The Role of Muslims in the Formation and Development of Sciences (Part 28)
The Role of Arab and Muslim Scholars in Trigonometry
The main goal of trigonometry is to measure large areas and long distances indirectly, such as measuring pyramids, or any dimension that is difficult to access, such as the length between two mountains and dimensions in the field of navigation.
The word “trigonometry” means measuring heights in all languages, and trigonometry is known as the science of ratios, because it is based on various relationships resulting from the ratio between the sides of a triangle. In our opinion, this definition is an acceptable definition that is sufficient in both brevity and accuracy of expression.
The role of Greek scholars in the science of trigonometry, headed by Abraxas, who is one of the greatest scholars of physics and astronomy, and Ptolemy, the author of the book “Al-Majisti”, was only to collect information that would help their astronomy and observations and to apply their geometric theories, because they believed that trigonometry was the only science that could be used to prove some of their geometric discoveries.
But Indian scholars have taken great steps in this field and they should be given credit for discovering and measuring the “sine of an angle”, which is one of the most important topics in the science of trigonometry. Therefore, the reader should not forget that Indians have played a prominent role in the development of trigonometry and, contrary to the claims of Western scientists who say that the Greeks were the scientific founders of this field, the truth is something else.
Muslim scholars organized the achievements of Indian and Greek scholars in trigonometry, combining their knowledge and adding new information to it in order to improve this science. Therefore, it is not surprising that historians of science believe that trigonometry is an Arabic and Islamic science, as is the case with geometry and its relationship with Greek scientists.
Muslim scholars who specialized in mathematics, including arithmetic, algebra, and geometry, were very interested in trigonometry in order to apply their mathematical theories. They also had a strong desire to learn about previous civilizations, both Western and Eastern, so much so that they collected a lot of information about trigonometry and translated most of the Indian and Greek sciences in this field into Arabic.
In 154 AH (771 AD), the Abbasid Caliph Abu Ja’afar Mansur encouraged translators to pay attention to the science of astronomy, which included trigonometry, and devoted a lot of money and attention to this work. Similarly, scholars translated the book “Al-Mujisti”, which was a Greek encyclopedia on astronomy, into Arabic. This book included topics such as: the spherical of the world, the fixedness of the Earth at the center of the universe according to the belief of that time, the constellations, the division of different countries, the movement of the sun, the spring and autumn equinoxes, night and day, the movement of the moon and its calculations, eclipses, and fixed stars and moving planets.
The Abbasid Caliph, Ma’mun, ordered the construction of an observatory in the north of Baghdad and another on Mount “Qasioun” in Damascus. Ma’mun also mentioned the use of observational instruments and asked the scholars of the “Bayt Al-Hekmah” in Baghdad to research the science of trigonometry. One of the important results obtained during the caliphate of Ma’mun was the measurement of the circumference of the Earth, which was estimated at about 41,248 kilometers, a value that is very close to the results obtained in the present era using electronic calculations.
It seems that the science of trigonometry progressed slowly because of the dominance of astronomy. Arab and Muslim scholars tried their best to separate this new science from its dependence on astronomy, but it emerged as a science independent of astronomy only in 854 AH (1450 AD).
Undoubtedly, the world’s scientists could not make any further progress in trigonometry until the end of the 13th AH (9th AD) century. At that time, new concepts of analytic quantities were created, and trigonometry became a science that was used not only for solving trigonometry, but also in other fields.
The great historians of this science, such as Florian Kajuri, George Sarton, David Eugene Smith and others, concluded that all the works of “Regiomontanus” (a German scientist 1436-1476 AD) were based on the works and research of Arab and Muslim scholars and that many of his research, especially in the science of trigonometry, were taken from them. Unfortunately, “Regiomontanus” attributed many trigonometric theories invented by Arab and Muslim scholars to his name, and some Western scientists also accepted this and introduced him as the greatest scientist in history in the field of “trigonometry”.
In short, Muslim scholars had many innovations in the science of trigonometry. They should be credited with recognizing the relationships between sine, tangent, cotangent and other similar equations, concepts that are used today in our school and university textbooks, but unfortunately, we often do not know where these concepts came from, and we assume that they were taken from Western scholars. But in fact, these achievements belong to Arab and non-Arab researchers who worked day and night to reveal the truth and give every right to its owner. Therefore, the science of trigonometry is an Islamic science.
One of the most important modern sciences that has had a great impact on scientific discoveries and inventions is the science of logarithms, which is an important tool for simplifying many natural, engineering and industrial research.
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