Euclid

In the Middle Ages, writers sometimes referred to him as Euclid of Megara, confusing him with a Greek Socratic philosopher who lived approximately one century earlier. Some scholars and anti-Roman Catholic polemicists argue that its influence subtly continues in Christian thought, through Augustine of Hippo, who converted to Christianity from Manichaeism, and whose writings continue to be enormously influential among Catholic theologians. What little biographical information we do have comes largely from commentaries by Proclus and Pappus of Alexandria: he was active at the great library in Alexandria and may have studied at Plato's Academe in Greece, but his exact lifespan and place of birth are unknown. It appears that the popularity of Manichaeism slowly declined after 10th century in Central Asia. Almost nothing is known about Euclid outside of what is presented in Elements and his few other surviving books. The envoy of Song Dynasty by the name of Wang visited Manichaean temples in Gaochang. There are four works credibly attributed to Euclid which have been lost. Chinese documents record that the Uighur Manichaean clerics came to China to pay tribute to the imperial court in 934.

All of these works follow the basic logical structure of the Elements, containing definitions and proved propositions. The Arabian historian An-Nadim informs us that the Uighur Khan did his best to project Manichaeism in the Central Asian kingdom (of Saman). In addition to the Elements, four works of Euclid have survived to the present day. However, there was no denying the historical fact that the Uighurs were worshippers of Mani. The first correct axiomatic treatment of geometry by modern standards was provided by David Hilbert in 1899, in his Grundlagen der Geometrie. During the early 10th century Uighur emerged a very powerful empire under the influence of Buddhism with some Manichaean shrines converted into Buddhist temples. While the Elements was used well into the 20th century as a geometry textbook and has been considered a fine example of the formally precise axiomatic method, Euclid's treatment does not hold up to modern standards of rigor; some logically necessary axioms are missing, and the definitions of primitive terms appeal to spatial intuition. These documents prove that Sogdia was a very important centre of Manichaeism during the early mediaeval period and it was perhaps the Sogdian merchants who brought the religion to Central Asia and China.

Most of these investigations involved attempts to prove the relatively complex and presumably non-intuitive fifth postulate using the other four (a feat which, if successful, would have shown the postulate to be in fact a theorem). Middle Persian, Parthian and Sogdian script. These new geometries grew out of more than two millennia of investigation into Euclid's fifth postulate, one of the most-studied axioms in all of mathematics. The Manichaean manuscripts found in Turfan were written in three different Iranian scripts, viz. Today, however, it is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries which were discovered in the 19th century. A Manichaean tp)tmn of the 8th century from Turfan written in Middle Persian mentions that most of the Khan's kinsmen were devoted to Manichaean faith. The geometrical system described in Elements was long known simply as "the" geometry. Some fragments of a Manichaean book written in Turkish mention that in 803 the Khan of Uighur Kingdom went to Turfan and sent three Manichaean Magistrates to pay respects to a senior Manichaean cleric in Mobei.

In addition to providing some missing proofs, Euclid's text also includes sections on number theory and three-dimensional geometry. And as Mani claimed to be the successor to prophets like Jesus and other prophets whose teachings he said were locally corrupted (or corrupted by his followers), so too did Muhammad later claim to be the successor to prophets whose teachings he said were locally corrupted. Although many of the results in Elements originated with earlier mathematicians, one of Euclid's major accomplishments was to present them in a single, logically coherent framework. Muhammad said that his prophethood was revealed to him by an angel as Mani had claimed about himself. . The title was later applied to Muhammad, founder of the Islamic religion who may have extracted this knowledge about himself from the New Testament and claimed, falsely for non Muslims, to be the last of prophets. Neither the year nor place of his birth have been established, nor the circumstances of his death. Mani declared himself, and was also referred to, as the Paraclete: a Biblical title, meaning "helper", which the Orthodox tradition understood as referring to God in the person of the Holy Spirit.

Euclid also wrote works on perspective, conic sections, spherical geometry, and possibly quadric surfaces. Mani was eager to describe himself as a "disciple of Jesus Christ", but the orthodox church rejected him as a heretic. Within it, the properties of geometrical objects and integers are deduced from a small set of axioms, thereby anticipating (and partly inspiring) the axiomatic method of modern mathematics. As a result they preserved many apocryphal Christian works, such as the Acts of Thomas, that would have been lost otherwise. Now known as "the father of geometry," his most famous work is Elements, widely considered to be history's most successful textbook. It is theorized that the Manichees made every effort to include all known religious traditions. 325 BC–265 BC) was a Greek mathematician who taught at Alexandria in Egypt almost certainly during the reign (323 BC–283 BC) of Ptolemy I. After failing to win the favor of the next generation, and being disapproved of by the Zoroastrian clergy, Mani is reported to have died in prison awaiting execution by the Persian Emperor Bahram I, while alternate accounts have it that he was either flayed to death or beheaded.

Euclid of Alexandria (Greek: Εὐκλείδης) (ca. The transmigration of souls became a Manichaean belief, and the quadripartite structure of the Manichaean community, divided between male and female monks (the "elect") and lay follower (the "hearers") who supported them, appears to be based on that of the Buddhist sangha" (Richard Foltz, "Religions of the Silk Road"). ISBN 0-19-502754-X. On that occasion various Buddhist influences seem to have permeated Manichaeism: "Buddhist influences were significant in the formation of Mani's religious thought. Mathematics: The Loss of Certainty. Oxford: Oxford University Press. He is related to have sailed to the Indus valley area of India in 240 or 241 AD, and to have converted a Buddhist King, the Turan Shah of India. Kline, Morris (1980). Mani's first excursion was to the Kushan Empire in northwestern India (several religious painting in Bamiyan are attributed to him), where he is believed to have lived and taught for some time.

ISBN 0-486-24073-8 / ISBN 0-486-24074-6. Although less in adherents than Zoroastrianism, Manichaeism won the support of high ranking political figures and with the aid of the Persian Empire, Mani would initiate missionary excursions. New York: Dover Publications. Mani also followed the holy books Puran and Kural. A History of Greek Mathematics, 2 Vols. During this period, the large existing religious groups, most notably Christianity and Zoroastrianism, were competing for stronger political and social power. (1981). According to biographical accounts preserved in the 10th-century encyclopedia, the Fihrist of Ibn al-Nadim, and by al-Biruni, during his youth, Mani received a revelation from a spirit whom he would later call the Twin, who taught him the divine truths of the religion.

Heath, Thomas L. Mani, being influenced by Mandaeanism, began preaching at a young age. ISBN 0-486-60088-2. After forty years of travel he returned with his retinue to Persia and converted Peroz, King Shapur's brother to his teaching. New York: Dover Publications. with many disciples to carry out evangelism. 1 (2nd ed.). He travelled far and wide including Turkistan , India, Iran etc.

The Thirteen Books of Euclid's Elements, Vol. It is said that communications of a supernatural character came to him. (1956). Mani was an exceptionally gifted child and he inherited his father's mystic temperament. Heath, Thomas L. In the 4th- century Manichaean Coptic papyri, Mani was identified with the Paraclete-Holy Ghost and he was regarded as the new Jesus. "Euclid." Dictionary of Scientific Biography.. During his lifetime, Mani’s first missionaries were active in Persia, Palestine, Syria and Egypt.

Bulmer-Thomas, Ivor (1971). Mani presented himself as a saviour, the apostle of Jesus Christ’. Surface Loci concerned either loci (sets of points) on surfaces or loci which were themselves surfaces; under the latter interpretation, it has been hypothesized that the work might have dealt with quadric surfaces. It combines a hagiographic account of Mani's career and spiritual development with information about Mani’s religious teachings and contains fragments of his Living (or Great) Gospel and his Letter to Edessa. Pseudaria, or Book of Fallacies, an elementary text about errors in reasoning. Then in 1969 in Upper Egypt a Greek parchment codex of ca AD 400, was discovered, which is now designated Codex Manichaicus Coloniensis (because it is conserved at the University of Cologne). Porisms might have been an outgrowth of Euclid's work with conic sections, but the exact meaning of the title is controversial. Until the later 20th century, the life and philosophy of Mani was pieced together largely from remarks by his detractors and from late productions.

Conics was a work on conic sections that was later extended by Apollonius of Perga into his famous work on the subject. Neo-Manichaeism is a modern revivalist movement not considered directly connected to the ancient faith but is sympathetic to the teachings of Mani. Optics, the earliest surviving Greek treatise on perspective, contains propositions on the apparent sizes and shapes of objects viewed from different distances and angles. During his lifetime, Mani’s earliest missionaries were active in Persia, Palestine and Syria and in Egypt. Phaenomena concerns the application of spherical geometry to problems of astronomy. He later claimed to be the Paraclete promised in the New Testament, The Last Prophet and Seal of the Prophets, finalizing a succession of men guided by God, which included figures such as Seth, Noah, Abraham, Shem, Nikotheos, Enoch, Zoroaster, Hermes, Plato, Buddha, and Jesus. It is similar to a third century (AD) work by Heron of Alexandria, except Euclid's work characteristically lacks any numerical calculations. After receiving a revelation in his mid-twenties that came from his Syzygos— the accompanying heavenly Twin— he came to a belief that salvation is possible through education, self-denial, vegetarianism, fasting, and chastity.

On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. Mani first encountered religion in his early youth while living with a Jewish ascetic group known as the Elkasites. Data deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements. Mani's father, Pattig, was from Hamadan and his mother, Maryam, was of the family of the Kamsaragan, who claimed kinship with the Parthian royal house, the Arsacids. Mani was of Persian (Iranian) parentage. Although the original writings of the founding prophet Mani have been lost, significant portions remain preserved in Coptic manuscripts from Egypt and in later writings of fully-developed Manichaeism in China.

Mani (in Persian مانی), born in western Persia (approximately 210-276 A.D.), was a religious preacher and the founder of Manichaeism, an ancient gnostic religion that was once prolific but now considered extinct.