Gerald J. Toomer | |
---|---|
Born | |
Nationality | British |
Academic background | |
Academic work | |
Discipline | History of science |
Institutions | Brown University Utrecht University |
Doctoral students | Jan Hogendijk |
Gerald James Toomer (born 23 November 1934) is a historian of astronomy and mathematics who has written numerous books and papers on ancient Greek and medieval Islamic astronomy. In particular,he translated Ptolemy's Almagest into English.
Formerly a fellow of Corpus Christi College,Cambridge University,he moved to Brown University as a special student in 1959 to study "the history of mathematics in antiquity and the transmission of these systems through Arabic into medieval Europe." [1] He joined the History of Mathematics department in 1963,became an associate professor in 1965,and was the chairman from 1980 to 1986. [2] [3]
Ḥasan Ibn al-Haytham, Latinized as Alhazen, was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq. Referred to as "the father of modern optics", he made significant contributions to the principles of optics and visual perception in particular. His most influential work is titled Kitāb al-Manāẓir, written during 1011–1021, which survived in a Latin edition.
Hipparchus was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. Hipparchus was born in Nicaea, Bithynia, and probably died on the island of Rhodes, Greece. He is known to have been a working astronomer between 162 and 127 BC.
Claudius Ptolemy was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importance to later Byzantine, Islamic, and Western European science. The first is the astronomical treatise now known as the Almagest, although it was originally entitled the Mathēmatikē Syntaxis or Mathematical Treatise, and later known as The Greatest Treatise. The second is the Geography, which is a thorough discussion on maps and the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the Apotelesmatika but more commonly known as the Tetrábiblos, from the Koine Greek meaning "Four Books", or by its Latin equivalent Quadripartite.
The zodiac is a belt-shaped region of the sky that extends approximately 8° north or south of the ecliptic, the apparent path of the Sun across the celestial sphere over the course of the year. The paths of the Moon and visible planets are within the belt of the zodiac.
The Almagest is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy. One of the most influential scientific texts in history, it canonized a geocentric model of the Universe that was accepted for more than 1,200 years from its origin in Hellenistic Alexandria, in the medieval Byzantine and Islamic worlds, and in Western Europe through the Middle Ages and early Renaissance until Copernicus. It is also a key source of information about ancient Greek astronomy.
Thābit ibn Qurra ; 826 or 836 – February 19, 901, was a mathematician, physician, astronomer, and translator who lived in Baghdad in the second half of the ninth century during the time of the Abbasid Caliphate.
Gerard of Cremona was an Italian translator of scientific books from Arabic into Latin. He worked in Toledo, Kingdom of Castile and obtained the Arabic books in the libraries at Toledo. Some of the books had been originally written in Greek and, although well known in Byzantine Constantinople and Greece at the time, were unavailable in Greek or Latin in Western Europe. Gerard of Cremona is the most important translator among the Toledo School of Translators who invigorated Western medieval Europe in the twelfth century by transmitting the Arabs' and ancient Greeks' knowledge in astronomy, medicine and other sciences, by making the knowledge available in Latin. One of Gerard's most famous translations is of Ptolemy's Almagest from Arabic texts found in Toledo.
Science in the medieval Islamic world was the science developed and practised during the Islamic Golden Age under the Umayyads of Córdoba, the Abbadids of Seville, the Samanids, the Ziyarids, the Buyids in Persia, the Abbasid Caliphate and beyond, spanning the period roughly between 786 and 1258. Islamic scientific achievements encompassed a wide range of subject areas, especially astronomy, mathematics, and medicine. Other subjects of scientific inquiry included alchemy and chemistry, botany and agronomy, geography and cartography, ophthalmology, pharmacology, physics, and zoology.
Theon of Alexandria was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's Elements and wrote commentaries on works by Euclid and Ptolemy. His daughter Hypatia also won fame as a mathematician.
Muḥammad ibn Mūsā al-Khwārizmī, or al-Khwarizmi was a Persian polymath from Khwarazm, who produced vastly influential works in mathematics, astronomy, and geography. Around 820 CE, he was appointed as the astronomer and head of the library of the House of Wisdom in Baghdad.
The Toledan Tables, or Tables of Toledo, were astronomical tables which were used to predict the movements of the Sun, Moon and planets relative to the fixed stars. They were a collection of mathematic tables that describe different aspects of the cosmos including prediction of calendar dates, times of cosmic events, and cosmic motion.
Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by Greek culture and the Greek language. The word "mathematics" itself derives from the Ancient Greek: μάθημα, romanized: máthēmaAttic Greek: [má.tʰɛː.ma]Koine Greek: [ˈma.θi.ma], meaning "subject of instruction". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is an important difference between Greek mathematics and those of preceding civilizations.
The climes in classical Greco-Roman geography and astronomy were the divisions of the inhabited portion of the spherical Earth by geographic latitude.
Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics and Indian mathematics. Important progress was made, such as full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra, and advances in geometry and trigonometry.
Islamic astronomy comprises the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age, and mostly written in the Arabic language. These developments mostly took place in the Middle East, Central Asia, Al-Andalus, and North Africa, and later in the Far East and India. It closely parallels the genesis of other Islamic sciences in its assimilation of foreign material and the amalgamation of the disparate elements of that material to create a science with Islamic characteristics. These included Greek, Sassanid, and Indian works in particular, which were translated and built upon.
During the Renaissance, great advances occurred in geography, astronomy, chemistry, physics, mathematics, manufacturing, anatomy and engineering. The collection of ancient scientific texts began in earnest at the start of the 15th century and continued up to the Fall of Constantinople in 1453, and the invention of printing allowed a faster propagation of new ideas. Nevertheless, some have seen the Renaissance, at least in its initial period, as one of scientific backwardness. Historians like George Sarton and Lynn Thorndike criticized how the Renaissance affected science, arguing that progress was slowed for some amount of time. Humanists favored human-centered subjects like politics and history over study of natural philosophy or applied mathematics. More recently, however, scholars have acknowledged the positive influence of the Renaissance on mathematics and science, pointing to factors like the rediscovery of lost or obscure texts and the increased emphasis on the study of language and the correct reading of texts.
Greek astronomy is astronomy written in the Greek language in classical antiquity. Greek astronomy is understood to include the Ancient Greek, Hellenistic, Greco-Roman, and Late Antiquity eras. It is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the language of scholarship throughout the Hellenistic world following the conquests of Alexander. This phase of Greek astronomy is also known as Hellenistic astronomy, while the pre-Hellenistic phase is known as Classical Greek astronomy. During the Hellenistic and Roman periods, much of the Greek and non-Greek astronomers working in the Greek tradition studied at the Museum and the Library of Alexandria in Ptolemaic Egypt.
The Tusi couple is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and forth in linear motion along a diameter of the larger circle. The Tusi couple is a 2-cusped hypocycloid.
Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics and Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy. In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata, who discovered the sine function. During the Middle Ages, the study of trigonometry continued in Islamic mathematics, by mathematicians such as Al-Khwarizmi and Abu al-Wafa. It became an independent discipline in the Islamic world, where all six trigonometric functions were known. Translations of Arabic and Greek texts led to trigonometry being adopted as a subject in the Latin West beginning in the Renaissance with Regiomontanus. The development of modern trigonometry shifted during the western Age of Enlightenment, beginning with 17th-century mathematics and reaching its modern form with Leonhard Euler (1748).
Egyptian astronomy began in prehistoric times, in the Predynastic Period. In the 5th millennium BCE, the stone circles at Nabta Playa may have made use of astronomical alignments. By the time the historical Dynastic Period began in the 3rd millennium BCE, the 365 day period of the Egyptian calendar was already in use, and the observation of stars was important in determining the annual flooding of the Nile.