pythagoreanism

 

  • The mathēmatikoi philosophers claimed that numbers were at the heart of everything and constructed a new view of the cosmos.

  • [46] Aristotle recorded in the 4th century BC on the Pythagorean astronomical system: 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.

  • However, Plato’s views that the primary role of mathematics was to turn the soul towards the world of forms, as expressed in Timaeus, is regarded as Platonic philosophy, rather
    than Pythagorean.

  • [49] A surviving fragment from the 3rd century BC by the late-Pythagorean philosopher Aesara reasoned that: I think human nature provides a common standard of law and justice
    for both the family and the city.

  • 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, … Early-Pythagorean philosophers such as Philolaus and Archytas held the conviction that mathematics could help in addressing important philosophical problems.

  • [27] Like the practitioners of Orphism, a religious tradition that developed in parallel to Pythagorean religious practice, Pythagoreanism believed that the soul was buried
    in the body as a punishment for a committed offense and that the soul could be purified.

  • [45] Late-Pythagorean philosophers were absorbed into the Platonic school of philosophy and in the 4th century AD the head of the Platonic Academy Polemon included vegetarianism
    in his concept of living according to nature.

  • [17] Philosophic traditions Following Pythagoras’ death, disputes about his teachings led to the development of two philosophical traditions within Pythagoreanism in Italy:
    akousmatikoi and mathēmatikoi.

  • A dominant symbolism was awarded to the number three, 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.

  • “[39] The fact that mathematics could explain the human sentimental world had a profound impact on the Pythagorean philosophy.

  • Pythagoras’ death and disputes about his teachings led to the development of two philosophical traditions within Pythagoreanism.

  • [53] However, only fragments of the early Pythagorean texts have survived, and it is not certain whether they believed the soul was immortal.

  • [30] Arithmetic and numbers[edit] The first six triangular numbers Pythagoras, in his teachings focused on the significance of numerology, he believed that numbers themselves
    explained the true nature of the Universe.

  • In ancient times Pythagoras was also noted for his discovery that music had mathematical foundations.

  • [45] The early-Pythagorean philosopher Philolaus believed that limited and unlimited things were the components of the cosmos, and these had existed ever since.

  • “[5] In a surviving fragment from Heraclitus, Pythagoras and his followers are described as follows: 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.

  • [7] According to Ion, Pythagoras was: … 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.

  • In Croton, Pythagoras established the first Pythagorean community, described as a secret society, and attained political influence.

  • History Pythagoras was already well known in ancient times for the mathematical achievement of the Pythagorean theorem.

  • [34] Pythagoreans thought numbers existed “outside of [human] minds” and separate from the world.

  • The surviving texts of the Pythagorean philosopher Philolaus 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.

  • 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.

  • Thus Porphyry 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.

  • [7] 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.

  • Text fragments have also survived from women philosophers of the late-Pythagorean period.

  • It was customary that family members became Pythagoreans, as Pythagoreanism developed into a philosophic tradition that entailed rules for everyday life and Pythagoreans were
    bound by secrets.

  • The one was related to the intellect and being, the two to thought, the number four was related to justice because and equally even.

  • 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.

  • Many of the surviving texts of women Pythagorean philosophers are part of a collection, known as pseudoepigrapha Pythagorica, which was compiled by Neopythagoreans in the
    1st or 2nd century.

  • Pythagoreans used different types of music to arouse or calm their souls,[40] 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.

  • In Pythagoreanism life in this world is social[50] and in the realm of society justice existed when each part of society received its due.

  • [66] Women were given equal opportunity to study as Pythagoreans and learned practical domestic skills in addition to philosophy.

  • [12] Scholars believe that Perictione I was an Athenian and contemporary of Plato, because in On the Harmony of Woman she wrote in Ionic and used the same terms of virtues
    as Plato had done in his Republic: andreia, sophrosyne, dikaiosyne and sophia.

  • Pythagorean philosophers believed that there was a close relationship between numbers and geometrical forms.

  • [42] This numeric harmony could be discovered in rules throughout nature.

  • Historic sources credit the Pythagorean philosophers with being the first to attempt a clarification of the planet sequence.

  • [43] Main article: Pythagorean astronomical system The philosopher Philolaus, one of the most prominent figures in Pythagoreanism,[44] was the precursor of Copernicus in moving
    the earth from the center of the cosmos and making it a planet.

  • Pythagorean philosophers believed that numbers were the elements of all beings and the universe as a whole was composed of harmony and numbers.

  • Most people–all, in fact, who regard the whole heaven as finite–say it lies at the center.

  • Neopythagorean philosophers, who authored many of the surviving sources on Pythagoreanism, continued the tradition of legend and fantasy.

  • But the Italian philosophers known as Pythagoreans take the contrary view.

  • Ancient sources record that early-Pythagoreans underwent a five-year initiation period of listening to the teachings (akousmata) in silence.

  • Antique sources that credit Pythagoras as the philosopher who first discovered music intervals also credit him as the inventor of the monochord, a straight rod on which a
    string and a movable bridge could be used to demonstrate the relationship of musical intervals.

  • [2] Philosophy Early Pythagoreanism was based on research and the accumulation of knowledge from the books written by other philosophers.

  • Philosophers who discussed Pythagoreanism, such as Anaximander, Andron of Ephesus, Heraclides and Neanthes had access to historical written sources as well as the oral tradition
    about Pythagoreanism, which by the 4th century BC was in decline.

  • 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.

  • [26] 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 reincarnation in another human body.

  • [34] Cosmology[edit] According to a collection of ancient philosophical texts by Stobaeus in the 5th century AD, Philolaus believed there was a “Counter-Earth” (Antichthon)
    orbiting a “central fire” but not visible from Earth.

  • [10] Early-Pythagorean sects were closed societies and new Pythagoreans were chosen based on merit and discipline.

  • 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.

  • [35] They had many mystical and magical interpretations of the roles of numbers in governing existence.

  • [37] According to ancient sources music was central to the lives of those practicing Pythagoreanism.

  • [28] Aside from conducting their daily lives according to strict rules Pythagorean also engaged in rituals to attain purity.

  • Until the demise of Pythagoreanism in the 4th century BC, the akousmatikoi continued to engage in a pious life by practicing silence, dressing simply and avoiding meat, for
    the purpose of attaining a privileged afterlife.

  • [54] However, the teaching most securely identified with Pythagoras is metempsychosis, or the “transmigration of souls”, which holds that every soul is immortal and, upon
    death, enters into a new body.

  • 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.

  • According to the 4th century BC philosopher Heraclides Ponticus, Pythagoras taught that “happiness consists in knowledge of the perfection of the numbers of the soul.

  • For example:.

  • [44] According to Aristotle’s student Eudemus of Cyprus, the first philosopher to determine quantitatively the size of the known planets and the distance between them was
    Anaximander, a teacher to Pythagoras, in the 6th century BC.

  • They further construct another earth in opposition to ours to which they give the name counterearth.

  • [22] 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 musical intervals, the definition of numbers, proportion and mathematical methods such as arithmetic and geometry.

  • 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.

  • The worship of Pythagoras continued in Italy and as a religious community Pythagoreans appear to have survived as part of, or deeply influenced, the Bacchic cults and Orphism.

  • Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans.

  • Philolaus called the number one an “even-odd” because it was able to generate both even and odd numbers.

  • [38] This ratio, also known as the “pure” perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed
    to the integer 3.

  • Pythagorean philosophers advanced the unshakable belief that the essence of all things are numbers and that the universe was sustained by harmony.

 

Works Cited

[‘Otto Neugebauer (1969). The Exact Sciences in Antiquity (Republication of 1957 Brown University Press 2nd ed.). Courier Dover Publications. p. 36. ISBN 0-486-22332-9.
2. ^ Jump up to:a b Christoph Riedweg (2008). Pythagoras: His Life, Teaching, and
Influence. Cornell University Press. p. 26. ISBN 978-0-8014-7452-1.
3. ^ Christoph Riedweg (2008). Pythagoras: His Life, Teaching, and Influence. Cornell University Press. p. 27. ISBN 978-0-8014-7452-1.
4. ^ Leonid Zhmud (2012). Pythagoras and
the Early Pythagoreans. Oxford University Press. p. 29. ISBN 978-0-19-928931-8.
5. ^ Jump up to:a b Leonid Zhmud (2012). Pythagoras and the Early Pythagoreans. Oxford University Press. p. 30. ISBN 978-0-19-928931-8.
6. ^ Jump up to:a b c Leonid
Zhmud (2012). Pythagoras and the Early Pythagoreans. Oxford University Press. p. 33. ISBN 978-0-19-928931-8.
7. ^ Jump up to:a b Leonid Zhmud (2012). Pythagoras and the Early Pythagoreans. Oxford University Press. p. 38. ISBN 978-0-19-928931-8.
8. ^
Leonid Zhmud (2012). Pythagoras and the Early Pythagoreans. Oxford University Press. p. 39. ISBN 978-0-19-928931-8.
9. ^ Leonid Zhmud (2012). Pythagoras and the Early Pythagoreans. Oxford University Press. p. 44. ISBN 978-0-19-928931-8.
10. ^
Jump up to:a b c Michelle Ballif; Michael G. Moran (2005). Classical Rhetorics and Rhetoricians: Critical Studies and Sources. Greenwood Publishing Group. p. 315. ISBN 978-0-313-32178-8.
11. ^ Pomeroy, Sarah B. (2013). Pythagorean Women. Baltimore,
MD: The Johns Hopkins University Press. p. xvi. ISBN 978-1-4214-0957-3.
12. ^ Jump up to:a b c d Michelle Ballif; Michael G. Moran (2005). Classical Rhetorics and Rhetoricians: Critical Studies and Sources. Greenwood Publishing Group. p. 316. ISBN
978-0-313-32178-8.
13. ^ Pomeroy, Sarah B. (2013). Pythagorean Women. Baltimore, MD: The Johns Hopkins University Press. p. 1. ISBN 978-1-4214-0957-3.
14. ^ Jump up to:a b c Richard D. McKirahan (2011). Philosophy Before Socrates (Second Edition):
An Introduction with Texts and Commentary: An Introduction with Texts and Commentary. Hackett Publishing. p. 79. ISBN 978-1-60384-612-7.
15. ^ Willers, Michael (2009). Algebra: The x and y of Everyday Math (2009 ed.). Quid Publishing. p. 43. ISBN
978-1-4351-1400-5.
16. ^ August Böckh (1819). Philolaos des Pythagoreers Lehren nebst den Bruchstücken seines Werkes. In der Vossischen Buchhandlung. p. 14. Pythagoras Lehren nebst den Bruchstücken seines Werkes.
17. ^ Jump up to:a b Stanford
Encyclopedia of Philosophy. “Philolaus”. Retrieved 30 May 2015.
18. ^ Walter William Rouse Ball (2013). A Short Account of the History of Mathematics. ISBN 978-0-486-20630-1.
19. ^ Richard D. McKirahan (2011). Philosophy Before Socrates (Second
Edition): An Introduction with Texts and Commentary: An Introduction with Texts and Commentary. Hackett Publishing. pp. 88–89. ISBN 978-1-60384-612-7.
20. ^ Charles H. Kahn (2001). Pythagoras and the Pythagoreans. Hackett Publishing. p. 72. ISBN
978-1-60384-682-0.
21. ^ Charles H. Kahn (2001). Pythagoras and the Pythagoreans. Hackett Publishing. pp. 73–74. ISBN 978-1-60384-682-0.
22. ^ Jump up to:a b Richard D. McKirahan (2011). Philosophy Before Socrates (Second Edition): An Introduction
with Texts and Commentary: An Introduction with Texts and Commentary. Hackett Publishing. p. 89. ISBN 978-1-60384-612-7.
23. ^ Richard D. McKirahan (2011). Philosophy Before Socrates (Second Edition): An Introduction with Texts and Commentary: An
Introduction with Texts and Commentary. Hackett Publishing. p. 90. ISBN 978-1-60384-612-7.
24. ^ Richard D. McKirahan (2011). Philosophy Before Socrates (Second Edition): An Introduction with Texts and Commentary: An Introduction with Texts and
Commentary. Hackett Publishing. p. 91. ISBN 978-1-60384-612-7.
25. ^ Charles H. Kahn (2001). Pythagoras and the Pythagoreans. Hackett Publishing. p. 21. ISBN 978-1-60384-682-0.
26. ^ Charles H. Kahn (2001). Pythagoras and the Pythagoreans. Hackett
Publishing. pp. 21–22. ISBN 978-1-60384-682-0.
27. ^ Charles H. Kahn (2001). Pythagoras and the Pythagoreans. Hackett Publishing. p. 52. ISBN 978-1-60384-682-0.
28. ^ Gabriele Cornelli; Richard McKirahan; Constantinos Macris (2013). On Pythagoreanism.
Walter de Gruyter. p. 174. ISBN 978-3-11-031850-0.
29. ^ Gabriele Cornelli; Richard McKirahan; Constantinos Macris (2013). On Pythagoreanism. Walter de Gruyter. p. 84. ISBN 978-3-11-031850-0.
30. ^ Leonid Zhmud (2012). Pythagoras and the Early
Pythagoreans. Oxford University Press. p. 415. ISBN 978-0-19-928931-8.
31. ^ Constantine J. Vamvacas (2009). The Founders of Western Thought – The Presocratics. Springer Science & Business Media. p. 64. ISBN 978-1-4020-9791-1.
32. ^ Jump up to:a
b Constantine J. Vamvacas (2009). The Founders of Western Thought – The Presocratics. Springer Science & Business Media. p. 65. ISBN 978-1-4020-9791-1.
33. ^ Jump up to:a b The Cambridge Companion to Early Greek Philosophy. Cambridge University
Press. 1999. p. 84. ISBN 978-0-521-44667-9.
34. ^ Jump up to:a b Constantine J. Vamvacas (2009). The Founders of Western Thought – The Presocratics. Springer Science & Business Media. p. 72. ISBN 978-1-4020-9791-1.
35. ^ Jump up to:a b c Singer,
Charles (1949). A Short History of Science to the Nineteenth Century. Oxford: Oxford University Press. pp. 18–19. ISBN 1-306-39093-1. OCLC 869524436.
36. ^ Jump up to:a b c Constantine J. Vamvacas (2009). The Founders of Western Thought – The Presocratics.
Springer Science & Business Media. p. 68. ISBN 978-1-4020-9791-1.
37. ^ Jump up to:a b Constantine J. Vamvacas (2009). The Founders of Western Thought – The Presocratics. Springer Science & Business Media. p. 69. ISBN 978-1-4020-9791-1.
38. ^
Bruce Benward and Marilyn Nadine Saker (2003). Music: In Theory and Practice, seventh edition, 2 vols. (Boston: McGraw-Hill). Vol. I: p. 56. ISBN 978-0-07-294262-0.
39. ^ Kenneth Sylvan Guthrie, David R. Fideler (1987). The Pythagorean Sourcebook
and Library: An Anthology of Ancient Writings which Relate to Pythagoras and Pythagorean Philosophy, p.24. Red Wheel/Weiser. ISBN 9780933999510.
40. ^ Christoph Riedweg (2008). Pythagoras: His Life, Teaching, and Influence. Cornell University Press.
p. 30. ISBN 978-0-8014-7452-1.
41. ^ Jump up to:a b c Constantine J. Vamvacas (2009). The Founders of Western Thought – The Presocratics. Springer Science & Business Media. p. 70. ISBN 978-1-4020-9791-1.
42. ^ Constantine J. Vamvacas (2009). The
Founders of Western Thought – The Presocratics. Springer Science & Business Media. p. 71. ISBN 978-1-4020-9791-1.
43. ^ Dante and the Early Astronomers by M. A. Orr, 1913
44. ^ Jump up to:a b c Philolaus, Stanford Encyclopedia of Philosophy.
45. ^
Jump up to:a b c d Christoph Riedweg (2008). Pythagoras: His Life, Teaching, and Influence. Cornell University Press. p. 84. ISBN 978-0-8014-7452-1.
46. ^ Jump up to:a b Christoph Riedweg (2008). Pythagoras: His Life, Teaching, and Influence. Cornell
University Press. p. 85. ISBN 978-0-8014-7452-1.
47. ^ Aristotle. “13”. On the Heavens. Vol. II. Retrieved Apr 17, 2016.
48. ^ Burch 1954: 272–273, quoted in Philolaus, Stanford Encyclopedia of Philosophy.
49. ^ Jump up to:a b David R. Fideler
(1987). The Pythagorean Sourcebook and Library. Red Wheel/Weiser. p. 33. ISBN 978-1-60925-394-3.
50. ^ Hans Kelsen (2000). What is Justice?: Justice, Law, and Politics in the Mirror of Science: Collected Essays. The Lawbook Exchange. p. 99. ISBN
978-1-58477-101-2.
51. ^ Ian Michael Plant (2004). Women Writers of Ancient Greece and Rome: An Anthology. Equinox Publishing. p. 81. ISBN 978-1-904768-02-9.
52. ^ Jump up to:a b c Gordon Lindsay Campbell (2014). The Oxford Handbook of Animals
in Classical Thought and Life. Oxford University Press. p. 539. ISBN 978-0-19-103515-9.
53. ^ Prudence Allen (2005). The Concept of Woman: The Early Humanist Reformation, 1250-1500, Part 1. Wm. B. Eerdmans Publishing. p. 5. ISBN 978-0-8028-3346-4.
54. ^
Prudence Allen (2005). The Concept of Woman: The Early Humanist Reformation, 1250-1500, Part 1. Wm. B. Eerdmans Publishing. p. 22. ISBN 978-0-8028-3346-4.
55. ^ Charles H. Kahn (2001). Pythagoras and the Pythagoreans. ISBN 0-87220-575-4.
56. ^
Zhmud 2012, p. 232.
57. ^ Ferguson 2008, p. 5.
58. ^ Burkert 1985, pp. 300–301.
59. ^ Copleston 2003, pp. 30–31.
60. ^ Leonid Zhmud (2012). Pythagoras and the Early Pythagoreans. OUP Oxford. pp. 232–233. ISBN 978-0-19-928931-8.
61. ^ Richard
D. McKirahan (2011). Philosophy Before Socrates (Second Edition): An Introduction with Texts and Commentary: An Introduction with Texts and Commentary. Hackett Publishing. p. 88. ISBN 978-1-60384-612-7.
62. ^ See for instance the popular treatise
by Antonio Cocchi, Del vitto pitagorico per uso della medicina, Firenze 1743, which initiated a debate on the “Pythagorean diet”.
63. ^ Jump up to:a b c Gordon Lindsay Campbell (2014). The Oxford Handbook of Animals in Classical Thought and Lifen.
Oxford University Press. p. 540. ISBN 978-0-19-103515-9.
64. ^ Charles H. Kahn (2001). Pythagoras and the Pythagoreans. Hackett Publishing. p. 72. ISBN 978-1-60384-682-0.
65. ^ Gordon Lindsay Campbell (2014). The Oxford Handbook of Animals in
Classical Thought and Lifen. Oxford University Press. p. 530. ISBN 978-0-19-103515-9.
66. ^ Pomeroy, Sarah B. (2013). Pythagorean Women. Baltimore, MD: The Johns Hopkins University Press. p. 52. ISBN 978-1-4214-0957-3.
67. ^ Glenn, Cheryl, Rhetoric
Retold: Regendering the Tradition from Antiquity Through the Renaissance. Southern Illinois University, 1997. 30–31.
68. ^ Jump up to:a b Michelle Ballif; Michael G. Moran (2005). Classical Rhetorics and Rhetoricians: Critical Studies and Sources.
Greenwood Publishing Group. p. 317. ISBN 978-0-313-32178-8.
69. ^ Jump up to:a b Constantine J. Vamvacas (2009). The Founders of Western Thought – The Presocratics. Springer Science & Business Media. p. 76. ISBN 978-1-4020-9791-1.
70. ^ Jump up
to:a b Richard D. McKirahan (2011). Philosophy Before Socrates (Second Edition): An Introduction with Texts and Commentary: An Introduction with Texts and Commentary. Hackett Publishing. p. 80. ISBN 978-1-60384-612-7.
71. ^ Richard D. McKirahan
(2011). Philosophy Before Socrates (Second Edition): An Introduction with Texts and Commentary: An Introduction with Texts and Commentary. Hackett Publishing. p. 81. ISBN 978-1-60384-612-7.
72. ^ Jump up to:a b Damien Janos (2012). Method, Structure,
and Development in al-Fārābī’s Cosmology. BRILL. p. 118. ISBN 978-90-04-21732-4.
73. ^ Pierre Pellegrin (2000). Greek Thought: A Guide to Classical Knowledge. Harvard University Press. p. 918. ISBN 978-0-674-00261-6.
74. ^ Jump up to:a b c d
Everett Ferguson (2013). Encyclopedia of Early Christianity, Second Edition. Routledge. p. 804. ISBN 978-1-136-61158-2.
75. ^ Christoph Riedweg (2008). Pythagoras: His Life, Teaching, and Influence. Cornell University Press. p. 73. ISBN 978-0-8014-7452-1.
76. ^
Jump up to:a b c Joost-Gaugier, Christiane L. (2007). Measuring Heaven: Pythagoras and His Influence on Thought and Art in Antiquity and the Middle Ages. Cornell University Press. p. 118. ISBN 978-0-8014-7409-5.
77. ^ Jump up to:a b Joost-Gaugier
(2007, p. 119)
78. ^ Jump up to:a b c Joost-Gaugier (2007, p. 117)
79. ^ Bruhn 2005, pp. 65–66.
80. ^ Riedweg 2005, p. 29.
81. ^ Kahn 2001, pp. 1–2.
82. ^ Jump up to:a b Joost-Gaugier (2007, pp. 117–118)
83. ^ Jump up to:a b c d Joost-Gaugier
(2007, p. 120)
84. ^ Joost-Gaugier (2007, p. 123)
85. ^ Joost-Gaugier (2007, p. 125)
86. ^ Joost-Gaugier (2007, p. 124)
87. ^ Joost-Gaugier (2007, p. 126)
88. ^ Anthony Grafton; Glenn W. Most (2010). The Classical Tradition. The Belknap
Press of Harvard University Press. p. 798. ISBN 978-0-674-03572-0.
89. ^ Joost-Gaugier (2007, pp. 121–122)
90. ^ David C. Lindberg; Roy Porter; Katharine Park; Lorraine Daston; Mary Jo Nye; Theodore M. Porter; Dorothy Ross (2003). The Cambridge
History of Science: Volume 3, Early Modern Science. Cambridge University Press. p. 599. ISBN 978-0-521-57244-6.
91. ^ Charles H. Kahn (2001). Pythagoras and the Pythagoreans: A Brief History. Hackett Publishing. pp. 55–62. ISBN 978-0-87220-575-8.
92. ^
Lloyd Ridgeon (2011). Jawanmardi. Edinburgh University Press. p. 158. ISBN 978-0-7486-8815-9.
93. ^ Rosen, E. (1978). Aristarchus of Samos and Copernicus. The Bulletin of the American Society of Papyrologists, 15(1/2), 85-93. http://www.jstor.org/stable/24518756
94. ^
Lindberg, David C.; Porter, Roy; Park, Katharine; Daston, Lorraine; Nye, Mary Jo; Porter, Theodore M.; Ross, Dorothy (2003). The Cambridge History of Science: Volume 3, Early Modern Science. Cambridge University Press. p. 603. ISBN 978-0-521-57244-6.
95. ^
Lindberg, David C.; Porter, Roy; Park, Katharine; Daston, Lorraine; Nye, Mary Jo; Porter, Theodore M.; Ross, Dorothy (2003). The Cambridge History of Science: Volume 3, Early Modern Science. Cambridge University Press. pp. 597–598. ISBN 978-0-521-57244-6.
96. ^
Lindberg, David C.; Porter, Roy; Park, Katharine; Daston, Lorraine; Nye, Mary Jo; Porter, Theodore M.; Ross, Dorothy (2003). The Cambridge History of Science: Volume 3, Early Modern Science. Cambridge University Press. p. 604. ISBN 978-0-521-57244-6.
97. ^
Lindberg, David C.; Porter, Roy; Park, Katharine; Daston, Lorraine; Nye, Mary Jo; Porter, Theodore M.; Ross, Dorothy (2003). The Cambridge History of Science: Volume 3, Early Modern Science. Cambridge University Press. p. 609. ISBN 978-0-521-57244-6.
98. ^
Jump up to:a b Constantine J. Vamvacas (2009). The Founders of Western Thought – The Presocratics. Springer Science & Business Media. p. 77. ISBN 978-1-4020-9791-1.
Photo credit: https://www.flickr.com/photos/marfis75/7002703410/’]