Pythagoreanism - Knowledge

1365: 1316:. The purpose of vegetarianism in Pythagoreanism was not self-denial; instead, it was regarded as conductive to the best in a human being. Pythagoreans advanced a grounded theory on the treatment of animals. They believed that any being that experienced pain or suffering should not have pain inflicted on it unnecessarily. Because it was not necessary to inflict pain on animals for humans to enjoy a healthy diet, they believed that animals should not be killed for the purpose of eating them. The Pythagoreans advanced the argument that unless an animal posed a threat to a human, it was not justifiable to kill an animal and that doing so would diminish the moral status of a human. By failing to show justice to the animal, humans diminish themselves. 31: 1088:

property of numbers was expressed in the harmonious interplay of opposite pairs. Harmony assured the balance of opposite forces. Pythagoras had in his teachings named numbers and the symmetries of them as the first principle and called these numeric symmetries harmony. This numeric harmony could be discovered in rules throughout nature. Numbers governed the properties and conditions of all beings and were regarded the causes of being in everything else. Pythagorean philosophers believed that numbers were the elements of all beings and the universe as a whole was composed of harmony and numbers.

2341: 226: 841: 605: 2018: 218: 2485: 7328: 1646: 1476:'s writings on physical cosmology, psychology, ethics and political philosophy in the 5th century BC. However, Plato adhered to the dominant Greek philosophy, and the Platonic philosophy suppressed the combination of experimental method and mathematics which was an inherent part of Pythagoreanism. The influence of Pythagoreanism extended throughout and beyond antiquity because the Pythagorean doctrine of reincarnation was recounted in Plato's 444:. In Croton, a house where Pythagoreans gathered was set on fire and all but two of the Pythagorean philosophers burned alive. Pythagorean meeting places in other cities were also attacked and philosophic leaders killed. These attacks occurred in the context of widespread violence and destruction in Magna Graecia. Following the political instability in the region, some Pythagorean philosophers fled to mainland Greece while others regrouped in 2189: 987: 1300: 674: 5218: 2570:. Vincenzo Galilei proclaimed that he had been a committed Pythagorean, until he "ascertained the truth by means of experiment, the teacher of all things." He devised an experiment which showed that the weights attached to the two strings needed to increase as the square of the string length. This public challenge to prevailing numerology in musical theory triggered an experimental and physical approach to 202: 1097: 132:(Academos). The Academy, the sacred grove of Academos, may have existed, as the contemporaries seem to have believed, since the bronze age, even pre-existing the Trojan War. Yet according to Plutarch it was the Athenian strategos (general) Kimon Milkiadou (c.510–450 BC) who converted this, "waterless and arid spot into a well watered grove, which he provided with clear running-tracks and shady walks". 1823: 7315: 2727: 1320:

avoided by killing an animal painlessly. The Pythagoreans also thought that animals were sentient and minimally rational. The arguments advanced by Pythagoreans convinced numerous of their philosopher contemporaries to adopt a vegetarian diet. The Pythagorean sense of kinship with non-humans positioned them as a counterculture in the dominant meat-eating culture. The philosopher

776:, a religious tradition that developed in parallel to Pythagorean religious practice, Pythagoreanism held that the soul was buried in the body as a punishment for a committed offense and that the soul could be purified. Aside from conducting their daily lives according to strict rules Pythagorean also engaged in rituals to attain purity. The 4th century Greek historian and 1376:, which was compiled by Neopythagoreans in the 1st or 2nd century. Some surviving fragments of this collection are by early-Pythagorean women philosophers, while the bulk of surviving writings are from late-Pythagorean women philosophers who wrote in the 4th and 3rd century BC. Female Pythagoreans are some of the first female philosophers from which texts have survived. 252:. Pythagoras had been credited with discovering that in a right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. In ancient times Pythagoras was also noted for his discovery that music had mathematical foundations. Antique sources that credit Pythagoras as the philosopher who first discovered 120:. It is wrong to say that the Pythagoreans were superseded by the Cynics in the 4th century BC, but it seems to be a distinction mark of the Cynics to disregard the hierarchy and protocol, ways of initiatory proceedings significant for the Pythagorean community; subsequently did the Greek philosophical traditions become more diverse. The 1382:, the wife of Pythagoras, is considered a major figure in early-Pythagoreanism. She was noted as distinguished philosopher and in the lore that surrounds her, is said to have taken over the leadership of the school after his death. Text fragments have also survived from women philosophers of the late-Pythagorean period. These include 1291:, although its version contains substantial differences. Unlike the Orphics, who considered metempsychosis a cycle of grief that could be escaped by attaining liberation from it, Pythagoras seems to postulate an eternal, endless reincarnation where subsequent lives would not be conditioned by any action done in the previous. 2001:. The Jewish Pythagorean numerology developed by Philo held that God as the unique One was the creator of all numbers, of which seven was the most divine and ten the most perfect. The medieval edition of the Kabbalah focused largely on a cosmological scheme of creation, in reference to early Pythagorean philosophers 421:. In Croton, Pythagoras established the first Pythagorean community, described as a secret society, and attained political influence. In the early 5th century BC Croton acquired great military and economic importance. Pythagoras emphasised moderation, piety, respect for elders and of the state, and advocated a 1255:

Pythagoreans believed that body and soul functioned together, and a healthy body required a healthy psyche. Early Pythagoreans conceived of the soul as the seat of sensation and emotion. They regarded the soul as distinct from the intellect. However, only fragments of the early Pythagorean texts have

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are created by the simple numerical ratio of the first four natural numbers which derive respectively from the relations of string length: the octave (1/2), the fifth (2/3) and the fourth (3/4). The sum of those numbers 1 + 2 + 3 + 4 = 10 was for Pythagoreans the perfect number, because it contained

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and discovered quantitative mathematical relationships of music through arithmetic ratios. Pythagoras attempted to explain subjective psychological and aesthetic feelings, such as the enjoyment of musical harmony. Pythagoras and his students experimented systematically with strings of varying length

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listed 235 Pythagoreans by name, among them 17 women whom he described as the "most famous" women practitioners of Pythagoreanism. It was customary that family members became Pythagoreans, as Pythagoreanism developed into a philosophic tradition that entailed rules for everyday life and Pythagoreans

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in the 17th century. Acoustics emerged as a mathematical field of music theory and later an independent branch of physics. In the experimental investigation of sound phenomena, numbers had no symbolic meaning and were merely used to measure physical phenomena and relationships such as frequency and

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Perictione I outlines the condition that enable women to nurture wisdom and self-control. These virtues will, according to Perictione I, bring "worthwhile things" for a woman, her husband, her children, the household and even the city "if, at any rate, such a woman should govern cities and tribes".

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For Pythagoreans, harmony signified the "unification of a multifarious composition and the agreement of unlike spirits". In Pythagoreanism, numeric harmony was applied in mathematical, medical, psychological, aesthetic, metaphysical and cosmological problems. For Pythagorean philosophers, the basic

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as a liberal philosophy which served to establish principles and allowed theorems to be explored abstractly and rationally. Pythagorean philosophers believed that there was a close relationship between numbers and geometrical forms. Early-Pythagorean philosophers proved simple geometrical theorems,

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to advance physical laws that reflected the inherent order of the universe. Twenty-one centuries after Pythagoreas had taught his disciples in Italy, Galileo announced to the world that "the great book of nature" could only be read by those who understood the language of mathematics. He set out to

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Pythagoreans believed that human beings were animals, but with an advanced intellect and therefore humans had to purify themselves through training. Through purification humans could join the psychic force that pervaded the cosmos. Pythagoreans reasoned that the logic of this argument could not be

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It is not known whether Philolaus believed Earth to be round or flat, but he did not believe the earth rotated, so that the Counter-Earth and the Central Fire were both not visible from Earth's surface, or at least not from the hemisphere where Greece was located. But the conclusion of Pythagorean

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family structure. The Croton Council appointed him to official positions. Among others Pythagoras was in charge of education in the city. His influence as political reformer reputedly extended to other Greek colonies in southern Italy and in Sicily. Pythagoras died shortly after an arson attack on

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It remains to speak of the earth, of its position, of the question whether it is at rest or in motion, and of its shape. As to its position, there is some difference of opinion. Most people–all, in fact, who regard the whole heaven as finite–say it lies at the center. But the Italian philosophers

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The fact that mathematics could explain the human sentimental world had a profound impact on the Pythagorean philosophy. Pythagoreanism became the quest for establishing the fundamental essences of reality. Pythagorean philosophers advanced the unshakable belief that the essence of all things are

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Neopythagoreans manifested a strong interest in numerology and the superstitious aspects of Pythagoreanism. They combined this with the teachings of Plato's philosophic successors. Neopythagorean philosophers engaged in the common ancient practice of ascribing their doctrines to the designated

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must produce a sound because they were large swiftly moving bodies. Pythagoreans also determined that stars revolved at distances and speeds that were proportional to each other. They reasoned that because of this numerical proportion the revolution of the stars produced a harmonic sound. The

877:(pebbles), to represent numbers in triangles, squares, rectangles and pentagons. This enabled a visual comprehension of mathematics and allowed for a geometrical exploration of numerical relationships. Pythagorean philosophers investigated the relationship of numbers extensively. They defined 1218:

with geometrical proportion, because proportion ensured that each part receives what it is due. Early-Pythagoreans believed that after the death of the body, the soul would be punished or rewarded. Humans could, through their conduct, ensure that their soul was admitted to another world. The

1015:, with brass discs of the same diameter but different thickness, and with identical vases filled with different levels of water. Early Pythagoreans established quantitative ratios between the length of a string or pipe and the pitch of notes and the frequency of string vibration. 1175:

known as Pythagoreans take the contrary view. At the centre, they say, is fire, and the earth is one of the stars, creating night and day by its circular motion about the center. They further construct another earth in opposition to ours to which they give the name counterearth.

689:(translated as "learning" or "studying") as part of their practice. While their scientific pursuits were largely mathematical, they also promoted other fields of scientific study in which Pythagoras had engaged during his lifetime. A sectarianism developed between the dogmatic 1166:

it produced an odd number. Philolaus further reasoned that the fitting together of the earth and the universe corresponded to the construction of the number one out of the even and the odd. Pythagorean philosophers believed that the even was unlimited and the odd was limited.

2082:, the estimation of agricultural values and business applications for the buying and selling of goods. There was little interest for the Pythagorean numerology that developed in the Latin world. The primary arithmetical system used by Islamic mathematicians was based on 1346:

identified Pythagoras as the first opponent to meat-eating. But the fuller argument Pythagoreans advanced against the maltreatment of animals did not sustain. Pythagoreans had argued that certain types of food arouse the passions and hindered spiritual ascent. Thus

768:. Pythagoreans preached an austere life. They believed that the soul was buried in the body, which acted as a tomb for the soul in this life. The highest reward a human could attain was for the soul to join in the life of the gods and thus escaped the cycle of 1079:, music for the purification of the soul. Pythagoreans used different types of music to arouse or calm their souls, and certain stirring songs could have notes that existed in the same ratio as the "distances of the heavenly bodies from the centre of" Earth. 283:. The surviving 5th century BC sources on Pythagoras and early Pythagoreanism are void of supernatural elements, while surviving 4th century BC sources on Pythagoras' teachings introduced legend and fable. Philosophers who discussed Pythagoreanism, such as 1364: 2451:

was translated and republished with commentary in the Arab and Jewish worlds. In the 12th century the study of Plato gave rise to a vast body of literature explicating the glory of God as it reflected in the orderliness of the universe. Writers such as

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indicate that while early Pythagoreans did not believe that the soul contained all psychological faculties, the soul was life and a harmony of physical elements. As such the soul passed away when certain arrangements of these elements ceased to exist.

1710:. Sunlight lit up the universe and was proof of God's presence. In the Middle Ages this numerological division of the universe was credited to the Pythagoreans, while early on it was regarded as an authoritative source of Christian doctrine by 440:. Pythagoras escaped to Metapontium. After these initial attacks and the death of Pythagoras, Pythagorean communities in Croton and elsewhere continued to flourish. At around 450 BC attacks on Pythagorean communities were carried out across 1966:' 10 book encyclopedia on Pythagoreanism from surviving fragments, leading to the popularisation of Iamblichus' description of Pythagorean physics, ethics and theology at the Byzantine court. Psellus was reputably in the possession of the 1360:

The biographical tradition on Pythagoras holds that his mother, wife and daughters were part of his inner circle. Women were given equal opportunity to study as Pythagoreans and learned practical domestic skills in addition to philosophy.

1539:, Aristotle refuted the Pythagorean doctrine on the harmony of the spheres. Nevertheless, he wrote a treatise on the Pythagoreans of which only fragments survive, in which he treats Pythagoras as a wonder-working religious teacher. 1239:

I think human nature provides a common standard of law and justice for both the family and the city. Whoever follows the paths within and searches will discover; for within is law and justice, which is the proper arrangement of the

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Early-Pythagorean sects were closed societies and new Pythagoreans were chosen based on merit and discipline. Ancient sources record that early-Pythagoreans underwent a five-year initiation period of listening to the teachings

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argued that "this mode of observing nature, which led in part to a true dominion over natural forces and thus contributes decisively to the development of humanity, in an unforeseen manner vindicated the Pythagorean faith".

136:(less known as Aristocles) lived almost a hundred years later, circa 427 to 348 BC. On the other hand it seems likely that this was a part of the re-building of Athens led by Kimon Milkiadou and Themosticles, following the 1771:

consisted of 451 sayings or principles, such as injunctions to love the truth, to avoid the pollution of the body with pleasure, to shun flatterers and to let one's tongue be harnessed by one's mind. The contents of the

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value. Aristotle's discussion of Pythagorean philosophy is difficult to interpret, because he had little patience for Pythagorean philosophic arguments, and Pythagoreanism does not fit with his philosophic doctrine. In

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would rely on the teachings of the Pythagoreans when arguing that abstinence from eating meat for the purpose of spiritual purification should be practiced only by philosophers, whose aim was to reach a divine state.

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reincarnation in this world equated to a punishment. In Pythagoreanism life in this world is social and in the realm of society justice existed when each part of society received its due. The Pythagorean tradition of

1227:. For Pythagorean philosophers the soul was the source of justice and through the harmony of the soul, divinity could be achieved. Injustice inverted the natural order. According to the 4th century BC philosopher 1142:, a teacher to Pythagoras, in the 6th century BC. Historic sources credit the Pythagorean philosophers with being the first to attempt a clarification of the planet sequence. The early-Pythagorean philosopher 1311:

Some Medieval authors refer to a "Pythagorean diet", entailing the abstention from eating meat, beans or fish. Pythagoreans believed that a vegetarian diet fostered a healthy body and enhanced the search for

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Early Pythagoreanism was based on research and the accumulation of knowledge from the books written by other philosophers. Pythagoras' philosophic teachings made direct reference to the philosophy of

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in the 11th century popularised Pythagorean numerology in his treatise on theology, arguing that Plato was the inheritor of the Pythagorean secret. Psellus also attributed arithmetical inventions by

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in the early 4th century BC. The Pythagorean schools and societies died out from the 4th century BC. Pythagorean philosophers continued to practice, albeit no organised communities were established.

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declined in Europe, the ideas of early-Pythagoreanism were revived. Mathematics regained importance and influenced philosophy as well as science. Mathematics was used by Kepler, Galileo, Descartes,

1188:. Instead, as Aristotle noted, the Pythagorean view of the astronomical system was grounded in a fundamental reflection on the value of individual things and the hierarchical order of the universe. 2089:

Besides the enthusiasm that developed in the Latin and Byzantine worlds in the Middle Ages for Pythagorean numerology, the Pythagorean tradition of perfect numbers inspired profound scholarship in

1464:, in which she assigned the virtue of moderation to women, but asserted that "courage and justice and wisdom are common to both" men and women. Phyntis defended the right of women to philosophise. 365:

Today scholars typically distinguish two periods of Pythagoreanism: early-Pythagoreanism, from the 6th until the 5th century BC, and late-Pythagoreanism, from the 4th until the 3rd century BC. The

351:... distinguished for his manly virtue and modesty, even in death has a life which is pleasing to his soul, if Pythagoras the wise truly achieved knowledge and understanding beyond that of all men. 1620:

and located him beyond the finite so that God could not come into contact with anything corporeal. Neopythagoreans insisted on a spiritual worship of God and that life had to be purified through

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could be applied to life. By the 12th century Pythagorean numerological concepts had become a universal language in Medieval Europe and were no longer recognised as Pythagorean. Writers such as

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numbers and that the universe was sustained by harmony. According to ancient sources music was central to the lives of those practicing Pythagoreanism. They used medicines for the purification (

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Al-Farabi rejected the notion of celestial harmony on the grounds that it was "plainly wrong" and that it was not possible for the heavens, orbs and stars to emit sounds through their motions.

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Empedocles described Pythagoras as "a man of surpassing knowledge, master especially of all kinds of wise works, who had acquired the upmost wealth of understanding." In the 4th century BC the

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and Galileo, had a keen interest in music and acoustics. By the late 17th century it was accepted that sound travels like a wave in the air at a finite speed and experiments to establish the

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were produced in the 11th and 12th centuries. In the Medieval Islamic world a Pythagorean tradition took hold, whereby spheres or stars produced music. This doctrine was further developed by

885:. This distinction was for the Pythagorean philosophers direct and visual, as they arranged triangular dots so that the even and odd numbers successively alternate: 2, 4, 6, ... 3, 5, 7, ... 335:

Pythagoras, the son of Mnesarchus, practised inquiry beyond all other men and selecting of these writings made for himself a wisdom or made a wisdom of his own: a polymathy, an imposture.

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measure whatever is measurable, and to render everything measurable that is not. The Pythagorean concept of cosmic harmony deeply influenced western science. It served as the basis for

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in the 4th century BC rejected mathematics as a tool for investigation and understanding of the world. He believed that numbers constituted simply a quantitative determinant and had no

1231:, Pythagoras taught that "happiness consists in knowledge of the perfection of the numbers of the soul. A surviving fragment from the 3rd century BC by the late-Pythagorean philosopher 1146:

believed that limited and unlimited things were the components of the cosmos, and these had existed ever since. The center of the universe, according to Philolaus, was the number one (

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and Pythagorean arithmetic provided the basis for Greek geometric algebra. By attempting to establish a system of concrete and permanent rules, Pythagoreans helped to establish strict

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found Pythagorean numerology so alluring that he set out to explain the human body entirely in numbers. In the 13th century the fashion for numerology dwindled. The Christian scholar

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in a treatise on arithmetic for business administrators in reference to Nicomachus. However, the primary interest of Islamic arithmeticians was in solving practical problems, such as

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Today, Pythagoras is mostly remembered for his mathematical ideas, and by association with the work early Pythagoreans did in advancing mathematical concepts and theories on harmonic

586:. The worship of Pythagoras continued in Italy in the two intervening centuries. As a religious community Pythagoreans appear to have survived as part of, or deeply influenced, the 2236:

developed this theory further, arguing that a fourfold path led to the attainment of knowledge. Arithmetic, music, geometry and astronomy went on to become the essential parts of

389:. They espoused to a rigorous life of the intellect and strict rules on diet, clothing and behavior. Their burial rites were tied to their belief in the immortality of the soul. 873:). But unlike their Greek contemporaries, the Pythagorean philosophers represented numbers graphically, not symbolically through letters. Pythagoreans used dots, also known as 2669:

The Pythagorean belief that all bodies are composed of numbers and that all properties and causes could be expressed in numbers, served as the basis for a mathematization of

7365: 2476:. William of Conches argued that Plato was an important Pythagorean. In this medieval Pythagorean understanding of Plato, God was a craftsman when he designed the universe. 1448:

Her assertion that a wife should remain devoted to her husband, regardless of his behavior, has been interpreted by scholars as a pragmatic response to the legal rights of

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that others were of this opinion. I have decided to set his words down here, so that they may be available to everybody: "Some think that the earth remains at rest. But

347:. Both were born in the 490s, after Pythagoras' death. By that time, he was known as a sage and his fame had spread throughout Greece. According to Ion, Pythagoras was: 2418:

world, where they had first been published in the 1st century, but also the Latin world when they were translated in the 9th century. The division of the universe into

2426:, and the 12 orders of heaven were credited as Pythagoras' teachings by an anonymous biographer, who was quoted in the treatise of the 9th century Byzantine patriarch 2264:. From the 9th century onwards, both the quadrivium and the trivium were commonly taught in schools and the newly emerging universities. They came to be known as the 896:

held the conviction that mathematics could help in addressing important philosophical problems. In Pythagoreanism numbers became related to intangible concepts. The

912:, Pythagoreans believed that the whole world and all things in it are summed up in this number, because end, middle and beginning give the number of the whole. The 9597: 2566:. Zarlino supported the theory that if two weights in the ratio of 2 to 1 were attached to two strings, the pitches generated by the two strings would produce the 108:(c.234–c.305 AD) seem to make the distinction of the two as that of 'beginner' and 'advanced'. As the Pythagorean cenobites practiced an esoteric path, like the 9925: 1027:

has called this formulation of musical arithmetic as "among the most powerful advances of human science" because it enables the measurement of sound in space.

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as those that were equal to the sum of all their divisors. For example: 28 = 1 + 2 + 4 + 7 + 14. The theory of odd and even numbers was central to Pythagorean

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popularised the belief that Pythagoras had been the basis for establishing key dates in Judaism. In the 4th century this assertion was further developed by

96:("those who listen"), who is conventionally regarded as more concerned with religious, and ritual elements, and associated with the oral tradition, and the 8699: 1135: 697:, who in their intellectual activism became regarded as increasingly progressive. This tension persisted until the 4th century BC, when the philosopher 2252:

with having written a book on quadrivium. The role of harmony had its roots in the triadic thinking of Plato and Aristotle and included the trivium of

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Pythagorean text modified to reflect a Christian viewpoint, existed from at least the 2nd century and remained popular among Christians well into the

397:) in silence. Initiates could through a test become members of the inner circle. However, Pythagoreans could also leave the community if they wished. 8886: 7358: 2558:

challenged the prevailing Pythagorean wisdom about the relationship between pitches and weights attached to strings. Vincenzo Galilei, the father of

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Pythagoreanism was a philosophic tradition as well as a religious practice. As a religious community they relied on oral teachings and worshiped the

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Mohammad Saleh, "Arabic and Islamic Philosophy of Mathematics", The Stanford Encyclopedia of Philosophy (Summer 2022 Edition), Edward N. Zalta (ed.)

1814:, then the written language of both Muslims and Jews, but only in the Latin world did they become a guide to daily life that was widely circulated. 1202:

early-Pythagorean philosopher Philolaus argued that the structure of the cosmos was determined by the musical numerical proportions of the diatonic

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has been discussed extensively. Plato's dialogues have become an important surviving source of Pythagorean philosophic arguments. Plato referenced

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expressed his preference for the Pythagorean vision of a universe governed by the mystical properties of certain numbers, over the newly emerging

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believed that the Earth, along with other celestial bodies, orbited around a central fire. This, they believed, constituted a celestial harmony.

190:. Even the early christian cenobitic traditions may be seen in light of the matematikoi. The biblical Greek name for 'disciple' is 'mathetes' 11543: 9355: 1307:, French, 1512/1514. Pythagoreans refused to eat beans. Already in antique times there was much speculation about the reason for this custom. 2062:

was referenced in Arabic manuscripts. Scholars in the Arabic world displayed a strong interest in Pythagorean concepts. In the 10th century

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Pythagoras pioneered the mathematical and experimental study of music. He objectively measured physical quantities, such as the length of a

7351: 2107:). Fibonacci had studied scripts from Egypt, Syria, Greece and Sicily, and was learned in Hindu, Arabic and Greek methodologies. Using the 2212:

in the 4th century BC and was a familiar concept among academics in the antiquity, it was attributed as Pythagorean in the 5th century by

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and wrote a Platonic adaptation of Philolaus' metaphysical system of limiters and unlimiteds. Plato also quoted from one of the surviving

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had for Pythagoreans an ethical dimension, as the goodness of each person was believed to be threefold: prudence, drive and good fortune.

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Following Pythagoras' death, disputes about his teachings led to the development of two philosophical traditions within Pythagoreanism in

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in Italy became the home for many practitioners of Pythagoreanism and later for Neopythagorean philosophers. Pythagoras had also lived in

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philosophers did not recognise them. Despite this, both groups were regarded by their contemporaries as practitioners of Pythagoreanism.

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had access to historical written sources as well as the oral tradition about Pythagoreanism, which by the 4th century BC was in decline.

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continued to engage in a pious life by practicing silence, dressing simply and avoiding meat, for the purpose of attaining a privileged

8896: 7774: 6112: 9893: 9717: 6390: 148:, the city walls of ancient Athens. It seems likely that the Athenians saw this as a rejuvenation of the sacred grove of Academos. 9543: 8901: 8692: 151:

Following political instability in Magna Graecia, some Pythagorean philosophers moved to mainland Greece while others regrouped in

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put forward a method of generating sets of three square numbers that satisfied the relationship first attributed to Pythagoras by

1694:, the books explained the relationship among celestial beings, humans, God and the universe. At the heart of the explanation were 10130: 4603: