no less concerned with scholars than the Seljuks. In 1259 AD, Hulagu Khan summoned the best Arab scholars to his court and established a large, exemplary observatory in Maragheh. Kublai Khan, Hulagu’s brother, soon transferred to China, which he had conquered, the books of the scholars of Baghdad and Cairo on astronomy. Today we know that the astronomers of China, especially Kushu Qing (1280) , derived their basic astronomical knowledge from those books. Therefore, we say that it was the Arabs who truly spread astronomy throughout the world.