From Wikipedia, the free encyclopedia
  (Redirected from Heliocentric)
Jump to: navigation, search
"Heliocentric" redirects here. For the albums, see Heliocentric (Paul Weller album) and Heliocentric (The Ocean Collective album). For heliocentric orbit, see Heliocentric orbit.
Andreas Cellarius's illustration of the Copernican system, from the Harmonia Macrocosmica (1708).



With the observations of William Herschel, Friedrich Bessel, and others, astronomers realized that the sun was not the center of the universe as heliocentrists at the time of Copernicus had supposed. Modern thinking is that there is no specific location that is the center of the universe, per Albert Einstein's principle of relativity.

Early developments[edit]



As these motions became better understood, more elaborate descriptions were required, the most famous of which was the geocentric Ptolemaic system, which achieved its full expression in the 2nd century. The Ptolemaic system was a sophisticated astronomical system that managed to calculate the positions for the planets to a fair degree of accuracy.[4] Ptolemy himself, in his Almagest, points out that any model for describing the motions of the planets is merely a mathematical device, and since there is no actual way to know which is true, the simplest model that gets the right numbers should be used.[5] However, he rejected the idea of a spinning earth as absurd as he believed it would create huge winds. His planetary hypotheses were sufficiently real that the distances of moon, sun, planets and stars could be determined by treating orbits' celestial spheres as contiguous realities. This made the stars' distance less than 20 Astronomical Units,[6] a regression, since Aristarchus of Samos's heliocentric scheme had centuries earlier necessarily placed the stars at least two orders of magnitude more distant.

Greek and Hellenistic world[edit]

See also: Greek astronomy


The non-geocentric model of the Universe was proposed by the Pythagorean philosopher Philolaus (d. 390 BC), who taught that at the center of the Universe was a "central fire", around which the Earth, Sun, Moon and Planets revolved in uniform circular motion. This system postulated the existence of a counter-earth collinear with the Earth and central fire, with the same period of revolution around the central fire as the Earth. The Sun revolved around the central fire once a year, and the stars were stationary. The Earth maintained the same hidden face towards the central fire, rendering both it and the "counter-earth" invisible from Earth. The Pythagorean concept of uniform circular motion remained unchallenged for approximately the next 2000 years, and it was to the Pythagoreans that Copernicus referred to show that the notion of a moving Earth was neither new nor revolutionary.[7] Kepler gave an alternative explanation of the Pythagoreans' "central fire" as the Sun, "as most sects purposely hid[e] their teachings".[8]

Heraclides of Pontus (4th century BC) said that the rotation of the Earth explained the apparent daily motion of the celestial sphere. It used to be thought that he believed Mercury and Venus to revolve around the Sun, which in turn (along with the other planets) revolves around the Earth.[9] Macrobius Ambrosius Theodosius (AD 395–423) later described this as the "Egyptian System," stating that "it did not escape the skill of the Egyptians," though there is no other evidence it was known in ancient Egypt.[10][11]

Aristarchus of Samos[edit]






Seleucus of Seleucia[edit]

Since Plutarch mentions the "followers of Aristarchus" in passing, it is likely that there were other astronomers in the Classical period who also espoused heliocentrism, but whose work was lost. The only other astronomer from antiquity known by name who is known to have supported Aristarchus' heliocentric model was Seleucus of Seleucia (b. 190 BC), a Hellenistic astronomer who flourished a century after Aristarchus in the Seleucid empire.[14] Seleucus adopted the heliocentric system of Aristarchus and is said to have proved the heliocentric theory.[15] According to Bartel Leendert van der Waerden, Seleucus may have proved the heliocentric theory by determining the constants of a geometric model for the heliocentric theory and by developing methods to compute planetary positions using this model. He may have used early trigonometric methods that were available in his time, as he was a contemporary of Hipparchus.[16] A fragment of a work by Seleucus has survived in Arabic translation, which was referred to by Rhazes (b. 865).[17]

Alternatively, his explanation may have involved the phenomenon of tides,[18] which he supposedly theorized to be caused by the attraction to the Moon and by the revolution of the Earth around the Earth-Moon 'center of mass'.

Medieval Europe[edit]


There were occasional speculations about heliocentrism in Europe before Copernicus. In Roman Carthage, the pagan Martianus Capella (5th century A.D.) expressed the opinion that the planets Venus and Mercury did not go about the Earth but instead circled the Sun.[19] Capella's model was discussed in the Early Middle Ages by various anonymous 9th-century commentators[20] and Copernicus mentions him as an influence on his own work.[21]



The earliest traces of a counter-intuitive[citation needed] idea that it is the Earth that is actually moving and the Sun that is at the centre of the solar system (hence the concept of heliocentrism) is found in several Vedic Sanskrit texts written in ancient India. Yajnavalkya (c. 9th– 8th century BC) recognized that the Earth is spherical and believed that the Sun was "the centre of the spheres" as described in the Vedas at the time. In his astronomical text Shatapatha Brahmana ( he states: "The sun strings these worlds - the earth, the planets, the atmosphere - to himself on a thread." He recognized that the Sun was much larger than the Earth, which would have influenced this early heliocentric concept. He also accurately measured the relative distances of the Sun and the Moon from the Earth as 108 times the diameters of these heavenly bodies, close to the modern measurements of 107.6 for the Sun and 110.6 for the Moon. He also described a solar calendar in the Shatapatha Brahmana.

The Vedic Sanskrit text Aitareya Brahmana (2.7) (c. 9th–8th century BC) also states: "The Sun never sets nor rises thats right. When people think the sun is setting, it is not so; they are mistaken." This indicates that the Sun is stationary (hence the Earth is moving around it), which is elaborated in a later commentary Vishnu Purana (2.8) (c. 1st century), which states: "The sun is stationed for all time, in the middle of the day. [...] Of the sun, which is always in one and the same place, there is neither setting nor rising." (See Haug, Martin and Basu (1974), Joseph (2000), Kak (2000) in Selin (2000), Teresi (2002) and Blavatsky (1877) for further information.)[23]



Medieval Islamic world[edit]


Muslim astronomers generally accepted the Ptolemaic system and the geocentric model,[31] but by the 10th century texts appeared regularly whose subject matter was doubts concerning Ptolemy (shukūk).[32] Several Muslim scholars questioned the Earth's apparent immobility[33][34] and centrality within the universe.[35] Some accepted that the Earth rotates around its axis, such as the 10th-century astronomer Abu Sa'id al-Sijzi (d. circa 1020).[36][37] According to al-Biruni, Sijzi invented an astrolabe called al-zūraqī based on a belief held by some of his contemporaries "that the motion we see is due to the Earth's movement and not to that of the sky."[37][38] The prevalence of this view is further confirmed by a reference from the 13th century which states:


Early in the 11th century Alhazen wrote a scathing critique of Ptolemy's model in his Doubts on Ptolemy (c. 1028), which some have interpreted to imply he was criticizing Ptolemy's geocentrism,[39] but most agree that he was actually criticizing the details of Ptolemy's model rather than his geocentrism.[40] Abu Rayhan Biruni (b. 973) discussed the possibility of whether the Earth rotated about its own axis and around the Sun, but in his Masudic Canon, he set forth the principles that the Earth is at the center of the universe and that it has no motion of its own.[41] He was aware that if the Earth rotated on its axis, this would be consistent with his astronomical parameters,[42] but he considered it a problem of natural philosophy rather than mathematics.[37][43]

In the 12th century, some Islamic astronomers developed complete alternatives to the Ptolemaic system (although not heliocentric), such as Nur ad-Din al-Bitruji, who considered the Ptolemaic model as mathematical, and not physical.[44][45] Al-Bitruji's alternative system spread through most of Europe in the 13th century, with debates and refutations of his ideas continued up to the 16th century.[45]

At the Maragha and Samarkand observatories, the Earth's rotation was discussed by al-Kātibī (d. 1277),[46] Tusi (b. 1201) and Qushji (b. 1403). The arguments and evidence used by Tusi and Qushji resemble those used by Copernicus to support the Earth's motion.[33][34] However, it remains a fact that the Maragha school never made the big leap to heliocentrism.[47] Some historians maintain that the thought of the Maragha school influenced Copernicus, in particular the mathematical devices known as the Urdi lemma and the Tusi couple.[43][48][49][50][51] Copernicus used such devices in the same planetary models as found in Arabic sources.[52] Furthermore, the exact replacement of the equant by two epicycles used by Copernicus in the Commentariolus was found in an earlier work by Ibn al-Shatir (d. c. 1375) of Damascus.[53] Ibn al-Shatir's lunar and Mercury models are also identical to those of Copernicus.[54] However, this remains speculative as no researcher has yet proven that Copernicus knew about Ibn al-Shatir's work or the Maragha school.[47][55][56] It has been argued that Copernicus could have independently discovered the Tusi couple or took the idea from Proclus's Commentary on the First Book of Euclid,[57] which Copernicus cited.[58] Another possible source for Copernicus's knowledge of this mathematical device is the Questiones de Spera of Nicole Oresme, who described how a reciprocating linear motion of a celestial body could be produced by a combination of circular motions similar to those proposed by al-Tusi.[59] Nevertheless, Copernicus cited some of the Islamic astronomers whose theories and observations he used in De Revolutionibus, namely al-Battani, Thabit ibn Qurra, al-Zarqali, Ibn Rushd, and al-Bitruji.[60]

Copernican revolution[edit]

Astronomical model[edit]


In the 16th century, Nicolaus Copernicus's De revolutionibus presented a discussion of a heliocentric model of the universe in much the same way as Ptolemy's Almagest had presented his geocentric model in the 2nd century. Copernicus discussed the philosophical implications of his proposed system, elaborated it in geometrical detail, used selected astronomical observations to derive the parameters of his model, and wrote astronomical tables which enabled one to compute the past and future positions of the stars and planets. In doing so, Copernicus moved heliocentrism from philosophical speculation to predictive geometrical astronomy. In reality, Copernicus's system did not predict the planets' positions any better than the Ptolemaic system.[61] This theory resolved the issue of planetary retrograde motion by arguing that such motion was only perceived and apparent, rather than real: it was a parallax effect, as an object that one is passing seems to move backwards against the horizon. This issue was also resolved in the geocentric Tychonic system; the latter, however, while eliminating the major epicycles, retained as a physical reality the irregular back-and-forth motion of the planets, which Kepler characterized as a "pretzel".[62]

Copernicus cited Aristarchus in an early (unpublished) manuscript of De Revolutionibus (which still survives), stating: "Philolaus believed in the mobility of the earth, and some even say that Aristarchus of Samos was of that opinion."[63] However, in the published version he restricts himself to noting that in works by Cicero he had found an account of the theories of Hicetas and that Plutarch had provided him with an account of the Pythagoreans Heraclides Ponticus, Philolaus, and Ecphantus. These authors had proposed a moving earth, which did not, however, revolve around a central sun.

Religious attitudes to heliocentrism[edit]


Circulation of Commentariolus (before 1515)[edit]

The first information about the heliocentric views of Nicolaus Copernicus was circulated in manuscript completed some time before May 1, 1514.[65] Although only in manuscript, Copernicus' ideas were well known among astronomers and others. His ideas contradicted the then-prevailing understanding of the Bible. In the King James Bible First Chronicles 16:30 state that "the world also shall be stable, that it be not moved." Psalm 104:5 says, "[the Lord] Who laid the foundations of the earth, that it should not be removed for ever." Ecclesiastes 1:5 states that "The sun also ariseth, and the sun goeth down, and hasteth to his place where he arose."

Nonetheless, in 1533, Johann Albrecht Widmannstetter delivered in Rome a series of lectures outlining Copernicus' theory. The lectures were heard with interest by Pope Clement VII and several Catholic cardinals.[66] On November 1, 1536, Archbishop of Capua Nikolaus von Schönberg wrote a letter to Copernicus from Rome encouraging him to publish a full version of his theory.

However, in 1539, Martin Luther said:


This was reported in the context of a conversation at the dinner table and not a formal statement of faith. Melanchthon, however, opposed the doctrine over a period of years.[68][69]

Publication of de Revolutionibus (1543)[edit]


Some years after the publication of De Revolutionibus John Calvin preached a sermon in which he denounced those who "pervert the order of nature" by saying that "the sun does not move and that it is the earth that revolves and that it turns".[70]

On the other hand, Calvin is not responsible for another famous quotation which has often been misattributed to him: "Who will venture to place the authority of Copernicus above that of the Holy Spirit?" It has long been established that this line cannot be found in any of Calvin's works.[71][72][73] It has been suggested[74] that the quotation was originally sourced from the works of Lutheran theologian Abraham Calovius.

Tycho Brahe's geo-heliocentric system c. 1587[edit]



Tycho appreciated the Copernican system, but objected to the idea of a moving Earth on the basis of physics, astronomy, and religion. The Aristotelian physics of the time (modern Newtonian physics was still a century away) offered no physical explanation for the motion of a massive body like Earth, whereas it could easily explain the motion of heavenly bodies by postulating that they were made of a different sort substance called aether that moved naturally. So Tycho said that the Copernican system "... expertly and completely circumvents all that is superfluous or discordant in the system of Ptolemy. On no point does it offend the principle of mathematics. Yet it ascribes to the Earth, that hulking, lazy body, unfit for motion, a motion as quick as that of the aethereal torches, and a triple motion at that."[75] Likewise, Tycho took issue with the vast distances to the stars that Aristarchus and Copernicus had assumed in order to explain the lack of any visible parallax. Tycho had measured the apparent sizes of stars (now known to be illusory – see stellar magnitude), and used geometry to calculate that in order to both have those apparent sizes and be as far away as heliocentrism required, stars would have to be huge (much larger than the sun; the size of Earth's orbit or larger). Regarding this Tycho wrote, "Deduce these things geometrically if you like, and you will see how many absurdities (not to mention others) accompany this assumption [of the motion of the earth] by inference."[76] He also cited the Copernican system's "opposition to the authority of Sacred Scripture in more than one place" as a reason why one might wish to reject it, and observed that his own geoheliocentric alternative "offended neither the principles of physics nor Holy Scripture".[77]


Publication of Starry messenger (1610)[edit]





1616 ban against Copernicanism[edit]

Main article: Galileo affair

In February 1615, prominent Dominicans including Thomaso Caccini and Niccolò Lorini brought Galileo's writings on heliocentrism to the attention of the Inquisition, because they appeared to violate Holy Scripture and the decrees of the Council of Trent.[80][81] Cardinal and Inquisitor Robert Bellarmine was called upon to adjudicate, and wrote in April that treating heliocentrism as a real phenomenon would be "a very dangerous thing," irritating philosophers and theologians, and harming "the Holy Faith by rendering Holy Scripture as false."[82]

In January 1616 Msgr. Francesco Ingoli addressed an essay to Galileo disputing the Copernican system. Galileo later stated that he believed this essay to have been instrumental in the ban against Copernicanism that followed in February.[83] According to Maurice Finocchiaro, Ingoli had probably been commissioned by the Inquisition to write an expert opinion on the controversy, and the essay provided the "chief direct basis" for the ban.[84] The essay focused on eighteen physical and mathematical arguments against heliocentrism. It borrowed primarily from the arguments of Tycho Brahe, and it notedly mentioned the problem that heliocentrism requires the stars to be much larger than the sun. Ingoli wrote that the great distance to the stars in the heliocentric theory "clearly proves ... the fixed stars to be of such size, as they may surpass or equal the size of the orbit circle of the Earth itself."[85] Ingoli included four theological arguments in the essay, but suggested to Galileo that he focus on the physical and mathematical arguments. Galileo did not write a response to Ingoli until 1624.[86]

In February 1616, the Inquisition assembled a committee of theologians, known as qualifiers, who delivered their unanimous report condemning heliocentrism as "foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture." The Inquisition also determined that the Earth's motion "receives the same judgement in philosophy and ... in regard to theological truth it is at least erroneous in faith."[87] Bellarmine personally ordered Galileo


— Bellarmine and the Inquisition's injunction against Galileo, 1616[88]

In March, after the Inquisition's injunction against Galileo, the papal Master of the Sacred Palace, Congregation of the Index, and Pope banned all books and letters advocating the Copernican system, which they called "the false Pythagorean doctrine, altogether contrary to Holy Scripture."[88][89] In 1618 the Holy Office recommended that a modified version of Copernicus' De Revolutionibus be allowed for use in calendric calculations, though the original publication remained forbidden until 1758.[89]



Publication of Dialogue concerning the two chief world systems[edit]

Pope Urban VIII encouraged Galileo to publish the pros and cons of Heliocentrism. Galileo's response, Dialogue concerning the two chief world systems, clearly advocated heliocentrism, despite his declaration in the preface that

I will endeavour to show that all experiments that can be made upon the Earth are insufficient means to conclude for its mobility but are indifferently applicable to the Earth, movable or immovable...[90]

and his straightforward statement,

I might very rationally put it in dispute, whether there be any such centre in nature, or no; being that neither you nor any one else hath ever proved, whether the World be finite and figurate, or else infinite and interminate; yet nevertheless granting you, for the present, that it is finite, and of a terminate Spherical Figure, and that thereupon it hath its centre...[90]

Some ecclesiastics also interpreted the book as characterizing the Pope as a simpleton, since his viewpoint in the dialogue was advocated by the character Simplicio. Urban VIII became hostile to Galileo and he was again summoned to Rome.[91] Galileo's trial in 1633 involved making fine distinctions between "teaching" and "holding and defending as true". For advancing heliocentric theory Galileo was forced to recant Copernicanism and was put under house arrest for the last few years of his life.

According to J. L. Heilbron,[92] informed contemporaries of Galileo's:


Subsequent developments[edit]

René Descartes postponed, and ultimately never finished, his treatise The World, which included a heliocentric model,[93] but the Galileo affair did little to slow the spread of heliocentrism across Europe, as Kepler's Epitome of Copernican Astronomy became increasingly influential in the coming decades.[94] By 1686 the model was well enough established that the general public was reading about it in Conversations on the Plurality of Worlds, published in France by Bernard le Bovier de Fontenelle and translated into English and other languages in the coming years. It has been called "one of the first great popularizations of science."[93]





The Roman Catholic Church currently operates the Vatican Observatory, home to multiple award winning scholars, showing their ultimate acceptance of heliocentrism by furthering the field.

Heliocentrism and Judaism[edit]




In 1629 a new Hebrew book "Elim" by Joseph Solomon Delmedigo (1591–1655) appeared. The author says that the arguments of Copernicus are so strong, that only an imbecile will not accept them.[100] Delmedigo studied at Padua and was acquainted with Galileo.[101]

The following wave of Hebrew literature on the subject is from the 18th century. Most of its authors were for Copernicus, although David Nieto and Tobias Cohn were exceptions. These two authors gave the same reason for opposing heliocentrism—namely, contradiction of the Bible—although Nieto merely rejected the new system on those grounds without much passion, whereas Hacohen went so far as to call Copernicus "a first-born of Satan". Hacohen also mentions the fact that the Sages of Talmud derived the Hebrew name of Earth from the verb "run".[101]

In later periods there were no explicit attacks on heliocentrism, although some Rabbis were not sure about the point.[102][103]

In the 20th century R. M.M. Schneerson suggested that the theory of relativity makes the question obsolete, as he writes; "on the basis of the presently accepted scientific view (in accordance with the theory of Relativity) that where two bodies in space are in motion relative to one another, it is impossible scientifically to ascertain which revolves around which, or which is stationary and the other in motion. Therefore, to say that there is, or can be, "scientific proof" that the earth revolves around the sun is quite an unscientific and uncritical statement."[104]

The view of modern science[edit]




Even if the discussion is limited to the solar system, the Sun is not at the geometric center of any planet's orbit, but rather approximately at one focus of the elliptical orbit. Furthermore, to the extent that a planet's mass cannot be neglected in comparison to the Sun's mass, the center of gravity of the solar system is displaced slightly away from the center of the Sun.[96] (The masses of the planets, mostly Jupiter, amount to 0.14% of that of the Sun.) Therefore, a hypothetical astronomer on an extrasolar planet would observe a small "wobble" in the Sun's motion.

Modern use of geocentric and heliocentric[edit]


See also[edit]


  2. ^ Dreyer (1953), pp.135–48; Linton (2004), pp.38–9). The work of Aristarchus's in which he proposed his heliocentric system has not survived. We only know of it now from a brief passage in Archimedes's The Sand Reckoner.
  3. ^ according to Lucio Russo, the heliocentric view was expounded in Hipparchus's work on gravity. (source: Lucio Rosso, The Forgotten Revolution, How Science was Born in 300BC and Why it had to be Reborn, pp 293-296)
  6. ^ Dennis Duke, Ptolemy's Universe
  10. ^ Otto E. Neugebauer (1975), A history of ancient mathematical astronomy, Berlin/Heidelberg/New York: Springer, p. 695, ISBN 3-540-06995-X 
  11. ^ Rufus, W. Carl (1923), "The astronomical system of Copernicus", Popular Astronomy 31: 510–521 [512], Bibcode:1923PA.....31..510R, at pp. 511-512 
  12. ^ Arenarius, I., 4–7
  14. ^ Murdin, Paul, Murdin, Paul, ed., Seleucus of Seleucia (c. 190 BC-?), Institute of Physics Publishing, Bibcode:2000eaa..bookE3998., doi:10.1888/0333750888, ISBN 0-333-75088-8, retrieved 2009-08-08 
  24. ^ a b Joseph (2000).
  25. ^ Thurston (1994).
  31. ^ Sabra, A. I. (1998). "Configuring the Universe: Aporetic, Problem Solving, and Kinematic Modeling as Themes of Arabic Astronomy". Perspectives on Science 6 (3): 288–330.  at pp. 317–18:


  39. ^ Qadir (1989), p. 5–10.
  40. ^ Nicolaus Copernicus, Stanford Encyclopedia of Philosophy (2004).
  43. ^ a b Saliba (1999).
  44. ^ Samsó, Julio (2007). "Biṭrūjī: Nūr al‐Dīn Abū Isḥāq [Abū Jaʿfar] Ibrāhīm ibn Yūsuf al‐Biṭrūjī". In Thomas Hockey; et al. The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 133–4. ISBN 978-0-387-31022-0.  (PDF version)
  46. ^ Hikmat al-'Ain, p. 78
  48. ^ Roberts, V.; Kennedy, E. S. (1959). "The Planetary Theory of Ibn al-Shatir". Isis 50: 232–234. doi:10.1086/348774. 
  50. ^ A. I. Sabra (1998).
  53. ^ Swerdlow, Noel M. (1973-12-31). "The Derivation and First Draft of Copernicus's Planetary Theory: A Translation of the Commentariolus with Commentary". Proceedings of the American Philosophical Society 117 (6): 424. ISSN 0003-049X. JSTOR 986461. 
  56. ^ Viktor Blåsjö, "A Critique of the Arguments for Maragha Influence on Copernicus", Journal for the History of Astronomy, 45 (2014), 183-195 ADS.
  62. ^ Gingerich, (2004, p. 51)
  63. ^ Gingerich, O. "Did Copernicus Owe a Debt to Aristarchus?" Journal for the History of Astronomy, Vol.16, NO.1/FEB, P. 37, 1985. As mentioned earlier in this article, Philolaus had the Earth moving round a Central Fire which was not the Sun, so Copernicus's reference to Aristarchus's model as possibly geodynamic does not necessarily imply that he thought it was heliocentric.
  65. ^ A library catalogue of a 16th-century historian, Matthew of Miechow, bears that date and contains a reference to the manuscript, so it must have begun circulating before that date (Koyré, 1973, p.85; Gingerich, 2004, p.32).
  66. ^ Speller (2008, p.51)
  67. ^ http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit3/response.html
  68. ^ Melanchthon, Elements of Physics, 1st. edition, 1549
  69. ^ Revolution in Science, I. Bernard Cohen, page 497.
  78. ^ Fantoli, 2003, p. 109
  79. ^ Arthur Koestler, The Sleepwalkers (Penguin Arkana, 1989 p. 433)
  80. ^ Langford (1992), p.56-57
  81. ^ Drake (1978, p.240), Sharratt (1994, pp.110−111), Favaro (1907, 19:297−298) (Italian).
  82. ^ Sharratt (1994, pp.110−115)
  84. ^ Finocchiaro (2010, pp. 72)
  85. ^ Graney (2015, pp. 71)
  87. ^ Favaro (1907, 19:320), Domínguez (2014); arXiv:1402.6168 Original text of the decision
  88. ^ a b Heilbron (2010), p.218
  90. ^ a b The Systeme of the World: in Four Dialogues (1661) Thomas Salusbury translation of Dialogo sopra i Due Massi Sistemi del Mondo (1632)
  91. ^ Arthur Koestler, The Sleepwalkers (Penguin Arkana, 1989 p. 491)
  92. ^ Heilbronn (1999, p.203)
  100. ^ Sefer Elim, Amsterdam, 1629, стр. 304
  103. ^ Hatam Sopher (1762–1839) "Kovetz Tshuvot", 26

External links[edit]