1056:, which asserted that the scholar fabricated his observations to fit his theories. Newton accused Ptolemy of systematically inventing data or doctoring the data of earlier astronomers, and labelled him "the most successful fraud in the history of science". One striking error noted by Newton was an autumn equinox said to have been observed by Ptolemy and "measured with the greatest care" at 2pm on 25 September 132, when the equinox should have been observed at 9:54am the day prior. Herbert Lewis, who had reworked some of Ptolemy's calculations, agreed with Newton that "Ptolemy was an outrageous fraud", and that "all those results capable of statistical analysis point beyond question towards fraud and against accidental error".
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because of his knowledge of precession, which distinguishes him from all his predecessors. Hipparchus' celestial globe had an ecliptic drawn in, but the coordinates were equatorial. Since
Hipparchus' star catalogue has not survived in its original form, but was absorbed into the Almagest star catalogue (and heavily revised in the 265 years in between), the Almagest star catalogue is the oldest one in which complete tables of coordinates and magnitudes have come down to us.
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great, if not indeed the first, scientific treatise." He continued, "Newton’s work does focus critical attention on the many difficulties and inconsistencies apparent in the fine structure of the
Almagest. In particular, his conclusion that the Almagest is not a historical account of how Ptolemy actually derived his models and parameters is essentially the same as mine, although our reasons for this conclusion and our inferences from it differ radically."
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indeed be traced back to
Hipparchus, but not that the complete star catalogue was simply "copied". Rather, Hipparchus' major errors are no longer present in the Almagest and, on the other hand, Hipparchus' star catalogue had some stars that are entirely absent from the Almagest. It can be concluded that Hipparchus' star catalogue, while forming the basis, has been reobserved and revised.
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Under the scrutiny of modern scholarship, and the cross-checking of observations contained in the
Almagest against figures produced through backwards extrapolation, various patterns of errors have emerged within the work. A prominent example is Ptolemy's use of measurements said to have been taken at
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Ptolemy's comprehensive treatise of mathematical astronomy superseded most older texts of Greek astronomy. Some were more specialized and thus of less interest; others simply became outdated by the newer models. As a result, the older texts ceased to be copied and were gradually lost. Much of what we
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adopted
Hipparchus' solar model, which consisted of a simple eccentric deferent. For the Moon, Ptolemy began with Hipparchus' epicycle-on-deferent, then added a device that historians of astronomy refer to as a "crank mechanism": he succeeded in creating models for the other planets, where Hipparchus
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Subtracting the systematic error leaves other errors that cannot be explained by precession. Of these errors, about 18 to 20 are also found in
Hipparchus' star catalogue (which can only be reconstructed incompletely). From this it can be concluded that a subset of star coordinates in the Almagest can
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Errors in
Ptolemy’s star catalogue: In blue are the stars in the Almagest’s list; in orange, the points of modern measurements transformed to the second century, taking proper motion into account; the orange and blue band is the ecliptic; and the blue curve is the equator. Figure inspired by Hoffmann
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Many of the longitudes and latitudes have been corrupted in the various manuscripts. Most of these errors can be explained by similarities in the symbols used for different numbers. For example, the Greek letters Α and Δ were used to mean 1 and 4 respectively, but because these look similar copyists
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consists of thirteen sections, called books. As with many medieval manuscripts that were handcopied or, particularly, printed in the early years of printing, there were considerable differences between various editions of the same text, as the process of transcription was highly personal. An example
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The catalogue actually contained 1,028 entries, but three of these were deliberate duplicates, because
Ptolemy regarded certain stars as being shared between adjacent constellations. Three other entries were non-stellar, i.e. the Double Cluster in Perseus, M44 (Praesepe) in Cancer, and the globular
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The layout of the catalogue has always been tabular. Ptolemy writes explicitly that the coordinates are given as (ecliptical) "longitudes" and "latitudes", which are given in columns, so this has probably always been the case. It is significant that
Ptolemy chooses the ecliptical coordinate system
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278 years earlier, rejected the qualification of fraud. John
Phillips Britton, Visiting Fellow at Yale University, wrote of R.R. Newton, "I think that his main conclusion with respect to Ptolemy’s stature and achievements as an astronomer is simply wrong, and that the Almagest should be seen as a
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Although no line figures have survived from antiquity, the figures can be reconstructed on the basis of the descriptions in the star catalogue: The exact celestial coordinates of the figures' heads, feet, arms, wings and other body parts are recorded. It is therefore possible to draw the stick
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The star catalogue contains 48 constellations, which have different surface areas and numbers of stars. In Book VIII, Chapter 3, Ptolemy writes that the constellations should be outlined on a globe, but it is unclear exactly how he means this: should surrounding polygons be drawn or should the
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covers motion in latitude, that is, the deviation of planets from the ecliptic. The final topic of this chapter also covers how to determine when a planet first becomes visible after being hidden by the glare of the sun, as well as the last time it is seen before being hidden by the sun's
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Even without the errors introduced by copyists, and even accounting for the fact that the longitudes are more appropriate for 58 AD than for 137 AD, the latitudes and longitudes are not fully accurate, with errors as great as large fractions of a degree. Some errors may be due to
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Of the stars in the catalogue, 108 (just over 10%) were classified by Ptolemy as 'unformed', by which he meant lying outside the recognized constellation figures. These were later absorbed into their surrounding constellations or in some cases used to form new constellations.
992:, was intended to supplant the old translation. The new translation was a great improvement; the new commentary was not, and aroused criticism. The Pope declined the dedication of George's work, and Regiomontanus's translation had the upper hand for over 100 years.
1151:, including detailed historical comments in a 69-page preface. It has been described as "suffer from excessive literalness, particularly where the text is difficult" by Toomer, and as "very faulty" by Serge Jodra. The scanned books are available in full at the
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existed.) This system is believed to have originated with Hipparchus. The stellar positions too are of Hipparchan origin, despite Ptolemy's claim to the contrary. Ptolemy identified 48 constellations: The 12 of the
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as a textbook of mathematical astronomy. It explained geometrical models of the planets based on combinations of circles, which could be used to predict the motions of celestial objects. In a later book, the
533:, which occurs when planets appear to pause, then briefly reverse their motion against the background of the zodiac. Ptolemy understood these terms to apply to Mercury and Venus as well as the outer planets.
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and the northern zodiac constellations (Aries through Virgo) are in the table at the end of Book VII, while the rest are in the table at the beginning of Book VIII. The brightest stars were marked first
606:, most of the stars of a given zodiac constellation in the catalog fall in the 30-degree range designated by the same name. The ecliptic longitudes are about 26° lower than those of AD 2000 (the
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wrote, "Unfortunately, Newton’s arguments in support of these charges are marred by all manner of distortions, misunderstandings, and excesses of rhetoric due to an intensely polemical style."
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The overall quality of Claudius Ptolemy's scholarship and place as "one of the most outstanding scientists of antiquity" has been challenged by several modern writers, most prominently by
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that all coordinates were calculated from Hipparchus' observations, whereby the precession constant, which was known too inaccurately at the time, led to a summation error (Delambre 1817);
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noon, but which systematically produce readings that are off by half an hour, as if the observations were taken at 12:30pm. However, an explanation for this error was found in 1969.
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which was 265 years earlier (Alm. VII, 2). But calculations show that his ecliptic longitudes correspond more closely to around the middle of the first century CE (+48 to +58).
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Example of a Greek manuscript of the Almagest, showing a table layout for the stars of Ursa Minor. The functions of the columns, colours and rows are labelled in this depiction.
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As mentioned, Ptolemy includes a star catalog containing 1022 stars. He says that he "observed as many stars as it was possible to perceive, even to the sixth magnitude". The
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covers problems associated with the daily motion attributed to the heavens, namely risings and settings of celestial objects, the length of daylight, the determination of
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and the eccentric deferent to astronomy. Hipparchus (2nd century BC) had crafted mathematical models of the motion of the Sun and Moon. Hipparchus had some knowledge of
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includes five main points, each of which is the subject of a chapter in Book I. What follows is a close paraphrase of Ptolemy's own words from Toomer's translation.
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are given in terms of a zodiac constellation and a number of degrees and fractions of a degree. The zodiac constellations each represent exactly 30°, starting with
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sometimes wrote the wrong one. In Arabic manuscripts, there was confusion between for example 3 and 8 (ج and ح). (At least one translator also introduced errors.
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The figure he used is based on Hipparchus' own estimate for precession, which was 1° in 100 years, instead of the correct 1° in 72 years. Dating attempts through
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Vogt, H. (1925). "Versuch einer Wiederherstellung von Hipparchs Fixsternverzeichnis" [Attempting a restoration of Hipparchus' fixed-star catalog].
836:, and he felt that Greek models should match those of the Babylonians in accuracy. He was unable to create accurate models for the remaining five planets.
405:, and other observations that change with the observer's position. There is also a study of the angles made by the ecliptic with the vertical, with tables.
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Ptolemy inherited from his Greek predecessors a geometrical toolbox and a partial set of models for predicting where the planets would appear in the sky.
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representing longitude 0° to 30°. The degrees are added to the lower limit of the 30-degree range to obtain the longitude. Unlike the situation with the
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Geometric construction used by Hipparchus in his determination of the distances to the Sun and Moon, which was later incorporated into Ptolemy's work
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A podcast discussion by Prof. M Heath and Dr A. Chapman of a recent re-discovery of a 14th-century manuscript in the university of Leeds Library
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These modern stick figures as a reconstruction of the historical constellations of the Almagest are available in the free planetarium software
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made a full translation accompanied by a commentary that was as long as the original text. George's translation, done under the patronage of
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Hamilton, N. T.; Swerdlow, N. M. (1987). "The Canobic Inscription: Ptolemy's Earliest Work". In Berggren, J. L.; Goldstein, B. R. (eds.).
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by Robert Van Gent. Positions for any date, translation of dates in calendars used by Ptolemy. Extensive list of references and articles.
668:, who translated an Arabic manuscript into Latin around 1175, put 300° for the latitude of several stars. He had apparently learned from
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made the first Latin translation directly from a Greek copy, but it was not as influential as a later translation into Latin made in
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made in the 12th century from an Arabic translation, which would endure until original Greek copies resurfaced in the 15th century.
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that were formally adopted by the International Astronomical Union in 1922, with official boundaries that were agreed in 1928.
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The Earth, in relation to the distance of the fixed stars, has no appreciable size and must be treated as a mathematical point.
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Although some have described the charges laid by Newton as "erudite and imposing", others have disagreed with the findings.
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Since Tycho Brahe found this offset, astronomers and historians investigated this problem and suggested several causes:
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Dambis, A. K.; Efremov, Yu. N. (2000). "Dating Ptolemy's Star Catalogue through Proper Motions: The Hipparchan Epoch".
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for Hipparchus. In the 13th century a Spanish version was produced, which was later translated under the patronage of
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355:'s cosmology: on the spherical form of the heavens, with the spherical Earth lying motionless as the center, with the
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which are now around ecliptic longitude 91° are attributed longitudes in the Almagest of 66° and 64°20' respectively.
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Kunitzsch, Paul (2008) . "Almagest: Its Reception and Transmission in the Islamic World". In Selin, Helaine (ed.).
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that the difference is a sum of individual errors of various kinds, including calibration with outdated solar data;
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In the 15th century, a Greek version appeared in Western Europe. The German astronomer Johannes Müller (known as
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The first translations into Arabic were made in the 9th century, with two separate efforts, one sponsored by the
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1299: = 6). Each numerical magnitude was considered twice the brightness of the following one, which is a
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806:(5th century AD) put Mercury and Venus in motion around the Sun. Ptolemy's authority was preferred by most
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causing stars that are low in the sky to appear higher than where they really are. A series of stars in
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was organized is given below; it is a Latin edition printed in 1515 at Venice by Petrus Lichtenstein.
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that the data had in fact been observed a century earlier by Menelaus of Alexandria (Björnbo 1901);
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2518:(24 February 1978). "Casting Doubt on Ptolemy: The Crime of Claudius Ptolemy. Robert R. Newton".
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A direct French translation from the Greek text was published in two volumes in 1813 and 1816 by
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in 1984, with a second edition in 1998. The third was a partial translation by Bruce M. Perry in
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cover the motions of the fixed stars, including precession of the equinoxes. They also contain a
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could not have been completed before about 150, a quarter-century after Ptolemy began observing.
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of the stars also appear to date the actual observation to Hipparchus' time instead of Ptolemy.
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1973:. Studies in the History of Mathematics and Physical Sciences. Vol. 14. Berlin: Springer.
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from the Arabic (finished in 1175). Gerard translated the Arabic text while working at the
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Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures
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614:(138 AD) and that he found that the longitudes had increased by 2° 40′ since the time of
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epoch). Ptolemy says that the ecliptic longitudes are for the beginning of the reign of
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680:), but the manuscript he was translating came from the East, where س was used for 60,
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PDFs of different resolutions. Edition of Petrus Liechtenstein, Latin translation of
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Gerard of Cremona's Latin translation made in Toledo about 1175 from the Arabic, ...
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Hanson, Norwood Russell (1960). "The Mathematical Power of Epicyclical Astronomy".
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2285:. In Juste, David; van Dalen, Benno; Hasse, Dag Nikolaus; Burnett, Charles (eds.).
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1295: = 1), while the faintest visible to the naked eye were sixth magnitude (
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3035:. Digitized version of manuscript made in Northern Italy c. 1200–1225 held by the
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cluster Omega Centauri. Ptolemy states that the longitudes (which increase due to
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Maimonides explaining why you need to learn Almagest first to understand science
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know about the work of astronomers like Hipparchus comes from references in the
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Hoskin, Michael (1999). "2. Astronomy in Antiquity". In Hoskin, Michael (ed.).
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figures in the modern sense so that they fit the description in the Almagest.
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that Ptolemy's instrument was wrongly calibrated and had a systematic offset.
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239:'greatest'. The Arabic name was popularized by a Latin translation known as
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1528 copy of a Latin translation of "Almagestum", translated from Greek by
980:) made an abridged Latin version at the instigation of the Greek churchman
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that was accepted for more than 1,200 years from its origin in Hellenistic
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Models and Precision: The Quality of Ptolemy's Observations and Parameters
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133:. One of the most influential scientific texts in history, it canonized a
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375:(the apparent path of the Sun through the stars); and an introduction to
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2679:(1977). "Scandal in the Heavens: Renowned Astronomer Accused of Fraud".
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French translation, with some diagrams animated, interactive, or random
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figures be sketched or even line figures be drawn? This is not stated.
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addresses general issues associated with creating models for the five
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299:, 'greatest') lies behind the Arabic name from which the English name
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2289:. Ptolemaeus Arabus et Latinus. Turnhout: Brepols. pp. 305–307.
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Around AD 150, Ptolemy wrote his great handbook of astronomy called
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by Christian Heinrich Friedrich Peters and Edward Ball Knobel, 1915
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Online luni-solar and planetary ephemeris calculator based on the
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1278:(138 AD), whereas the latitudes do not change with time (but see
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3013:. PDF scans of Heiberg's Greek edition, now in the public domain
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3925:
3417:
3113:
2576:"The Star Catalogue Commonly Appended to the Alfonsine Tables"
412:
390:
2279:
George of Trebizond on Planetary Order, Distances, and Orbs (
2190:
Ptolemy's Catalogue of the Stars – A Revision of the Almagest
1017:("The Ultimate Grasp of the Divisions of Spheres", 1138–39).
281:
255:
229:
2226:
The Almagest: Introduction to the Mathematics of the Heavens
1142:
The Almagest: Introduction to the Mathematics of the Heavens
1719:
1717:
696:
are off by a couple of degrees, including the star we call
363:
revolving around the Earth. Then follows an explanation of
74:
68:
3004:
Syntaxis mathematica in J.L. Heiberg's edition (1898–1903)
2376:"Ptolemy's Determination of the Obliquity of the Ecliptic"
2317:
A Sourcebook for Ancient Greek: Grammar, Poetry, and Prose
71:
59:
2008:(in French). Vol. 1. Paris: J. Hermann – via
1786:
1784:
1576:
1574:
557:
The celestial realm is spherical, and moves as a sphere.
2175:– via Astronomy Library of the Vienna University.
945:
No Latin translation was made before the 12th century.
787:
Other classical writers suggested different sequences.
165:. It is also a key source of information about ancient
32:
2970:
Islamic Science and the Making of European Renaissance
2901:
Early Physics and Astronomy: A Historical Introduction
2725:(in French) (Online ed.) – via Imago Mundi.
2252:
Islamic Science and the Making of European Renaissance
2026:(in French). Vol. 2. Paris: H. Grand – via
1813:
1811:
5201:
2961:– via MDZ/München, Bayerische Staatsbibliothek.
1657:"How Ptolemy’s spare stars became new constellations"
1312:, 21 to the north of the zodiac, and 15 to the south.
852:
had failed, by introducing a third device called the
423:
of the equinoxes and begins explaining the theory of
411:
covers the length of the year, and the motion of the
89:
77:
2124:(2nd ed.). Berlin: Springer. pp. 140–141.
1771:
1769:
872:
or partial spheres. In contrast to the mathematical
223:
213:
202:
80:
62:
5118:
4996:
4946:
4920:
4842:
4824:
4723:
4716:
4572:
4534:
4351:
3959:
3893:
3872:
3781:
3730:
3669:
3451:
2504:
Quarterly Journal of the Royal Astronomical Society
2479:
Quarterly Journal of the Royal Astronomical Society
1756:
1754:
1752:
1750:
1748:
1746:
1744:
716:These constellations form the basis for the modern
473:of 1022 stars, described by their positions in the
65:
56:
2440:Monthly Notices of the Royal Astronomical Society
2287:Ptolemy's Science of the Stars in the Middle Ages
802:) placed the Sun second in order after the Moon.
1373:
1174:Ptolemy's catalogue of stars; a revision of the
1114:into English have been published. The first, by
900:became an authoritative work for many centuries.
2435:"On the Origin of Ptolemy's Catalogue of Stars"
942:is thought to be the first Arabic translator.
3937:
3429:
3125:
2786:Bulletin of the American Mathematical Society
2756:The History and Practice of Ancient Astronomy
1592:
8:
3088:Animation of Ptolemy's model of the universe
2903:(2nd ed.). Cambridge University Press.
2549:"The Genesis of Hipparchus' Celestial Globe"
1636:
1620:
1604:
1549:
1468:
1397:
1012:
752:Ptolemy assigned the following order to the
290:), and the superlative form of this (Greek:
240:
208:
197:
2812:A History of Ancient Mathematical Astronomy
2782:"Mathematical Methods in Ancient Astronomy"
2224:— (2014). Donahue, William H. (ed.).
2037:From Ancient Omens to Statistical Mechanics
2020:Composition mathématique de Claude Ptolémée
2002:Composition mathématique de Claude Ptolémée
265:
4950:
4720:
3944:
3930:
3922:
3436:
3422:
3414:
3132:
3118:
3110:
2553:Mediterranean Archaeology and Archaeometry
2500:"Ptolemy Revisited - Reply to R.R. Newton"
2095:The Cambridge Concise History of Astronomy
1094:Claudii Ptolemaei opera quae exstant omnia
1003:, brought back Arabic disputations of the
153:worlds, and in Western Europe through the
2797:
2591:
2564:
2452:
2294:
2219:. Chicago: Encyclopaedia Brittanica, Inc.
1929:(1st ed.). New York: Facts on File.
1841:
1829:
1790:
1708:
1385:
1361:
810:and late medieval European astronomers.
736:16th-century representation of Ptolemy's
563:The Earth is at the center of the cosmos.
27:Astronomical treatise by Claudius Ptolemy
1537:
1516:
1501:
1274:) are for the beginning of the reign of
1098:
104:treatise on the apparent motions of the
5291:
5284:
5208:
1969:The History of Ptolemy's Star Catalogue
1865:
1817:
1802:
1652:
1456:
1425:
1409:
1354:
1279:
1262:
1164:
371:; observations of the obliquity of the
172:Ptolemy set up a public inscription at
4973:Latin translations of the 12th century
2996:(Almagest), original Greek, edited by
1853:
1735:
1692:
1680:
1668:
1565:
1444:
4703:Straightedge and compass construction
3031:Latin translation from the Arabic by
1901:
1889:
1877:
1775:
1723:
7:
4668:Incircle and excircles of a triangle
2580:Journal for the History of Astronomy
2405:Journal for the History of Astronomy
2181:Peters, Christian Heinrich Friedrich
1760:
1580:
1014:Muntahā al-idrāk fī taqāsīm al-aflāk
999:, who had been on an embassy to the
880:is sometimes described as a book of
704:Constellations in the star catalogue
328:, translated to Latin from Greek by
324:Table of contents to a 1528 copy of
180:was earlier than the version in the
2612:Lewis, H. A. G. (1979). "Review of
2374:Britton, John Phillips (Dec 1969).
1926:Encyclopedia of Space and Astronomy
1282:). The constellations north of the
1126:, was included in volume 16 of the
209:
198:
2922:(2nd ed.). Berlin: Springer.
2394:10.1111/j.1600-0498.1969.tb00132.x
2254:(2nd ed.). Cambridge, Mass.:
2195:Carnegie Institution of Washington
1303:. (The ratio was subjective as no
1190:Epytoma Ioannis de Monte Regio in
1096:, vols. 1.1 and 1.2 (1898, 1903).
25:
2735:"Star Tales – Ptolemy's Almagest"
2250:(2011) . Buchwald, Jed Z. (ed.).
5310:Ancient Greek astronomical works
5271:
5259:
5247:
5235:
5223:
5211:
5185:
5172:
3400:
3399:
2228:. Translated by Perry, Bruce M.
2028:Bibliothèque nationale de France
2010:Bibliothèque nationale de France
1199:
1183:
1167:
1129:Great Books of the Western World
756:, beginning with the innermost:
393:is vertical, the shadows of the
274:. The treatise was later titled
52:
2799:10.1090/S0002-9904-1948-09089-9
2062:(in German). Berlin: Springer.
1944:Britton, John Phillips (1992).
727:
674:used the letter س (sin) for 300
479:ecliptic longitude and latitude
286:, "The Great Treatise"; Latin:
248:The work was originally titled
5005:A History of Greek Mathematics
4518:The Quadrature of the Parabola
2532:10.1126/science.199.4331.872.a
2157:Claudius Ptolemaeus Almagestum
2130:10.1007/978-1-4020-4425-0_8988
1923:Angelo, Joseph A. Jr. (2006).
1032:(only fragments survive), and
1:
3834:Inferior and superior planets
3057:Almagest Ephemeris Calculator
2614:The Crime of Claudius Ptolemy
2547:Hoffmann, Susanne M. (2018).
2154:Lichtenstein, Petrus (1515).
2058:Hoffmann, Susanne M. (2017).
2041:Copenhagen University Library
1939:– via books.google.com.
1054:The Crime of Claudius Ptolemy
818:
792:
123:
118:
4786:Intersecting secants theorem
3140:48 constellations listed by
3019:Toomer's English translation
2877:(Rev. ed.). Cambridge:
2701:10.1126/science.198.4318.707
1374:Hamilton & Swerdlow 1987
959:Toledo School of Translators
912:'s Latin translation of the
295:
276:
250:
235:
228:being a corruption of Greek
4781:Intersecting chords theorem
4648:Doctrine of proportionality
2741:(Revised, online ed.).
2216:Ptolemy, Copernicus, Kepler
2205:(1952). "The Almagest". In
1430:Ptolemy’s 48 constellations
1013:
224:
214:
203:
196:The name comes from Arabic
36:An edition in Latin of the
5341:
4477:On the Sphere and Cylinder
4430:On the Sizes and Distances
3911:Medieval Islamic astronomy
3708:On the Sizes and Distances
2966:Shank, Michael H. (2009).
2602:10.1177/002182868601700202
2426:10.1177/002182860003100202
2398:Reprinted as Chapter 1 of.
2296:10.1484/M.PALS-EB.5.120189
2273:Shank, Michael H. (2020).
2103:Cambridge University Press
1110:Three translations of the
976:, after his birthplace of
682:like the Hebrew ס (samekh)
445:, the motion of the lunar
389:, the points at which the
291:
282:
256:
230:
5179:Ancient Greece portal
5168:
4983:Philosophy of mathematics
4953:
4898:Ptolemy's table of chords
3953:Ancient Greek mathematics
3901:Medieval European science
3631:Sosigenes the Peripatetic
3397:
3149:
3037:State Library of Victoria
2648:Astronomische Nachrichten
2630:10.1080/03085697908592494
2433:Dreyer, J. L. E. (1917).
2076:10.1007/978-3-658-18683-8
1979:10.1007/978-1-4612-4468-4
1593:Dambis & Efremov 2000
1459:, Book I, Chapter 5, p.9.
1157:French National library.
995:During the 16th century,
870:three-dimensional spheres
728:Ptolemy's planetary model
652:Errors in the coordinates
4850:Aristarchus's inequality
4423:On Conoids and Spheroids
3090:by Andre Rehak (YouTube)
2920:A Survey of the Almagest
2918:Pedersen, Olaf (2011) .
2669:10.1002/asna.19252240202
2574:Kunitzsch, Paul (1986).
2498:Gingerich, Owen (1981).
2314:Tomarchio, John (2022).
2232:, NM: Green Lion Press.
2207:Hutchins, Robert Maynard
1637:Peters & Knobel 1915
1621:Peters & Knobel 1915
1605:Peters & Knobel 1915
1550:Peters & Knobel 1915
1321:For instance, the stars
1132:in 1952. The second, by
984:. Around the same time,
569:The Earth does not move.
437:cover the motion of the
4958:Ancient Greek astronomy
4771:Inscribed angle theorem
4761:Greek geometric algebra
4416:Measurement of a Circle
3626:Sosigenes of Alexandria
3445:Ancient Greek astronomy
2760:Oxford University Press
2060:Hipparchs Himmelsglobus
1965:Graßhoff, Gerd (1990).
1007:, such as the works of
953:by the Italian scholar
455:covers solar and lunar
351:contains an outline of
5192:Mathematics portal
4978:Non-Euclidean geometry
4933:Mouseion of Alexandria
4806:Tangent-secant theorem
4756:Geometric mean theorem
4741:Exterior angle theorem
4736:Angle bisector theorem
4440:On Sizes and Distances
3698:On Sizes and Distances
3043:University of Vienna:
2566:10.5281/ZENODO.1477980
2475:"Was Ptolemy a Fraud?"
2454:10.1093/mnras/77.7.528
2367:Journals and magazines
1107:
1084:under the Latin title
920:
901:
844:
834:Mesopotamian astronomy
749:
690:atmospheric refraction
644:
583:
560:The Earth is a sphere.
544:
515:covers the motions of
501:covers the motions of
377:spherical trigonometry
332:
287:
266:
241:
41:
4880:Pappus's area theorem
4816:Theorem of the gnomon
4693:Quadratrix of Hippias
4616:Circles of Apollonius
4564:Problem of Apollonius
4542:Constructible numbers
4366:Archimedes Palimpsest
3809:Deferent and epicycle
3738:Antikythera mechanism
2754:Evans, James (1998).
2717:Jodra, Serge (2013).
2516:Goldstein, Bernard R.
1950:. New York: Garland.
1194:Ptolomei, Latin, 1496
1116:R. Catesby Taliaferro
1102:
907:
895:
842:
830:deferent and epicycle
828:) had introduced the
782:Sphere of fixed stars
735:
641:
581:
549:The cosmology of the
340:illustrating how the
323:
35:
5096:prehistoric counting
4893:Ptolemy's inequality
4834:Apollonius's theorem
4673:Method of exhaustion
4643:Diophantine equation
4633:Circumscribed circle
4450:On the Moving Sphere
3880:Babylonian astronomy
3571:Hippocrates of Chios
2998:Johan Ludvig Heiberg
2994:Syntaxis Mathematica
2943:Syntaxis mathematica
2938:Ptolemaeus, Claudius
2814:. Berlin: Springer.
2616:, by R. R. Newton".
2320:. Washington, D.C.:
2160:(in Latin). Venice.
2146:Mathematike Syntaxis
1414:"Ptolemy’s Almagest"
1221:Abū al-Wafā' Būzjānī
1086:Syntaxis mathematica
1061:Bernard R. Goldstein
1030:Pappus of Alexandria
1020:Commentaries on the
914:Syntaxis Mathematica
878:Planetary Hypotheses
866:Planetary Hypotheses
529:covers stations and
491:, and the motion of
337:Syntaxis Mathematica
314:Syntaxis Mathematica
267:Syntaxis Mathematica
251:Mathēmatikḕ Sýntaxis
5182: •
4988:Neusis construction
4908:Spiral of Theodorus
4801:Pythagorean theorem
4746:Euclidean algorithm
4688:Lune of Hippocrates
4557:Squaring the circle
4313:Theon of Alexandria
3988:Aristaeus the Elder
3651:Theon of Alexandria
2693:1977Sci...198..707W
2661:1925AN....224...17V
2593:1986JHA....17...89K
2491:1980QJRAS..21..253G
2418:2000JHA....31..115D
2185:Knobel, Edward Ball
2068:2017hihi.book.....H
1738:, pp. 217–221.
1726:, pp. 305–307.
1595:, pp. 115–134.
1388:, pp. 140–141.
1232:Book of Fixed Stars
1223:(who also wrote an
1124:Annapolis, Maryland
1105:George of Trebizond
1026:Theon of Alexandria
986:George of Trebizond
910:George of Trebizond
815:Apollonius of Perga
592:ecliptic longitudes
419:' discovery of the
415:. Ptolemy explains
330:George of Trebizond
257:Μαθηματικὴ Σύνταξις
178:Canopic Inscription
96:) is a 2nd-century
4875:Menelaus's theorem
4865:Irrational numbers
4678:Parallel postulate
4653:Euclidean geometry
4621:Apollonian circles
4163:Isidore of Miletus
3885:Egyptian astronomy
3799:Circle of latitude
2344:Ptolemy's Almagest
2211:Adler, Mortimer J.
1138:Ptolemy's Almagest
1120:St. John's College
1108:
982:Cardinal Bessarion
921:
902:
859:Ptolemy wrote the
845:
750:
645:
584:
574:The star catalogue
333:
277:Hē Megálē Sýntaxis
264:, and also called
145:, in the medieval
112:paths, written by
42:
5325:2nd-century books
5199:
5198:
5164:
5163:
4916:
4915:
4903:Ptolemy's theorem
4776:Intercept theorem
4626:Apollonian gasket
4552:Doubling the cube
4525:The Sand Reckoner
3919:
3918:
3794:Celestial spheres
3411:
3410:
3051:Gerard of Cremona
3033:Gerard of Cremona
2972:by George Saliba"
2929:978-1-4939-3922-0
2910:978-0-521-40899-8
2888:978-0-7188-9478-8
2879:Lutterworth Press
2792:(11): 1013–1041.
2769:978-0-19-509539-5
2687:(4318): 707–709.
2526:(4331): 872–873.
2357:978-0-387-91220-2
2331:978-1-949822-20-5
2306:978-2-503-58639-7
2265:978-0-262-51615-0
2239:978-1-88800-943-9
2203:Ptolemy, Claudius
2139:978-1-4020-4559-2
2112:978-0-521-57291-0
2085:978-3-658-18682-1
2050:978-8-7770-9002-8
1936:978-0-8160-5330-8
1583:, pp. 17–54.
1469:Lichtenstein 1515
1398:Lichtenstein 1515
1301:logarithmic scale
1052:in the 1977 book
1040:Modern assessment
955:Gerard of Cremona
804:Martianus Capella
754:planetary spheres
676:(like the Hebrew
666:Gerard of Cremona
531:retrograde motion
489:naked eye planets
283:Ἡ Μεγάλη Σύνταξις
16:(Redirected from
5332:
5320:Works by Ptolemy
5295:
5289:
5276:
5275:
5274:
5264:
5263:
5262:
5252:
5251:
5240:
5239:
5238:
5228:
5227:
5216:
5215:
5207:
5190:
5189:
5177:
5176:
5175:
4951:
4938:Platonic Academy
4885:Problem II.8 of
4855:Crossbar theorem
4811:Thales's theorem
4751:Euclid's theorem
4721:
4638:Commensurability
4599:Axiomatic system
4547:Angle trisection
4512:
4502:
4464:
4454:
4444:
4434:
4410:
4400:
4383:
3946:
3939:
3932:
3923:
3906:Indian astronomy
3859:Sublunary sphere
3829:Hipparchic cycle
3768:Mural instrument
3743:Armillary sphere
3722:
3712:
3702:
3692:
3682:
3438:
3431:
3424:
3415:
3403:
3402:
3344:Piscis Austrinus
3234:Corona Australis
3134:
3127:
3120:
3111:
3103:
3095:
3084:
3021:Duckworth, 1984.
2983:
2962:
2960:
2958:
2933:
2914:
2892:
2866:
2837:
2808:Neugebauer, Otto
2803:
2801:
2778:Neugebauer, Otto
2773:
2742:
2726:
2723:cosmovisions.com
2704:
2672:
2641:
2608:
2595:
2570:
2568:
2543:
2511:
2494:
2466:
2456:
2429:
2397:
2361:
2335:
2310:
2298:
2269:
2243:
2220:
2198:
2193:. Vol. 86.
2176:
2174:
2172:
2150:
2116:
2097:(1st ed.).
2089:
2054:
2031:
2025:
2017:— (1816).
2013:
2007:
1992:
1972:
1961:
1940:
1905:
1899:
1893:
1887:
1881:
1875:
1869:
1863:
1857:
1851:
1845:
1839:
1833:
1827:
1821:
1815:
1806:
1800:
1794:
1788:
1779:
1773:
1764:
1758:
1739:
1733:
1727:
1721:
1712:
1706:
1700:
1690:
1684:
1678:
1672:
1666:
1660:
1650:
1644:
1634:
1628:
1618:
1612:
1602:
1596:
1590:
1584:
1578:
1569:
1563:
1557:
1547:
1541:
1535:
1520:
1514:
1505:
1499:
1476:
1466:
1460:
1454:
1448:
1442:
1433:
1423:
1417:
1407:
1401:
1395:
1389:
1383:
1377:
1371:
1365:
1359:
1343:
1336:
1330:
1319:
1313:
1298:
1294:
1280:the star catalog
1267:
1238:Star cartography
1203:
1187:
1171:
1088:, was edited by
1050:Robert R. Newton
1034:Ammonius Hermiae
1024:were written by
1016:
997:Guillaume Postel
947:Henry Aristippus
827:
823:
820:
808:medieval Islamic
801:
797:
794:
738:geocentric model
545:Ptolemy's cosmos
477:, together with
359:and the various
298:
293:
285:
284:
279:
269:
259:
258:
253:
244:
238:
233:
232:
227:
217:
212:
211:
206:
201:
200:
135:geocentric model
128:
125:
122:
120:
114:Claudius Ptolemy
92:
87:
86:
83:
82:
79:
76:
73:
70:
67:
64:
61:
58:
21:
5340:
5339:
5335:
5334:
5333:
5331:
5330:
5329:
5315:Astronomy books
5300:
5299:
5298:
5290:
5286:
5282:
5272:
5270:
5260:
5258:
5246:
5236:
5234:
5222:
5210:
5202:
5200:
5195:
5184:
5173:
5171:
5160:
5126:Arabian/Islamic
5114:
5103:numeral systems
4992:
4942:
4912:
4860:Heron's formula
4838:
4820:
4712:
4708:Triangle center
4698:Regular polygon
4575:and definitions
4574:
4568:
4530:
4510:
4500:
4462:
4452:
4442:
4432:
4408:
4398:
4381:
4347:
4318:Theon of Smyrna
3963:
3955:
3950:
3920:
3915:
3889:
3868:
3854:Spherical Earth
3789:Callippic cycle
3777:
3758:Equatorial ring
3726:
3720:
3710:
3700:
3690:
3680:
3665:
3656:Theon of Smyrna
3447:
3442:
3412:
3407:
3393:
3239:Corona Borealis
3145:
3138:
3101:
3093:
3082:
2990:
2978:(Book review).
2965:
2956:
2954:
2936:
2930:
2917:
2911:
2895:
2889:
2869:
2840:
2834:
2806:
2776:
2770:
2753:
2750:
2748:Further reading
2745:
2729:
2716:
2712:
2707:
2675:
2644:
2611:
2573:
2546:
2514:
2497:
2471:Gingerich, Owen
2469:
2432:
2401:
2373:
2369:
2364:
2358:
2348:Duckworth Books
2338:
2332:
2313:
2307:
2275:"Regiomontanus
2272:
2266:
2246:
2240:
2223:
2201:
2179:
2170:
2168:
2153:
2140:
2119:
2113:
2092:
2086:
2057:
2051:
2034:
2023:
2016:
2005:
1995:
1989:
1964:
1958:
1943:
1937:
1922:
1918:
1913:
1908:
1900:
1896:
1888:
1884:
1876:
1872:
1864:
1860:
1852:
1848:
1840:
1836:
1828:
1824:
1816:
1809:
1801:
1797:
1789:
1782:
1774:
1767:
1759:
1742:
1734:
1730:
1722:
1715:
1707:
1703:
1691:
1687:
1679:
1675:
1667:
1663:
1651:
1647:
1635:
1631:
1619:
1615:
1603:
1599:
1591:
1587:
1579:
1572:
1564:
1560:
1548:
1544:
1536:
1523:
1515:
1508:
1500:
1479:
1467:
1463:
1455:
1451:
1443:
1436:
1424:
1420:
1408:
1404:
1396:
1392:
1384:
1380:
1372:
1368:
1360:
1356:
1352:
1347:
1346:
1337:
1333:
1320:
1316:
1296:
1292:
1268:
1264:
1259:
1254:
1217:
1210:
1204:
1195:
1188:
1179:
1172:
1163:
1078:
1076:Modern editions
1042:
990:Pope Nicholas V
890:
825:
821:
799:
795:
785:
730:
706:
654:
576:
547:
369:table of chords
318:
309:
194:
167:Greek astronomy
126:
117:
90:
55:
51:
28:
23:
22:
15:
12:
11:
5:
5338:
5336:
5328:
5327:
5322:
5317:
5312:
5302:
5301:
5297:
5296:
5283:
5281:
5280:
5268:
5256:
5244:
5232:
5220:
5197:
5196:
5169:
5166:
5165:
5162:
5161:
5159:
5158:
5153:
5148:
5143:
5138:
5133:
5128:
5122:
5120:
5119:Other cultures
5116:
5115:
5113:
5112:
5111:
5110:
5100:
5099:
5098:
5088:
5087:
5086:
5076:
5075:
5074:
5064:
5063:
5062:
5052:
5051:
5050:
5040:
5039:
5038:
5028:
5027:
5026:
5016:
5015:
5014:
5000:
4998:
4994:
4993:
4991:
4990:
4985:
4980:
4975:
4970:
4968:Greek numerals
4965:
4963:Attic numerals
4960:
4954:
4948:
4944:
4943:
4941:
4940:
4935:
4930:
4924:
4922:
4918:
4917:
4914:
4913:
4911:
4910:
4905:
4900:
4895:
4890:
4882:
4877:
4872:
4867:
4862:
4857:
4852:
4846:
4844:
4840:
4839:
4837:
4836:
4830:
4828:
4822:
4821:
4819:
4818:
4813:
4808:
4803:
4798:
4793:
4791:Law of cosines
4788:
4783:
4778:
4773:
4768:
4763:
4758:
4753:
4748:
4743:
4738:
4732:
4730:
4718:
4714:
4713:
4711:
4710:
4705:
4700:
4695:
4690:
4685:
4683:Platonic solid
4680:
4675:
4670:
4665:
4663:Greek numerals
4660:
4655:
4650:
4645:
4640:
4635:
4630:
4629:
4628:
4623:
4613:
4608:
4607:
4606:
4596:
4595:
4594:
4589:
4578:
4576:
4570:
4569:
4567:
4566:
4561:
4560:
4559:
4554:
4549:
4538:
4536:
4532:
4531:
4529:
4528:
4521:
4514:
4504:
4494:
4491:Planisphaerium
4487:
4480:
4473:
4466:
4456:
4446:
4436:
4426:
4419:
4412:
4402:
4392:
4385:
4375:
4368:
4363:
4355:
4353:
4349:
4348:
4346:
4345:
4340:
4335:
4330:
4325:
4320:
4315:
4310:
4305:
4300:
4295:
4290:
4285:
4280:
4275:
4270:
4265:
4260:
4255:
4250:
4245:
4240:
4235:
4230:
4225:
4220:
4215:
4210:
4205:
4200:
4195:
4190:
4185:
4180:
4175:
4170:
4165:
4160:
4155:
4150:
4145:
4140:
4135:
4130:
4125:
4120:
4115:
4110:
4105:
4100:
4095:
4090:
4085:
4080:
4075:
4070:
4065:
4060:
4055:
4050:
4045:
4040:
4035:
4030:
4025:
4020:
4015:
4010:
4005:
4000:
3995:
3990:
3985:
3980:
3975:
3969:
3967:
3961:Mathematicians
3957:
3956:
3951:
3949:
3948:
3941:
3934:
3926:
3917:
3916:
3914:
3913:
3908:
3903:
3897:
3895:
3891:
3890:
3888:
3887:
3882:
3876:
3874:
3870:
3869:
3867:
3866:
3861:
3856:
3851:
3846:
3841:
3836:
3831:
3826:
3821:
3816:
3811:
3806:
3801:
3796:
3791:
3785:
3783:
3779:
3778:
3776:
3775:
3770:
3765:
3760:
3755:
3750:
3745:
3740:
3734:
3732:
3728:
3727:
3725:
3724:
3718:On the Heavens
3714:
3704:
3694:
3691:(Eratosthenes)
3684:
3673:
3671:
3667:
3666:
3664:
3663:
3658:
3653:
3648:
3643:
3638:
3633:
3628:
3623:
3618:
3613:
3608:
3603:
3598:
3596:Philip of Opus
3593:
3588:
3583:
3578:
3573:
3568:
3563:
3558:
3553:
3548:
3543:
3538:
3533:
3528:
3523:
3518:
3513:
3508:
3503:
3498:
3493:
3488:
3483:
3478:
3473:
3468:
3463:
3457:
3455:
3449:
3448:
3443:
3441:
3440:
3433:
3426:
3418:
3409:
3408:
3398:
3395:
3394:
3392:
3391:
3386:
3381:
3376:
3371:
3366:
3361:
3356:
3351:
3346:
3341:
3336:
3331:
3326:
3321:
3316:
3311:
3306:
3301:
3296:
3291:
3286:
3281:
3276:
3271:
3266:
3261:
3256:
3251:
3246:
3241:
3236:
3231:
3226:
3221:
3216:
3211:
3206:
3201:
3196:
3191:
3186:
3181:
3176:
3171:
3166:
3161:
3156:
3150:
3147:
3146:
3139:
3137:
3136:
3129:
3122:
3114:
3108:
3107:
3099:
3091:
3085:
3073:
3068:
3060:
3054:
3040:
3022:
3016:
3006:
3001:
2989:
2988:External links
2986:
2985:
2984:
2963:
2934:
2928:
2915:
2909:
2897:Pedersen, Olaf
2893:
2887:
2867:
2855:10.1086/348869
2849:(2): 150–158.
2838:
2832:
2804:
2774:
2768:
2749:
2746:
2744:
2743:
2739:ianridpath.com
2727:
2713:
2711:
2708:
2706:
2705:
2677:Wade, Nicholas
2673:
2655:(2–3): 17–54.
2642:
2609:
2571:
2559:(4): 281–287.
2544:
2512:
2495:
2467:
2430:
2412:(2): 115–134.
2399:
2370:
2368:
2365:
2363:
2362:
2356:
2336:
2330:
2311:
2305:
2270:
2264:
2248:Saliba, George
2244:
2238:
2221:
2199:
2177:
2151:
2138:
2117:
2111:
2090:
2084:
2055:
2049:
2032:
2014:
1997:Halma, Nicolas
1993:
1987:
1962:
1956:
1941:
1935:
1919:
1917:
1914:
1912:
1909:
1907:
1906:
1894:
1882:
1870:
1858:
1846:
1842:Gingerich 1981
1834:
1830:Gingerich 1980
1822:
1807:
1795:
1791:Goldstein 1978
1780:
1765:
1740:
1728:
1713:
1709:Kunitzsch 1986
1701:
1685:
1673:
1661:
1645:
1629:
1613:
1597:
1585:
1570:
1568:, p. 528.
1558:
1542:
1521:
1506:
1477:
1461:
1449:
1434:
1418:
1402:
1390:
1386:Kunitzsch 2008
1378:
1366:
1362:Tomarchio 2022
1353:
1351:
1348:
1345:
1344:
1331:
1314:
1305:photodetectors
1276:Antoninus Pius
1261:
1260:
1258:
1255:
1253:
1250:
1249:
1248:
1240:
1235:
1228:
1216:
1213:
1212:
1211:
1205:
1198:
1196:
1189:
1182:
1180:
1173:
1166:
1162:
1159:
1149:Nicholas Halma
1077:
1074:
1065:Owen Gingerich
1041:
1038:
1001:Ottoman Empire
940:Sahl ibn Bishr
889:
886:
784:
783:
780:
777:
774:
771:
768:
765:
762:
758:
729:
726:
718:constellations
705:
702:
698:Alpha Centauri
653:
650:
636:
635:
632:
629:
626:
612:Antoninus Pius
602:of modern-day
575:
572:
571:
570:
567:
564:
561:
558:
546:
543:
542:
541:
534:
524:
510:
496:
482:
475:constellations
471:star catalogue
460:
450:
428:
406:
380:
317:
310:
308:
305:
288:Magna Syntaxis
199:اَلْمَجِسْطِيّ
193:
190:
174:Canopus, Egypt
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5337:
5326:
5323:
5321:
5318:
5316:
5313:
5311:
5308:
5307:
5305:
5293:
5288:
5285:
5279:
5269:
5267:
5257:
5255:
5250:
5245:
5243:
5233:
5231:
5226:
5221:
5219:
5214:
5209:
5205:
5194:
5193:
5188:
5181:
5180:
5167:
5157:
5154:
5152:
5149:
5147:
5144:
5142:
5139:
5137:
5134:
5132:
5129:
5127:
5124:
5123:
5121:
5117:
5109:
5106:
5105:
5104:
5101:
5097:
5094:
5093:
5092:
5089:
5085:
5082:
5081:
5080:
5077:
5073:
5070:
5069:
5068:
5065:
5061:
5058:
5057:
5056:
5053:
5049:
5046:
5045:
5044:
5041:
5037:
5034:
5033:
5032:
5029:
5025:
5022:
5021:
5020:
5017:
5013:
5009:
5008:
5007:
5006:
5002:
5001:
4999:
4995:
4989:
4986:
4984:
4981:
4979:
4976:
4974:
4971:
4969:
4966:
4964:
4961:
4959:
4956:
4955:
4952:
4949:
4945:
4939:
4936:
4934:
4931:
4929:
4926:
4925:
4923:
4919:
4909:
4906:
4904:
4901:
4899:
4896:
4894:
4891:
4889:
4888:
4883:
4881:
4878:
4876:
4873:
4871:
4868:
4866:
4863:
4861:
4858:
4856:
4853:
4851:
4848:
4847:
4845:
4841:
4835:
4832:
4831:
4829:
4827:
4823:
4817:
4814:
4812:
4809:
4807:
4804:
4802:
4799:
4797:
4796:Pons asinorum
4794:
4792:
4789:
4787:
4784:
4782:
4779:
4777:
4774:
4772:
4769:
4767:
4766:Hinge theorem
4764:
4762:
4759:
4757:
4754:
4752:
4749:
4747:
4744:
4742:
4739:
4737:
4734:
4733:
4731:
4729:
4728:
4722:
4719:
4715:
4709:
4706:
4704:
4701:
4699:
4696:
4694:
4691:
4689:
4686:
4684:
4681:
4679:
4676:
4674:
4671:
4669:
4666:
4664:
4661:
4659:
4656:
4654:
4651:
4649:
4646:
4644:
4641:
4639:
4636:
4634:
4631:
4627:
4624:
4622:
4619:
4618:
4617:
4614:
4612:
4609:
4605:
4602:
4601:
4600:
4597:
4593:
4590:
4588:
4585:
4584:
4583:
4580:
4579:
4577:
4571:
4565:
4562:
4558:
4555:
4553:
4550:
4548:
4545:
4544:
4543:
4540:
4539:
4537:
4533:
4527:
4526:
4522:
4520:
4519:
4515:
4513:
4509:
4505:
4503:
4499:
4495:
4493:
4492:
4488:
4486:
4485:
4481:
4479:
4478:
4474:
4472:
4471:
4467:
4465:
4461:
4457:
4455:
4451:
4447:
4445:
4441:
4437:
4435:
4433:(Aristarchus)
4431:
4427:
4425:
4424:
4420:
4418:
4417:
4413:
4411:
4407:
4403:
4401:
4397:
4393:
4391:
4390:
4386:
4384:
4380:
4376:
4374:
4373:
4369:
4367:
4364:
4362:
4361:
4357:
4356:
4354:
4350:
4344:
4341:
4339:
4338:Zeno of Sidon
4336:
4334:
4331:
4329:
4326:
4324:
4321:
4319:
4316:
4314:
4311:
4309:
4306:
4304:
4301:
4299:
4296:
4294:
4291:
4289:
4286:
4284:
4281:
4279:
4276:
4274:
4271:
4269:
4266:
4264:
4261:
4259:
4256:
4254:
4251:
4249:
4246:
4244:
4241:
4239:
4236:
4234:
4231:
4229:
4226:
4224:
4221:
4219:
4216:
4214:
4211:
4209:
4206:
4204:
4201:
4199:
4196:
4194:
4191:
4189:
4186:
4184:
4181:
4179:
4176:
4174:
4171:
4169:
4166:
4164:
4161:
4159:
4156:
4154:
4151:
4149:
4146:
4144:
4141:
4139:
4136:
4134:
4131:
4129:
4126:
4124:
4121:
4119:
4116:
4114:
4111:
4109:
4106:
4104:
4101:
4099:
4096:
4094:
4091:
4089:
4086:
4084:
4081:
4079:
4076:
4074:
4071:
4069:
4066:
4064:
4061:
4059:
4056:
4054:
4051:
4049:
4046:
4044:
4041:
4039:
4036:
4034:
4031:
4029:
4026:
4024:
4021:
4019:
4016:
4014:
4011:
4009:
4006:
4004:
4001:
3999:
3996:
3994:
3991:
3989:
3986:
3984:
3981:
3979:
3976:
3974:
3971:
3970:
3968:
3966:
3962:
3958:
3954:
3947:
3942:
3940:
3935:
3933:
3928:
3927:
3924:
3912:
3909:
3907:
3904:
3902:
3899:
3898:
3896:
3892:
3886:
3883:
3881:
3878:
3877:
3875:
3871:
3865:
3862:
3860:
3857:
3855:
3852:
3850:
3847:
3845:
3842:
3840:
3839:Metonic cycle
3837:
3835:
3832:
3830:
3827:
3825:
3824:Heliocentrism
3822:
3820:
3817:
3815:
3812:
3810:
3807:
3805:
3804:Counter-Earth
3802:
3800:
3797:
3795:
3792:
3790:
3787:
3786:
3784:
3780:
3774:
3771:
3769:
3766:
3764:
3761:
3759:
3756:
3754:
3751:
3749:
3746:
3744:
3741:
3739:
3736:
3735:
3733:
3729:
3723:
3719:
3715:
3713:
3711:(Aristarchus)
3709:
3705:
3703:
3699:
3695:
3693:
3689:
3685:
3683:
3679:
3675:
3674:
3672:
3668:
3662:
3659:
3657:
3654:
3652:
3649:
3647:
3644:
3642:
3639:
3637:
3634:
3632:
3629:
3627:
3624:
3622:
3619:
3617:
3614:
3612:
3609:
3607:
3604:
3602:
3599:
3597:
3594:
3592:
3589:
3587:
3584:
3582:
3579:
3577:
3574:
3572:
3569:
3567:
3564:
3562:
3559:
3557:
3554:
3552:
3549:
3547:
3544:
3542:
3539:
3537:
3534:
3532:
3529:
3527:
3524:
3522:
3519:
3517:
3514:
3512:
3509:
3507:
3504:
3502:
3499:
3497:
3494:
3492:
3489:
3487:
3484:
3482:
3479:
3477:
3474:
3472:
3469:
3467:
3464:
3462:
3459:
3458:
3456:
3454:
3450:
3446:
3439:
3434:
3432:
3427:
3425:
3420:
3419:
3416:
3406:
3396:
3390:
3387:
3385:
3382:
3380:
3377:
3375:
3372:
3370:
3367:
3365:
3362:
3360:
3357:
3355:
3352:
3350:
3347:
3345:
3342:
3340:
3337:
3335:
3332:
3330:
3327:
3325:
3322:
3320:
3317:
3315:
3312:
3310:
3307:
3305:
3302:
3300:
3297:
3295:
3292:
3290:
3287:
3285:
3282:
3280:
3277:
3275:
3272:
3270:
3267:
3265:
3262:
3260:
3257:
3255:
3252:
3250:
3247:
3245:
3242:
3240:
3237:
3235:
3232:
3230:
3227:
3225:
3222:
3220:
3217:
3215:
3212:
3210:
3207:
3205:
3202:
3200:
3197:
3195:
3192:
3190:
3187:
3185:
3182:
3180:
3177:
3175:
3172:
3170:
3167:
3165:
3162:
3160:
3157:
3155:
3152:
3151:
3148:
3143:
3135:
3130:
3128:
3123:
3121:
3116:
3115:
3112:
3106:
3100:
3098:
3092:
3089:
3086:
3081:
3077:
3074:
3072:
3069:
3067:
3066:
3061:
3058:
3055:
3052:
3048:
3046:
3041:
3038:
3034:
3030:
3028:
3023:
3020:
3017:
3015:(Koine Greek)
3014:
3012:
3011:De Analemmate
3007:
3005:
3002:
2999:
2995:
2992:
2991:
2987:
2981:
2977:
2973:
2971:
2964:
2953:
2949:
2945:
2944:
2939:
2935:
2931:
2925:
2921:
2916:
2912:
2906:
2902:
2898:
2894:
2890:
2884:
2880:
2876:
2872:
2868:
2864:
2860:
2856:
2852:
2848:
2844:
2839:
2835:
2833:3-540-06995-X
2829:
2825:
2821:
2817:
2813:
2809:
2805:
2800:
2795:
2791:
2787:
2783:
2779:
2775:
2771:
2765:
2761:
2757:
2752:
2751:
2747:
2740:
2736:
2732:
2728:
2724:
2720:
2719:"L'Almageste"
2715:
2714:
2709:
2702:
2698:
2694:
2690:
2686:
2682:
2678:
2674:
2670:
2666:
2662:
2658:
2654:
2651:(in German).
2650:
2649:
2643:
2639:
2635:
2631:
2627:
2623:
2619:
2615:
2610:
2607:
2603:
2599:
2594:
2589:
2586:(49): 89–98.
2585:
2581:
2577:
2572:
2567:
2562:
2558:
2554:
2550:
2545:
2541:
2537:
2533:
2529:
2525:
2521:
2517:
2513:
2509:
2505:
2501:
2496:
2492:
2488:
2484:
2480:
2476:
2472:
2468:
2464:
2460:
2455:
2450:
2446:
2442:
2441:
2436:
2431:
2427:
2423:
2419:
2415:
2411:
2407:
2406:
2400:
2395:
2391:
2387:
2383:
2382:
2377:
2372:
2371:
2366:
2359:
2353:
2349:
2345:
2341:
2340:Toomer, G. J.
2337:
2333:
2327:
2323:
2319:
2318:
2312:
2308:
2302:
2297:
2292:
2288:
2284:
2282:
2278:
2271:
2267:
2261:
2257:
2253:
2249:
2245:
2241:
2235:
2231:
2227:
2222:
2218:
2217:
2212:
2208:
2204:
2200:
2196:
2192:
2191:
2186:
2182:
2178:
2167:
2163:
2159:
2158:
2152:
2149:
2147:
2141:
2135:
2131:
2127:
2123:
2118:
2114:
2108:
2104:
2100:
2096:
2091:
2087:
2081:
2077:
2073:
2069:
2065:
2061:
2056:
2052:
2046:
2042:
2038:
2033:
2029:
2022:
2021:
2015:
2011:
2004:
2003:
1998:
1994:
1990:
1988:3-540-97181-5
1984:
1980:
1976:
1971:
1970:
1963:
1959:
1957:0-8153-0215-0
1953:
1949:
1948:
1942:
1938:
1932:
1928:
1927:
1921:
1920:
1915:
1910:
1903:
1898:
1895:
1891:
1886:
1883:
1879:
1874:
1871:
1867:
1862:
1859:
1855:
1850:
1847:
1843:
1838:
1835:
1831:
1826:
1823:
1819:
1814:
1812:
1808:
1804:
1799:
1796:
1792:
1787:
1785:
1781:
1777:
1772:
1770:
1766:
1762:
1757:
1755:
1753:
1751:
1749:
1747:
1745:
1741:
1737:
1732:
1729:
1725:
1720:
1718:
1714:
1711:, p. 89.
1710:
1705:
1702:
1698:
1694:
1689:
1686:
1683:, p. 78.
1682:
1677:
1674:
1671:, p. 44.
1670:
1665:
1662:
1658:
1654:
1649:
1646:
1642:
1638:
1633:
1630:
1626:
1622:
1617:
1614:
1610:
1606:
1601:
1598:
1594:
1589:
1586:
1582:
1577:
1575:
1571:
1567:
1562:
1559:
1555:
1551:
1546:
1543:
1539:
1538:Graßhoff 1990
1534:
1532:
1530:
1528:
1526:
1522:
1518:
1517:Hoffmann 2018
1513:
1511:
1507:
1503:
1502:Hoffmann 2017
1498:
1496:
1494:
1492:
1490:
1488:
1486:
1484:
1482:
1478:
1474:
1470:
1465:
1462:
1458:
1453:
1450:
1446:
1441:
1439:
1435:
1431:
1427:
1422:
1419:
1415:
1411:
1406:
1403:
1399:
1394:
1391:
1387:
1382:
1379:
1375:
1370:
1367:
1364:, p. xv.
1363:
1358:
1355:
1349:
1341:
1335:
1332:
1328:
1324:
1318:
1315:
1311:
1306:
1302:
1290:
1285:
1281:
1277:
1273:
1266:
1263:
1256:
1251:
1247:
1246:
1241:
1239:
1236:
1234:
1233:
1229:
1226:
1222:
1219:
1218:
1214:
1209:, Latin, 1515
1208:
1202:
1197:
1193:
1186:
1181:
1177:
1170:
1165:
1160:
1158:
1156:
1155:
1150:
1145:
1143:
1139:
1135:
1131:
1130:
1125:
1121:
1117:
1113:
1106:
1101:
1097:
1095:
1091:
1090:J. L. Heiberg
1087:
1083:
1075:
1073:
1070:
1066:
1062:
1057:
1055:
1051:
1046:
1039:
1037:
1035:
1031:
1027:
1023:
1018:
1015:
1010:
1006:
1002:
998:
993:
991:
987:
983:
979:
975:
974:Regiomontanus
970:
968:
964:
960:
956:
952:
948:
943:
941:
937:
934:
929:
927:
919:
915:
911:
906:
899:
894:
887:
885:
883:
879:
875:
871:
867:
862:
857:
855:
850:
841:
837:
835:
831:
826: 190 BC
816:
811:
809:
805:
800: 347 BC
790:
781:
778:
775:
772:
769:
766:
763:
760:
759:
757:
755:
747:
743:
739:
734:
725:
721:
719:
714:
710:
703:
701:
699:
695:
691:
685:
683:
679:
675:
671:
667:
661:
659:
658:proper motion
651:
649:
640:
633:
630:
627:
624:
623:
622:
619:
617:
613:
609:
605:
601:
597:
593:
588:
580:
573:
568:
565:
562:
559:
556:
555:
554:
552:
538:
535:
532:
528:
525:
522:
518:
514:
511:
508:
504:
500:
497:
494:
490:
486:
483:
480:
476:
472:
468:
464:
461:
458:
454:
451:
448:
444:
440:
436:
432:
429:
426:
422:
418:
414:
410:
407:
404:
400:
396:
392:
388:
384:
381:
378:
374:
370:
366:
362:
358:
354:
350:
347:
346:
345:
343:
338:
331:
327:
322:
315:
311:
306:
304:
302:
297:
289:
278:
273:
268:
263:
252:
246:
243:
237:
226:
221:
216:
205:
191:
189:
187:
183:
179:
175:
170:
168:
164:
160:
156:
152:
148:
144:
140:
136:
132:
115:
111:
107:
103:
99:
95:
94:
85:
49:
48:
39:
34:
30:
19:
5292:Britton 1992
5287:
5278:Solar System
5183:
5170:
5012:Thomas Heath
5003:
4886:
4870:Law of sines
4726:
4658:Golden ratio
4523:
4516:
4507:
4501:(Theodosius)
4497:
4489:
4482:
4475:
4468:
4459:
4449:
4443:(Hipparchus)
4439:
4429:
4421:
4414:
4405:
4395:
4387:
4382:(Apollonius)
4378:
4370:
4359:
4358:
4333:Zeno of Elea
4093:Eratosthenes
4083:Dionysodorus
3717:
3707:
3701:(Hipparchus)
3697:
3688:Catasterismi
3687:
3677:
3676:
3536:Eratosthenes
3144:after 150 AD
3076:Star catalog
3064:
3044:
3026:
3010:
2979:
2975:
2969:
2955:. Retrieved
2946:(in Greek).
2942:
2919:
2900:
2874:
2871:Ridpath, Ian
2846:
2842:
2811:
2789:
2785:
2755:
2738:
2731:Ridpath, Ian
2722:
2684:
2680:
2652:
2646:
2621:
2617:
2613:
2605:
2583:
2579:
2556:
2552:
2523:
2519:
2507:
2503:
2482:
2478:
2444:
2438:
2409:
2403:
2385:
2379:
2343:
2316:
2286:
2280:
2276:
2251:
2225:
2215:
2189:
2169:. Retrieved
2156:
2145:
2143:
2121:
2094:
2059:
2036:
2019:
2001:
1968:
1946:
1925:
1897:
1885:
1873:
1866:Ptolemy 2014
1861:
1849:
1837:
1825:
1818:Britton 1992
1803:Britton 1969
1798:
1731:
1704:
1688:
1676:
1664:
1653:Ridpath 2023
1648:
1632:
1616:
1600:
1588:
1561:
1545:
1464:
1457:Ptolemy 1952
1452:
1426:Ridpath 2023
1421:
1410:Ridpath 2023
1405:
1393:
1381:
1369:
1357:
1334:
1317:
1265:
1244:
1230:
1224:
1206:
1191:
1175:
1152:
1146:
1141:
1137:
1134:G. J. Toomer
1127:
1111:
1109:
1093:
1085:
1081:
1079:
1058:
1053:
1047:
1043:
1021:
1019:
1004:
994:
971:
962:
944:
930:
925:
922:
917:
913:
897:
877:
873:
865:
860:
858:
848:
846:
812:
786:
751:
746:Cosmographia
745:
722:
715:
711:
707:
686:
662:
655:
646:
620:
589:
585:
550:
548:
536:
526:
512:
498:
484:
466:
462:
452:
434:
430:
408:
382:
348:
341:
336:
334:
325:
313:
300:
247:
195:
185:
184:. Hence the
181:
177:
171:
102:astronomical
98:mathematical
46:
45:
43:
37:
29:
18:The Almagest
5266:Outer space
5230:Mathematics
5079:mathematics
4887:Arithmetica
4484:Ostomachion
4453:(Autolycus)
4372:Arithmetica
4148:Hippocrates
4078:Dinostratus
4063:Dicaearchus
3993:Aristarchus
3819:Geocentrism
3731:Instruments
3721:(Aristotle)
3526:Cleostratus
3491:Aristarchus
3471:Anaximander
3453:Astronomers
3354:Sagittarius
3209:Capricornus
3204:Canis Minor
3199:Canis Major
3102:(in Hebrew)
3094:(in French)
2624:: 105–107.
2618:Imago Mundi
2101:, England:
1854:Toomer 1984
1736:Saliba 2011
1693:Toomer 1984
1681:Angelo 2006
1669:Hoskin 1999
1607:, pp.
1566:Dreyer 1917
1540:, p. .
1519:, p. .
1504:, p. .
1447:, p. .
1445:Toomer 1984
1400:, p. .
1376:, p. .
1342:since 2019.
908:Picture of
742:Peter Apian
357:fixed stars
262:Koine Greek
159:Renaissance
155:Middle Ages
131:Koine Greek
5304:Categories
5131:Babylonian
5031:arithmetic
4997:History of
4826:Apollonius
4511:(Menelaus)
4470:On Spirals
4389:Catoptrics
4328:Xenocrates
4323:Thymaridas
4308:Theodosius
4293:Theaetetus
4273:Simplicius
4263:Pythagoras
4248:Posidonius
4233:Philonides
4193:Nicomachus
4188:Metrodorus
4178:Menaechmus
4133:Hipparchus
4123:Heliodorus
4073:Diophantus
4058:Democritus
4038:Chrysippus
4008:Archimedes
4003:Apollonius
3973:Anaxagoras
3965:(timeline)
3894:Influenced
3873:Influences
3844:Octaeteris
3773:Triquetrum
3661:Timocharis
3646:Theodosius
3606:Posidonius
3566:Hipparchus
3556:Heraclides
3496:Aristyllus
3481:Apollonius
3476:Andronicus
3384:Ursa Minor
3379:Ursa Major
3374:Triangulum
3214:Cassiopeia
3174:Argo Navis
3083:(in Latin)
3045:Almagestum
3009:Ptolemy's
2976:Aestimatio
2875:Star Tales
2447:(7): 528.
2346:. London:
1902:Halma 1816
1890:Halma 1813
1878:Jodra 2013
1776:Lewis 1979
1724:Shank 2020
1695:, p.
1639:, p.
1623:, p.
1552:, p.
1471:, p.
1340:Stellarium
1327:62 Orionis
1323:nu Orionis
1272:precession
1252:References
1207:Almagestum
1192:Almagestum
1069:Hipparchus
1028:(extant),
1009:al-Kharaqī
978:Königsberg
896:Ptolemy's
824: – c.
822: 262
798: – c.
796: 427
616:Hipparchus
421:precession
417:Hipparchus
242:Almagestum
204:al-majisṭī
163:Copernicus
157:and early
143:Alexandria
127: 170
38:Almagestum
5242:Astronomy
4592:Inscribed
4352:Treatises
4343:Zenodorus
4303:Theodorus
4278:Sosigenes
4223:Philolaus
4208:Oenopides
4203:Nicoteles
4198:Nicomedes
4158:Hypsicles
4053:Ctesibius
4043:Cleomedes
4028:Callippus
4013:Autolycus
3998:Aristotle
3978:Anthemius
3748:Astrolabe
3681:(Ptolemy)
3601:Philolaus
3591:Oenopides
3576:Hypsicles
3521:Cleomedes
3516:Callippus
3506:Autolycus
3461:Aglaonice
3319:Ophiuchus
3259:Delphinus
3219:Centaurus
3154:Andromeda
3025:Ptolemy.
2952:767751182
2899:(1993) .
2873:(2018) .
2388:: 29–41.
2381:Centaurus
2322:CUA Press
2256:MIT Press
2166:644484399
2099:Cambridge
1761:Wade 1977
1581:Vogt 1925
1350:Citations
1289:magnitude
1243:Euclid's
1144:in 2014.
967:Alfonso X
936:Al-Ma'mun
888:Influence
882:cosmology
694:Centaurus
604:astrology
537:Book XIII
463:Books VII
425:epicycles
403:solstices
399:equinoxes
353:Aristotle
303:derives.
218:meaning '
147:Byzantine
110:planetary
5156:Japanese
5141:Egyptian
5084:timeline
5072:timeline
5060:timeline
5055:geometry
5048:timeline
5043:calculus
5036:timeline
5024:timeline
4727:Elements
4573:Concepts
4535:Problems
4508:Spherics
4498:Spherics
4463:(Euclid)
4409:(Euclid)
4406:Elements
4399:(Euclid)
4360:Almagest
4268:Serenus
4243:Porphyry
4183:Menelaus
4138:Hippasus
4113:Eutocius
4088:Domninus
3983:Archytas
3849:Solstice
3782:Concepts
3678:Almagest
3621:Seleucus
3581:Menelaus
3541:Euctemon
3405:Category
3359:Scorpius
3284:Hercules
3274:Eridanus
3269:Equuleus
3159:Aquarius
3065:Almagest
3027:Almagest
2982:: 63–72.
2957:10 April
2810:(1975).
2780:(1948).
2733:(2023).
2710:Websites
2540:17757580
2510:: 40–44.
2473:(1980).
2463:10340650
2342:(1984).
2281:Almagest
2230:Santa Fe
2213:(eds.).
2187:(1915).
1999:(1813).
1245:Elements
1225:Almagest
1215:See also
1176:Almagest
1112:Almagest
1082:Almagest
1036:(lost).
1022:Syntaxis
1005:Almagest
963:Abrachir
926:Syntaxis
918:Almagest
898:Almagest
874:Syntaxis
861:Syntaxis
849:Syntaxis
678:ש (shin)
551:Syntaxis
527:Book XII
457:eclipses
443:parallax
441:, lunar
431:Books IV
409:Book III
387:latitude
373:ecliptic
342:Syntaxis
326:Almagest
307:Contents
301:Almagest
186:Almagest
182:Almagest
139:Universe
121:AD 100 –
93:-mə-jest
47:Almagest
5204:Portals
5136:Chinese
5091:numbers
5019:algebra
4947:Related
4921:Centers
4717:Results
4587:Central
4258:Ptolemy
4253:Proclus
4218:Perseus
4173:Marinus
4153:Hypatia
4143:Hippias
4118:Geminus
4108:Eudoxus
4098:Eudemus
4068:Diocles
3753:Dioptra
3616:Pytheas
3611:Ptolemy
3561:Hicetas
3551:Geminus
3546:Eudoxus
3501:Attalus
3466:Agrippa
3364:Serpens
3349:Sagitta
3334:Perseus
3329:Pegasus
3224:Cepheus
3142:Ptolemy
3000:, 1898.
2689:Bibcode
2681:Science
2657:Bibcode
2638:1150735
2588:Bibcode
2520:Science
2487:Bibcode
2485:: 253.
2414:Bibcode
2064:Bibcode
1911:Sources
1161:Gallery
1154:Gallica
776:Jupiter
764:Mercury
517:Jupiter
513:Book XI
493:Mercury
485:Book IX
453:Book VI
397:at the
383:Book II
361:planets
296:megístē
292:μεγίστη
236:megístē
231:μεγίστη
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