Ancient Zodiacs, Star Names, and Constellations: Essays and Critiques


Early Greek Astronomers and Astronomy by Gary D. Thompson

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Early Greek Astronomers and Astronomy

Introduction

A clear and detailed understanding of the history of Greek astronomy is extremely difficult. Our knowledge of Greek astronomy before the 4th century BCE is very incomplete, and is likely to remain this way. Also, Greek astronomy before circa 400 BCE cannot be considered in isolation from the history of Greek philosophy (and the speculative constructions of the natural philosophers). Much reconstruction is highly speculative due to the dependence upon fragments of information preserved in diverse ancient and medieval sources. An important reason for this is the successful reception of Ptolemy's Almagest in the 2nd-century CE resulted in the loss of most of the earlier Greek texts on astronomy. Otto Neugebauer expressed the position: The use of a few obscure citations from late authors for the establishment of an understanding of early Greek astronomy and mathematics is fraught with difficulties. The fragments not only give a very incomplete picture of the now lost early writings but were certainly very much distorted by the writers from whose works they are taken.

The earliest recorded use of astronomy among the Greeks appear in the poems of Homer and Hesiod (circa 8th-century BCE). In Babylonia/Mesopotamia observational astronomy had been systematically practiced and recorded since the 8th-century BCE and astronomical systems (for periodic motions of the celestial bodies i.e., moon and planets) were already being developed. The early period of Greek astronomy was not concerned with planetary motion. Early Greek astronomy is concerned with a fundamentally different set of issues than later Greek astronomy. Specifically, early Greek astronomy is more concerned with the yearly phases of the fixed stars than with planetary motion. Fixed star astrometeorology was the concern of early Greek astronomy. Also, correct causal explanations dating to the early 5th-century BCE (i.e., eclipses of the moon) indicate that systematic observations were being made.

It is difficult to ascertain a clear understanding of astronomical knowledge in the time of Homer and Hesiod - the earliest references to Greek astronomy that we have. The Iliad and the Odyssey, are a source of information about the scientific and technological knowledge of ancient Greeks in both pre-Homeric and Homeric times. The two Homeric epic poems, dated in the 8th-century BCE, include, inter alia, a number of astronomical elements, informing about the Earth, the Sky, the stars and constellations such as Ursa Major, Boötes, Orion, Sirius, the Pleiades and the Hyades. They also reflect the cosmological views of his period. The model of the Universe that is presented is continuous and has three levels: the lower level corresponds to the underworld, the middle one to the Earth and the upper one to the sky. The Homeric and Hesiodic texts do establish that at this period the astronomical knowledge of the Greeks enabled them to navigate and to reliably perform agricultural work. The only reference to stellar navigation occurs in Homer's Odyssey (Odyssey (Book) 5.271-277) when Odysseus sails from Ogygia after receiving instructions from Calypso. The conspicuous constellations that are mentioned in this passage - the Pleiades, Boötes, Orion, and the Great Bear - are obviously connected with navigation. (The Homeric text indicates use of stellar navigation before the time of Homer.)

According to ancient sources Thales (circa 620-circa 546 BCE, an Ionian Greek of Phoenician descent) was exposed to the mathematical and astronomical traditions of Egypt and Mesopotamia. In Herodotus' account of the battle between the armies of King Alyattes of the Lydians and King Cyaxaros of the Medes, Thales is said to have predicted the eclipse "for the year" in which it actually occurred. As far as is known, no astronomical theory capable of predicting solar eclipses existed in Thales' time. The Greek identification of the "morning star" and the "evening star" being identical i.e., the planet Venus, is variously attributed Pythagoras (6th-century BCE) and Parmenides of Elea, an Eleatic philosopher (5th-century BCE).

Greek astronomy can be divided into 2 distinct phases: Phase 1: observational and descriptive; and Phase 2: scientific and mathematical. The earliest phase (observational and descriptive) extends from the 8th-century BCE to the time of Plato (circa 425-circa 345 BCE). This first phase is defined by the construction of calendars in the form of parapegmata. A tradition of cosmological theorising is also contemporary with this period. (There was a Greek tradition of cosmological speculation which was independent of Greek astronomy.) The starting point of the 2nd phase (scientific and mathematical) begins with Eudoxus (and also Meton can be included). Eudoxus' (4th-century BCE) synthesis of cosmological speculation and parapegmata with the introduction of models to explain the motion of the celestial bodies established a boundary-line for what had gone before. Eudoxus was the Greek astronomer largely responsible for turning Greek astronomy into a mathematical science, that is, a deductive mathematical explanation of physical phenomena. Eudoxus' inspiration was drawn from 2 sources: the 1st was the science of music; and the 2nd was the cosmological speculation of the Pythagoreans and Plato. An earlier possible boundary-line involves the work of Meton (5th-century BCE) who may be considered the 1st Greek scientific astronomer. First, because he made made actual observations using purpose-built instruments; and second, because he attempted to fit the agricultural calendar into a civil calendar. Not a single Greek specialist in mathematical astronomy is known to be active in the 40 year period between the work of Meton and Euctemon and the work of Eudoxus.

(1) Calendar Establishment

The development of Greek astronomy was not intimately/exclusively linked with the development of the Greek calendar(s). The original and basic impetus for the development of astronomical science in Greece was not the desire to to establish a reliable calendar. Ptolemy's achievement was to construct a viable planetary theory. However, calendar establishment was connected with an emphasis on the establishment of parapegmata. The construction of an astronomical calendar which related weather changes to the heliacal risings of different stars through the year was a long-standing Greek tradition - likely unrelated to Babylonian parallels. It appears that all aspects of Greek astronomy prior to Eudoxus were concerned with the calendar and calendaric cycles. The establishment of parapegmata (star calendars arranged according to the solar year), especially from the 5th-century BCE onwards, also provided an important impetus to the naming of the constellations/stars.

Ptolemy cites 12 parapegmatists, beginning with Meton, Euctemon, and Democritus in the 5th-century BCE and Eudoxus, Callippus, and Philippus in the 4th-century. In some of their calendars the dates are simply listed in zodiacal months. Also, the stars are not assigned co-ordinates and precise measurement was involved in determining their risings and settings.

Important persons included:

Meton of Athens (late 5th-century BCE), Greek astronomer.

Euctemon of Athens (5th-century BCE, flourished 432 BCE), Greek astronomer.

Democritus of Abdera (Thrace) (circa 460-circa 370 BCE), Greek philosopher, a disciple of Leucippus (an Ionian).

Eudoxus of Cnidus (circa 390-circa 340 BCE), Greek mathematician and astronomer, studied geometry under Archytas of Tarentum (a Greek Pythagorean mathematician without independent achievements in astronomy). Eudoxus was a parapegmatist.

Callipus of Cyzicus (circa 370-300 BCE), Greek astronomer, studied under Eudoxus.

Philippus of Opus (4th-century BCE), Greek astronomer, a pupil of Plato.

Aratus of Soli (circa 315 BCE/310 BCE–240 BCE), Greek star calendar poet and agricultural parapegmatist (Phaenomena). (The Phaenomena is an astronomical calendar based on the stars.)

Dositheos (flourished circa late 3rd-century BCE), Alexandrian astronomer, a pupil of Konon and associate of Archimedes.

Sosigenes of Alexandria (flourished 1st-century BCE), Greek astronomer and mathematician.

Geminos (Geminus) of Rhodes (flourished 1st-century BCE), Greek astronomer and mathematician.

Greek astronomy - as the very name astronomy suggests - began with the organisation of the (brighter) fixed stars into groupings (constellations). Although the early Greeks had identified a number of the brightest stars and formed prominent star groups into constellations they had no notion of dividing the whole visible sky into constellations. Early Greek astronomy was concerned with the construction of parapegmata correlating the risings and settings of stars and constellations with meteorological phenomena and reliable calendar cycles. It appears this was achieved without a system of co-ordinates and without precise measurements to determine star/constellation risings and settings. Ancient sources of parapegmata take two forms: archaeological artifacts and written texts. The earliest evidence for parapegmata dates from the 5th-century BCE. It seems that the earliest parapegmata were developed by Meton and Euctemon at Athens circa 430 BCE.

Very few details have survived concerning Meton and Euctemon. They made observations in Thrace, Macedonia, the Cyclades islands, and Athens. Their pupils determined the date of the summer solstice in 432 BCE. They used the signs of the zodiac to describe positions on the ecliptic. Meton suggested that a period of 19 years, which contains almost exactly a whole number (235) of months, could be used to correlate the solar and lunar calendars. (See: Early Astronomy by Hugh Thurston (1994, Page 111).

An important purpose of the early Greek calendrical cycles was to facilitate the use of parapegmata (= farmer's almanacs). These calendar cycles - Oktaeteris = 8-year cycle, and so-called Metonic cycle = 19 year cycle - were used to correlate dates in the parapegmata with dates in a lunar calendar. The outcome was that by means of these calendar cycles the Greeks were able to co-ordinate dates in the parapegmata with dates in their various civil calendars, calendars which though lunar were subject to intercalation for astronomical and for non-astronomical reasons.

Astronomy was a practical matter for the early Greeks. Astronomy for them was a means to fix the times for performing agricultural operations (i.e., start plowing) or religious rituals/observances (i.e., to go to a sanctuary for a festival), or begin sea voyages (or not engage in such) at a period when they had no adequate/accurate calendar. Farmers relied on an agricultural calendar that was marked by the stars. The purpose of parapegmata was to construct a calendar by correlating dates and weather phenomena with the risings and settings of fixed stars/constellations. (The heliacal rising (eastern rising just before sunrise) and the acronychal rising (eastern rising a few minutes after sunset) were especially significant as markers.) The tradition of this method forms the framework of Hesiod's Works and Days, and persists throughout Greek history, and is prominent in Ptolemy's Phaseis. In his Phaseis, Ptolemy examines the many winds and assigns names and attributes to the most common ones, depending upon the cardinal point from which they originate, and incorporates them into his parapegma. (Of the 2 books comprising Phaseis only the 2nd book has come down to us. It is not certain what was contained in the 1st book.)

Most of Meton's astronomical activity was directed towards the traditional Greek astronomy of the agricultural astronomy: he constructed what was perhaps (at least) the first Greek parapegma. (There is evidence for earlier Egyptian parapegmata.) A Greek parapegma was an engraved stone or written list of the principal annual astronomical events (risings and settings of particular stars, the solstices and equinoxes, combined with weather predictions, etc.), with holes along the sides into which a movable peg was inserted to mark the current day.

Source: Lehoux, Daryn. (2006). "Rethinking Parapegmata: The Puteoli Fragment." (Zeitschrift fur Papyrologie und Epigraphik, Band 157, Pages 95-104; Page 95).

Source: Lehoux, Daryn. (2006). "Rethinking Parapegmata: The Puteoli Fragment." (Zeitschrift fur Papyrologie und Epigraphik, Band 157, Pages 97-98).

(2) Constellation Description

It is usual to state that the main influence on early Greek astronomy was Egyptian and it was the Babylonians who influenced later Greek ideas on astronomy. The Greeks largely established their own constellations and certainly were not influenced by the large constellation constructions of the Egyptians. Constellation description was usually in the form of astronomical poetry. Poetry was connected with astronomy long before the great astronomical poets of the 3rd-century BCE (Aratus and Eratosthenes). The contribution of poetry to the naming of the constellations/stars was likely extensive. A later Latin work similar to the Phainomena by Aratus is the Astronomica by the Roman poet Marcus Manilius. Though the book deals mostly with astrology rather than astronomy it contains frequent references to constellation lore.

Important persons included:

Homer (flourished circa 8th-century BCE), Greek court singer and story teller.

Hesiod (flourished circa 7th-century BCE), Greek poet, rhapsode (a professional performer of epic poetry), and farmer.

Excursus: Did Homer and Hesiod Exist?: It is disputed whether Homer actually existed. However, it has been generally accepted that Hesiod existed. Despite personal details being given by Hesiod it is now thought this may be a generic construct within the didactic poetic tradition of the time.

Cleostratus of Tenedos (flourished 6th-century BCE), Greek writer.

Eudoxos of Cnidus (408-355 BCE), Greek astronomer and mathematician.

Aratus of Soli (circa 315–circa 245 BCE), Greek poet, member of the Stoic sect of philosophers.

Eratosthenes of Cyrene (circa 276-circa 194 BCE), Greek mathematician, astronomer, geographer, poet, and music theorist, who worked in Alexandria.

The earliest explicit mention of Greek constellations is by Homer and Hesiod. No earlier hints of Greek constellations exist. The so-called 'argument from silence' cannot be used to determine how many constellations Homer and Hesiod knew. It cannot be confidently assumed that they only knew the constellations they mentioned. It is possible that they both knew more constellations but did not mention them. However, the likely reason why homer stated that the Great Bear alone was never bathed in the ocean was that the Great Bear (the stars comprising the big dipper) was the only part of the arctic sky that had been constellated in Homer's time. The astronomical poem Phainomena (Appearances) by Aratus is the earliest complete description of the Greek constellation set extant. It is also a compendium of astral mythology/lore. It is the starting point for all studies of Greek constellations. It was written circa 275 BCE by the Stoic poet Aratus and is based on a book of the same name written in the 4th-century BCE by Eudoxus. The essay Catasterisms attributed to Eratosthenes (circa 276-194 BCE) is the next landmark in the study of Greek constellation lore. Because it is not certain that Eratosthenes was the author of Catasterisms the author is usually referred to as pseudo-Eratosthenes. The essay is the oldest detailed collection of Greek star myths. It is an additional primary source for information on the earliest Greek constellations. It gives the mythology of 42 separate constellations (the Pleaides star cluster is treated individually). The version of Catasterisms that has survived only comprises a summary of the original. The anonymous author of the summary has used the earlier collection of traditional constellation myths assembled by Eratosthenes in his well-known Hellenistic work of the same name. The antiquity of the sources used in Catasterisms is certain because in places the author quotes from Hesiod's lost work on astronomy. These constellation myths and those in the later work Poeticon Astronomicon by a Roman author named Hyginus (1st-century or 2nd-century CE) imply the existence of an earlier, well-developed traditional of Greek constellation lore. However, there is little indication of constellation lore in Homer's Iliad and Odyssey, and Hesiod's Works and Days. The Poeticon Astronomicon is based on the constellations listed by Eratosthenes (excepting Hyginus includes the Pleiades under Taurus), and it contains many additional constellation stories.

The Greek scheme for the placement of their constellations was likely heavily dependent on the Babylonian scheme of constellations. As example: The Greek Centaurus matches the description of the Centaurs on Kassite kudurru.

(3) Stellar Observations

There is no evidence for scientific astronomical/calendaric theory in Greece before the 5th-century BCE. The determination of fixed star declinations was an important step in Greek astronomy.

Important persons included:

Timocharis (Timochus) of Alexandria (circa 320-260 BCE), Greek astronomer and philosopher.

Aristyllus of Alexandria (flourished 1st half of 3rd-century BCE), Greek astronomer, probably a pupil of Timocharis.

Hipparchus of Nicaea (circa 190, Nicaea-circa 120 BCE, Rhodes), Greek astronomer, mathematician and geographer. Before the ancient Greek astronomers from Hipparchus of Rhodes (2nd-century BCE) onwards developed a co-ordinate system the constellations provided the usual means for identifying the position of anything in the night sky.

Ptolemy of Alexandria (circa 90-circa 165 CE), Greco-Egyptian astronomer, mathematician, geographer, and astrologer.

Alan Bowen and Bernard Goldstein have reiterated the point that a characteristic feature of scientific astronomy is the use of precise positional data at specified moments of time. The introduction of empirical data to Greek astronomy dates from the 3rd-century BCE and not before. This correlates with the exposure of the Greeks to Babylonian astronomy after their military/political entry into the Near East. However, the introduction and use of Babylonian observational data - which goes back to the 8th-century BCE - into the Greek world is not understood in any detail. Also, the transmission of Babylonian observational methods.

Until the 5th-century BCE the ancient Greeks had no precise method for counting the divisions of the day or hours. From the 5th-century BCE onwards2 time-measurement devices were were used: the sun-dial or gnomon (which was introduced from the Near East), and the clepsydra or "water clock" in which water ran out of a marked vase at a constant rate.

The earliest precise angular measurements (of stellar declinations) were made circa 280 BCE by Timocharis (and also his pupil Aristyllus). The stellar observations by Timocharis are the earliest observations of stellar positions in Greek astronomy. James Evans has commented that Timocharis may be considered the founder of careful and systematic observations among the Greeks. From Timocharis to Ptolemy stellar declinations were given without their right ascensions. Declinations are relatively easy to observe. An observer with knowledge of the observing site's latitude can determine a star's declination by measuring its altitude at meridian crossing. However, making right ascension measurements are much more difficult and involve determining a star's angular distance from the right ascension zero point or from a star of presumed known right ascension.

The accuracy of the stellar declinations in the Almagest demonstrates a sophisticated knowledge of astronomy and a sophisticated instrument-making technology regarding the armillary sphere.

The ancient Greek astronomers from Eudoxus onwards refined astronomy, bringing it from being an observational science, with an element of prediction, into a full-blown theoretical science. Eudoxus introduced mathematics into astronomy and is considered the founder of mathematical astronomy. He was the first to construct and use a planisphere and to explain the apparent movements of the heavenly bodies by a geometric model. In planetary astronomy he devised an ingenious planetary system based on a theory of concentric spheres (a spherical lemniscate). Eudoxus was also the founder of celestial mechanics in that he invented a method to calculate the distance of the sun and the moon from Earth. The ancient Greeks made accurate measurements and moved the idea of the structure of the universe away from gods and superstition. The ancient Greeks drew on the immense body of accurate observations and the mathematical techniques developed by the Babylonians, and refined and advanced them. Babylonian and Greek traditions of mathematical astronomy merged during the late Hellenistic period. A characteristic feature of late Greek astronomy is the use of geometric models to explain planetary motion. Ancient Greek astronomers/mathematicians used geometry to create models of how the planets moved. To the Greeks, the universe was a machine that ran upon mechanical and mathematical principles, which could be deduced through logic and reasoning. Eudoxus envisioned the universe as containing the static earth at the centre, with the stars occupying an outermost crystal sphere (per Plato). The sun, inside this sphere, rotated around the earth at the same speed as the stars, but was attached to the astral sphere and also rotated about this axis once per year. Hipparchus succeeded circa 128 BCE to measure the positions of the solstices and equinoxes. After the homocentric, concentric spheres model of planetary motion by Eudoxus there is the epicycle-on-deferent constructions for planetary motion by Ptolemy. The goal of Greek mathematical astronomy was the computation of the planetary positions for any given time. These geometrical models are completely different to the Babylonian use of certain planetary numerical parameters. For the computation of planetary positions the late Greek astronomers ignored the arithmetic schemes of the Babylonians and favoured geometric models. (Ptolemy does not make use of Babylonian arithmetic schemes.) Using trigonometry, Hipparchus and Ptolemy devised the idea of epicycles, where the sun, moon, and planets moved around the earth in circles, but rotated in smaller circles within this cycle. Ptolemy of Alexandria wrote the classic comprehensive presentation of geocentric astronomy, the Megale Syntaxis (Great Synthesis), better known by its Arabic title Almagest. Unfortunately the geocentric model and epicycles of the ancient Greek astronomers persisted until the European Renaissance. In his catalogue of stars in the Almagest, Ptolemy introduced orthogonal spherical co-ordinates.

Also of note was the development of the astrolabe by either Hipparchus or Ptolemy.

Appendix 1: Parapegmata

A parapegma is the name of a time counting device. A parapegma (plural parapegmata) is basically an astronomical weather calendar. The weather wisdom of parapegma derives from the weather wisdom of farmers and sea-farers. Bernard Goldstein and Alan Bowen have suggested that the construction of parapegmata was a defining characteristic of early Greek astronomy. Also, that weather prediction may have been a motivating factor in much early Greek astronomical work.

According to Daryn Lehoux the term 'parapegma' has the meaning 'to fix (something) beside (something else).' A parapegma is a farmer's almanac (= peg-calendar regarding sowing and reaping). The basic technology of the originally parapegma was drilled holes and itemised inscriptions indexed with a moving peg. The term 'parapegma' denoted the fact that the stone (or plaster, or wood) parapegmata used a system of a movable peg (or movable pegs) in holes to fix the position of the lunar months within the solar year. The peg-holes (placed beside the text) were provided in order to represent each day. All statements are embedded in a fixed, year long chronological framework. The framework id represented by drilled holes representing each of the 365 days of the year. If a hole has a statement or statements next to it, the statements apply to that day. Days with no associated statements are represented by rows of the appropriate number of holes. A peg was moved each day by a person (operator) from one hole to the next to indicate where the current date fell within the cycle. The main difference between the literary parapegmata and the earlier inscriptional parapegmata was that the inscriptional parapegmata had peg holes whereas the later literary texts had calendar entries, organised according to the zodiacal month, or a substitute for a calendar. (The title parapegma does not appear in the literary versions.) Originally, the parapegmata was an inscription in stone, plaster, or wood. The star/constellation risings and settings had a 2-fold function: (1) serving as an indicator of the stage of the solar year, and (2) serving as an indicator of weather signs (weather prediction/prognostications). It is indicated there were both separate and combined astronomical and astrometeorological parapegmata (the 2 most important classes of such inscriptions). Some stone parapegma seem to list only astronomical events (were essentially calendars), but others also include meteorological events (were also almanacs). By the 3rd-century BCE the association of weather (including winds) with the annual risings/settings of particular stars/constellations were recorded as year-length ordered lists in parapegmata. The parapegmata functioned as tracking instruments for the astronomical and meteorological cycles.

A recent discussion (The Star of Bethlehem and the Magi: Interdisciplinary Perspectives edited by Peter Barthel and George van Kooten (2015)) has placed the Greek use of weather forecasting within the category of event-driven astrology. It is explained that the earliest kinds of event-driven astrology in the Greek-speaking world, prior to the entry of Mesopotamian astral omens were methods of weather prediction. These are identified as comprising 2 types. One type operated through correlations of observed sign and predicted outcome expressed in a similar way to Mesopotamian omen texts. The other type of Greek astral weather prediction correlated weather patterns with the first and last appearances of stars after sunset and before sunrise.

The linkage of weather phenomena with the fixed stars is an old custom (Hesiod's Works and Days). The comprehensive presentation of calendar dates in conjunction with weather and astronomical phenomena was a later practice.

There were single parapegmata composed by one single author, and collected parapegmata that combined various lists. (Were a compilation of information from earlier parapegmata.) The earliest known authors of single parapegmata are Meton, Euctemon, and Democritus. Until circa the 1900s the only known parapegmata were literary and found in manuscripts of, for example, Ptolemy and Geminus. Four fragments of 2 stone (marble) parapemata, one dating to the late 2nd-century BCE and the other dating to the early 1st-century BCE were excavated in a Greek theatre at Miletus in 1902 (by the renowned German archaeologist Theodor Wiegand). Another (5th) fragment found earlier in 1899 was identified as belonging with the other fragments. The 2 parapegmata are somewhat different from each other and the fragments comprising them are the best preserved and most important parapegmata fragments recovered to date. Geminus/Geminos of Rhodes, in his Elementa Astronomiae in an appendix to the "Isogage," preserves a collected parapegma, or a list of dates of the annual risings and settings of stars combined with weather predictions as cited by various authors. It is the best preserved collected parapegmata. The dating of the Geminus literary parapegma is far from certain. (Both epigraphic (archaeological) and literary parapegmata contain references to named sources indicating that individual astronomers and authors produced their own parapegmata with to named authorities.)

Written parapegma very often were in the form of tables or lists. It is in the written texts - in the absence of movable pegs - that different sorts of cycles are recorded and correlated.

Though it it required some expertise to use the parapegmata it seems that there were a number of public parapegmata. It is indicated that the earliest of the 2 parapegma recovered from Miletus included directions for use. The parapegmata eliminated the need to observe the night sky. In the Works and Days by Hesiod a reader is actually expected to observe the sky and recognise particular astronomical events and to correlate those events with the text by Hesiod.

Ptolemy had a strong interest in prediction of weather and of astronomical phenomena. However, Ptolemy organised the year quite differently to the traditional parapegmatists. He introduced certain important innovations such as working with 1st magnitude stars rather than constellations. Ptolemy's "Phaseis" contains more than 60 weather predictions made by Hipparchus, related to the rising and setting of stars and constellations.

It is worth noting that several modern commentators have made the point that the weather-forecasting literature was not really practical and perhaps was not used by farmers, sailors, and others. Geographic location also needs consideration. The Works and Days by Hesiod does not mention, for example, crops other than grain, grapes, and olives, although we know from Theophrastus and other sources that Greek farmers also grew beans, lentils, chickpeas, millet, sesame, and still other crops and that planting a wide variety of crops was considered wise and prudent. Furthermore, the Greek world was large, and Greece itself full of microclimates. So, while the Works and Days enjoyed Panhellenic circulation, farmers in Ionia, Southern Italy, the Black Sea region, Arcadia, and Attica would all have worked on different timetables and, in many cases, planted different crops, as each followed the dictates of local conditions.

Appendix 2: Extract from: "The Athenian Calendar." by Christopher Planeaux (Ancient History Encyclopedia; Article published 6 November 2015; http://www.ancient.eu/article/833/)

Parapegma (Seasonal) Calendar (Parapegmata recorded seasonally recurring weather changes in relation to the first and last appearances of stars.)

Ancient Athenians also make reference to a Seasonal Calendar, the παράπηγμα (parapegma; pl. parapegmata) sometimes referred to by scholars as the "Greek Almanac." Unlike the Olympiad Calendar, however, the Seasonal Calendar did not calculate dates in successive years but rather noted specific visible astronomical phenomena within a given year. Thus, we too would not consider it a true calendar in the modern sense.

Catalogued for centuries by various astronomers, parapegmata recorded either on stone or parchment a list of seasonally recurring weather changes in relation to the first and last appearances of stars and/or constellations alongside solar events like equinoxes and solstices – along with, in many cases, the phases of the moon. The primary need for a Seasonal Calendar emerged, because Ancient Greeks needed to mark the beginning of weather changes to regulate certain human activities such as agriculture, navigation, and warfare.

More specifically, a Seasonal Calendar observed the first and last risings above the horizons of certain stars and particular constellations (at either sunrise or sunset) in relation to the equinoxes and solstices to mark important dates. Athenians then keyed the first appearance of specific stars and constellations to certain tasks. For instance, Hesiod (Works and Days) tells farmers to harvest when Pleiades rises. Ptolemy, furthermore, advocated that astronomical phenomena actually caused the changes in seasonal weather.

Some parapegmata included observations on other annual phenomena like eclipses, bird migrations, or they might track the sun's path through zodiacal signs. Some of them also aligned the lunar cycles with solar cycles through intercalations of alternating 12 and 13 synodic months in a 19 year cycle (see Metonic Calendar below). An example of a parapegma might read something like:

We begin with the summer solstice.

The sun passes through Cancer in 31 days.

Day 1: Cancer begins to rise. Sign of changing weather.

Day 9: South Winds begin

Day 11: Orion rises as a whole in the morning.

Day 16: Corona begins to set in the morning.

Day 23: Sirius first appears in Egypt

Day 25: Sirius rises in the morning

Day 27: End of Cancer rising. The Etesian winds blow for the next 53 days.

Day 28: Aquila sets in the morning. There will be a storm at sea.

Day 30: Leo begins to rise. South wind blows.

Athenians and other Greeks engraved important astronomical events on stone tables with drilled holes for movable wooden pegs to track the passage of the required stellar observations. In other cases, like the one cited above, they simply presented the observations in written texts. We know of several parapegmata, some authored by one individual, while several authors compiled others. The Ancient Greek astronomer Euctemon, who observed the Summer Solstice at Athens in 432 BCE, composed the earliest known systematic parapegma. We have also uncovered the oldest known example of a stone and peg parapegma in the Ceramicus district of Athens.

Appendix 3: Greek Calendar Cycles

"In classical Greece, an eight-year cycle called 'oktaeteris' was known. It approximated the length of the tropical year with (365 + 1/4) d and the lunar year (i. e. 12 synodic months) with 354 days. Thus, eight lunar years have 8 · 354 d = 2832 d, and eight tropical years have 8 · (365 + 1/4) d = 2922 d. The difference between those two lengths is 90 days, or three 30-day lunar months. So in a period of eight years, a 30-day month would have to be intercalated three times to reconcile the lengths of lunar and tropical year. Soon it was discovered that the assumed length of the lunar year was not correct. A more precise approximation of the lunar year (354 + 1/3) d resulted in a difference of (87 + 1/3) d between eight tropical and eight lunar years. In eight years, the 'oktaeteris' would thus be out of step by more than two days. A more precise cycle is attributed to Meton. This cycle assumes 19 tropical years to have 6940 days, as well as 235 lunar months (110 of them ‘hollow’ and 125 ‘full’). Since 12 · 12 + 7 · 13 = 235, seven years of the 19-year cycle would have to have 13 months, the other years 12 months. The assumed length of a lunar month of (29 + 25/47) d is only about 2 min longer than the actual synodic month. The tropical year however was approximated with (365 + 5/19) d which is more than 30 min too long and thus less precise than the value of (365 + 1/4 ) d. The length of the tropical year assumed for the 19-year cycle was about 1/76 day too long. Callippus multiplied the Metonic cycle by four (4 · 19 a = 76 a) and removed one day so that 76 years had 6940 d · 4 − 1 d = 27759 d. Thus, a tropical year of (365 + 1/4) d and a lunar month of (29 + 499/940) d were assumed. The assumption for the lunar month is only about 22 seconds longer than the actual length of a synodic month. Interestingly, these cycles never seemed to have been used for the civil calendars in classical Greece." (Source: http://www.ortelius.de/kalender/greek_en.php)

Appendix 4: Chronology of Greek Astronomers BCE

Hesiod (circa 800 to 700):

Hesiod (flourished circa 7th-century BCE), Greek poet, rhapsode (a professional performer of epic poetry), and farmer. "... [T]he Works and Days presents an apparent jumble of myths, fables, proverbs, advice, as well as fairly incoherent precepts on farming and sailing." (Hesiod's Cosmos by Jenny Clay (2003, Page 2).)

Cleostratus (circa 550 to 500):

One of the founders of Greek astronomy. Cleostratus of Tenedos (life dates circa 520 BCE-circa 432 BCE) was a Greek astronomer who appears to have made 2 major contributions to Greek astronomy. It is stated in ancient sources that Cleostratus introduced the zodiac (zodiacal signs?) and the solar calendar i.e., 8 years' cycle of intercalations = the octaeteris (oktaeteris). The intercalation period of 8 years introduced by Cleostratus presumed the year to be 365¼ days long. (Aristotle (384 BCE-322 BCE) is the earliest extent Greek writer who mentions the zodiacal circle. It is likewise mentioned by Autolcus. The zodiac was undoubtedly known to Eudoxus. A century later, Aratus, in his astronomical poem, names the zodiacal circle. The evidence seems to suggest that the zodiac was introduced almost fully developed into Greece. Although the Greek had no great traditions of planetary observations, the idea of the ecliptic and the system of zodiacal constellations seems to have been widely known to them by circa 400 BCE.)

In astronomy, an octaeteris is the period of 8 solar years after which the moon phase occurs on the same day of the year plus 1 or 2 days. This period is also in a very good synchronicity with 5 Venusian visibility cycles (the Venusian synodic period) and 13 Venusian revolutions around the sun (Venusian sidereal period). This means, that if Venus is visible beside the moon, after 8 years the two will be again close together near the same date of the calendar. Such a cycle was also known to the Babylonians. The 8-year cycle of intercalations - introduced for calendrical purposes - is a period containing an exact number of days, months, and solar years: 365¼ days x 8 years = 2922 days = 99 months. (Because 99 monthly periods are correctly 2923½ days its practical use over an extended period of time was limited.)

The octaeteris is an 8-year lunar intercalation scheme. Cleostratus intercalated alternatively, one 4years with 1 month, and the next 4 years with 2 months. In application it prescribed intercalary months in the years 3, 6, and 8 of the cycle, and also prescribes the scheme of full months (30 days) and hollow months (29 days).

The octaeteris had the added benefit that it fell in step with another important cycle in Greek culture, the 4-year cycle of the Olympic games. (The cycle of 4 years was the tetaeteris.) The octaeteris, invented by Cleostratus, gave way to the Metonic and Callippic cycles of 19 and 76 years respectively. The 76 year cycle contains exactly 4 so-called Metonic cycles of 19 years.

See: "Cleostratus." by J. K. Fotheringham (The Journal of Hellenic Studies, Volume 39, November 1919, Pages 164-184). The author includes a detailed discussion on intercalation.

Oenopides (flourished circa 450):

Oenopides of Chios was a Greek mathematician (geometer), and astronomer, life dates circa 490-420 BCE. He was born on the island of Chios, but perhaps mostly worked in Athens.

Oenopides claimed the first to discover the obliquity of the zodiac. However, the Babylonians the Egyptians, and the Pythagoreans must have realized from early days that the apparent path of the sun was inclined to the celestial equator. The main accomplishment of Oenopides as an astronomer was his determination of the angle the obliquity of the ecliptic in relation to the celestial equator. He determined this angle to be 24°. In effect this amounted to measuring the inclination of the earth axis. Oenopides's result remained the standard value for two centuries, until Eratosthenes measured it with greater precision.

Oenopides appears to have been the first to give a more exact figure for the period of the Great Year. In later Greek astronomy the Great Year came to mean a period in which all the heavenly bodies returned to their original relative positions i.e., the period after which the motions of the sun, moon and planets all repeated themselves so in the period of one Great Year all should have returned to their positions at the beginning of the Great Year. However, in early period of Greek astronomy only the motions of the sun and moon were taken into account and the Great Year was was the period after which the motions of the sun and moon came to repeat themselves i.e., was the least number of solar years which coincided with an exact number of lunations. Oenopides gave the value of the Great Year as 59 years. Before Oenopides it was calculated that the sun and the moon returned to the same relative positions after a period of 8 years, the octaëteris.

Philolaus (flourished circa 430):

Philolaus of Tarentum (formerly the Greek colony of Taras, Italy) or Croton (southern Italy) was a Greek Pythagorean and Presocratic philosopher, mathematician, and astronomer who lived from circa 470 to circa 385 BCE. He is one of the 3 most prominent figures in the Pythagorean tradition.

Philolaus systematized the number theory of Pythagoras. He stressed the importance of numerical groupings and the divine properties of number. The extraordinary originality of Philolaus as an astronomer went unnoticed in ancient Greece. The astronomical system of Philolaus is the best attested early Pythagorean astronomical system.

Philolaus was the precursor of Copernicus in moving the earth from the centre of the cosmos and making it a planet. Philolaus was the first to declare that the Earth was not the stationary centre of the cosmos, but moved around a central fire along with the fixed stars, the 5 planets, the Sun, Moon, and a mysterious "counter-earth." The "counter-earth" (Greek word ‘Antichthon’) is a hypothetical body of the solar system hypothesized by Philolaus to support his non-geocentric cosmology, in which all objects in the universe revolve around an unseen "Central Fire" (distinct from the Sun which also revolves around it). The central holy fire was not the Sun, but some mysterious thing between the Earth and "counter-earth." Philolaus named the unseen “central fire" "estia," the hearth of the universe, the house of Zeus, and the mother of the gods, after the goddess of fire and hearth Hestia. He maintained an idea of the Earth's rotation around its axis, claiming that the earth always turned away from the central fire as it revolved around it. Philolaus' theory of a central fire is of great significance since it removes for the first time the earth from the centre of the universe. Philolaus supposed the Sun to be a disk of glass which reflects the light of the universe. The astronomical system of Philolaus was a significant attempt to try to explain the phenomena but also had mythic and religious significance.

Philolaus made the lunar month consist of 29½ days, the lunar year of 354, and the solar year of 365½ days. His ideas about the nature of the Earth's place in the cosmos later influenced Aristarchus of Samos.

See: "On Philolaus' Astronomy." by Daniel Graham (Archive for History of Exact Sciences, Volume 69, Issues 2, March, 2015, Pages 217-230).

Meton (flourished circa 430):

Meton of Athens (late 5th-century BCE), Greek astronomer.

The most famous example of 5th-century Greek astronomy is Meton of Athens. Meton is said to have observed the summer solstice of 432 BCE, to have calculated a 19-year cycle of intercalations that would keep a calendar based upon lunar months in synchronization with the solar cycle, and to have put up some kind of instrument for astronomical observations in a public space, either on the Pnyx or in the deme Kolonos. The extent to which Meton influenced Athenian timekeeping, however, has been the subject of much discussion. Many modern historians believe Meton was likely not a calendar reformer but worked within an intellectual tradition whose practical applications were in the realm of weather prediction rather than that of calendar reform.

Archytas (circa 400 to 350):

Archytas was a Greek philosopher, mathematician, astronomer, statesman, and strategist (life dates: 428 BCE-347 BCE). He was born in in Tarentum, Magna Graecia (southern Italy). He belonged to the Pythagorean school and the reputed founder of mathematical mechanics. He was a good friend of Plato.

Practically nothing is known of Archytas' astronomy. However, it is quite clear that Archytas' astronomy does deal with the visible heavens, with the risings and settings of the stars and planets.

Eudoxus (circa 400 to 350):

Eudoxus was taught astronomy by Archytas (Architus) of Tarentum (in Magna Graecia, an area of southern Italy which was under Greek control in the 5th-century BCE), a Pythagorean. Archytas (428-347 BCE) was an ancient Greek philosopher, mathematician, astronomer, statesman, and strategist. He was a scientist of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato. He spent most of his life residing in Italy.

Eudoxus of Cnidus had an astronomy school at Cyzicus. He was a contemporary of Plato. Eudoxus was the most significant geometer in the pre-Euclidian period. His 4th-century BCE geographical treatise, the Gēs periodos ('Circuit of the Earth'), systematically described the lands and people of the known world, from Asia in the east to the western Mediterranean. Eudoxus produced works of a descriptive and empirical type in astronomy and geography. His astronomical works are thought to have included observations of the stars - a systematic almanac of celestial events. Eudoxus eventually built an observatory on Cnidus (not much higher than the dwelling-houses) and from there he observed the star Canopus, the lowest visible bright star in Cnidus ( Strabo (65 BCE-23 CE, Greek geographer and historian, Geography, Book 2). Eudoxus was the founder of the first known observatory. (At the time of Eudoxus, Cnidus was locate at 36° 41' north (the city having moved from an earlier site in 390 BCE. The declination of Canopus at this epoch was -52.839, giving a true altitude at transit of 0.478 degrees, which is refracted to 0.904 degrees. Canopus would be visible at any extinction coefficient < 0.2 magnitude per air mass.) The first comprehensive Greek star map was established by Eudoxus. The principal astronomical accomplishment of Eudoxus appears to have been the development of a descriptive map of the visible night sky - he composed a detailed description of the constellations. The observations made at his observatory in Cnidus, as well as those made at the observatory near Heliopolis, formed the basis of 2 books referred to by Hipparchus. These 2 (almost identical) prose works (both 4th-century BCE) were the Enoptron ('Mirror') and the Phaenomena ('Appearances'), the latter being thought by some scholars to be a revision of Enoptron. Hipparchus in his Commentary states us that the works concerned the rising and setting of the constellations. The Greeks had begun the process of naming constellations before the time of Eudoxus but Eudoxus undertook to comprehensively describe the entire visible night sky. All the works of Eudoxus, have been lost.

The object of Eudoxus may have been to develop a practical manual for finding the time (hour) of night. Unlike later Greek astronomers (and modern astronomers), Eudoxus did not deal with the stars singly, and define their places by celestial measurement (i.e., he did not define their right ascension and declination, nor their latitude and longitude). Eudoxus instead gave a sort of geographical description of the territorial location (position and limits) of stars using a system of constellations distinguished by unique names. The method used by Eudoxus for determining the places of stars was to distribute named constellations over the entire visible night sky and then define stars partly by their juxtaposition, and partly by their relation to the zodiac, and to the tropical and arctic circles.

Eudoxus may have been the first Greek to employ Babylonian zodiacal signs each equal to one twelfth of the ecliptic circle. It appears that Eudoxus was aware of the Babylonian division of the ecliptic into 12 equal parts. (Plato may not have been aware of the Babylonian division of the ecliptic into 12 equal parts.) The classicist and philologist François Lasserre (Die Fragmente des Eudoxus von Knidos (F. 2., 1966, P. 39)) refers to an anonymous commentator on Aratus claiming that Eudoxus brought "the Assyrian sphere" to Greece.

There is reason to believe that during the lifetime of Eudoxus representations of the night sky on a plane surface was in use. The evidence is that in the description of some of the northern constellations a misplacement occurs which Attalus explained had arisen from the circumstance that the figures constellation figures are drawn as seen from a point on the exterior of the sphere; and Hipparchus, in his remarks concerning the passage, asserting the mistake, states that the constellation figures are drawn just as we see them, meaning that they are drawn as seen by an observer placed at the centre of the sphere. Attalus of Rhodes (flourished 2nd-century BCE) was a Greek grammarian, astronomer, and mathematician, and was a contemporary of Hipparchus. Attalus wrote a commentary on the Phaenomena of Aratus. Attalus sought to defend both Aratus and Eudoxus against criticisms from contemporary astronomers and mathematicians. Although this work has not come down to us Hipparchus cites him in his Commentary on the Phaenomena of Eudoxus and Aratus.

Note: Circa 270 BCE the Stoic poet Aratus paraphrased the description of the constellations composed by Eudoxus. The paraphrase by Aratus follows the geographical method of Eudoxus and describes only the positions of the constellations and the principal stars in them relative to each other. There is no mention made of the longitudes or latitudes, the right ascensions or declinations of the stars singly. The only circles of the celestial sphere mentioned are the tropics, the equator, the ecliptic (and the Galaxy as if it were a circle of the sphere).

Polemarchus (circa 370):

Polemarchus (Polemarch) of Cyzicus was an ancient Athenian philosopher and pupil of Eudoxus and studied his theory of homocentric spheres. Teacher of Callippus. Polemarchus appears to have been aware of the variation in the distances of each planet (demonstrated by the differences in brightness of the planets, especially Venus and Mars).

Autolycus (flourished circa 330):

Autolycus of Pitane (on the western coast of Asia Minor) was a Greek mathematician and astronomer. Autolycus relied heavily on Eudoxus for his view of astronomy. He was born circa 360 BCE and lived until circa 290 BCE. Autolycus was a strong supporter of Eudoxus' theory of homocentric spheres which consisted of a number of rotating spheres, each sphere rotating about an axis through the centre of the Earth.

Two of his books have survived in the original Greek and it is thought they are the earliest 2 mathematics works to have survived. Of these books, On the Moving Sphere is a work on the geometry of the sphere which is the same as being a mathematical astronomy text. The 2nd work On Risings and Settings is a book more on observational astronomy. On Risings and Settings is a work which consists of 2 books, both versions of the same piece of work. The 2nd book/edition is a revised and expanded edition of the first, which contains substantial new material. It is also a better constructed book. Autolycus assumed a spherical universe and deduced the circular orbits of the stars.

Callippus (circa 370 to circa 300):

The most famous and capable Greek astronomer of his time. A pupil of Eudoxus. Callippus made improvements to the system of Eudoxus.

Euclid (flourished circa 330/300):

Sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "Father of Geometry."

Euclid wrote the astronomical work, the Phenomena. It is simply a work on spherical geometry, justified by its application to astronomy. He does not attempt to give any theory to describe the motions of the sun, moon and planets. The Phenomena covered in 18 theorems some important elementary features of spherical astronomy. Euclid believed the Earth was located in the middle of the cosmos and occupied the position of centre with respect to the cosmos.

Eudemus (flourished circa 320):

The History of Astronomy by Eudemus of Rhodes (circa 370-300 BCE), a Greek philosopher and historian of science, has not come down to the present-day.

Pytheas of Massalia (flourished circa 320):

Pytheas of Massalia (born circa 380/350 BCE-died circa 285 BCE) was a Greek navigator, geographer, astronomer, and explorer from the Greek colony of Massalia, Gaul (modern-day Marseille, France). He made a voyage of exploration to northwestern Europe circa 325 BCE, but his description of it has not survived. He was the first Greek to visit and describe the British Isles and the Atlantic coast of Scotland. Pytheas supposedly measured the height of the sun during the summer solstice with a gnomon, from which a value of the obliquity of the ecliptic of 23° 49' can be deduced. (Paul Ahnert, 1990, found the modern value for 300 BCE is 23° 44'.) However, the Pytheas value is based on Strabo' Geography II.5.8 & 41. That the value obtained by Pytheas seems quite accurate is just coincidence. A critical discussion of Pytheas is: "The Obliquity of the Ecliptic." by Bernard Goldstein (Archives Internationales d'Histoire des Sciences, Volume 33, 1983, Pages 3-14). For a discussion of ancient obliquity of the ecliptic 'determinations' see: "The Observations of the Ancients concerning the Obliquity of the Zodiac." by Edward Bernard (Philosophical Transactions [of the Royal Society of London], Volume 14, 1 January, 1684, Pages 155-166 & 721-725).

Hypsicles of Alexandria (circa 190-120 BCE

Greek mathematician and astronomer. Firm evidence of a 360 degree zodiac in Greece comes only from the 2nd-century BCE with Hypsicles (a Greek astronomer of Alexandria, circa 190-120 BCE) and Hipparchus.

Hipparchus (circa 190 to 120):

Greek astronomer and mathematician of major importance who made fundamental contributions to the advancement of astronomy as a mathematical science and to the foundations of trigonometry. Much of Hipparchus' work was concerned with the fixed stars. The chronological order of Hipparchus' work is uncertain. Hipparchus was not only the likely founder of trigonometry but also the person who transformed Greek astronomy from a purely theoretical into a practical, predictive science. Commonly ranked as one of the greatest scientists of antiquity. Very little is known about his life, but he is known to have been born in Nicaea in Bithynia (in northwestern Asia Minor). Only one of his numerous writings is still in existence. Most of the knowledge of the rest of his work relies on 2nd-hand reports, especially in the Almagest by Ptolemy (2nd-century CE).

Hipparchus' many important and lasting contributions to astronomy included practical and well as theoretical innovations. In order to eliminate most of the contradictions of the geocentric model he used and perfected the geometrical models, including the deferent-epicycle and eccentric previously used by Apollonius of Perga (flourished circa 200 BCE). One of Hipparchus' contributions appears to have been the incorporation of numerical data based on observations into the geometrical models developed to account for the astronomical motions.

It is indicated that Hipparchus began his scientific career in Bithynia and moved to Rhodes some time before 141 BCE. While still young, Hipparchus compiled records of local weather patterns throughout the year. It is probable that Hipparchus spent the whole of his later career at Rhodes.

He made an early contribution to trigonometry producing a table of chords, an early example of a trigonometric table. Given the chord function, Hipparchus could solve any plane triangle by using the equivalent of the modern sine formula. In Greek astronomy most problems arising from computations of the positions of the heavenly bodies were either problems in plane trigonometry or could be reduced to such by replacing the small spherical triangles involved by plane triangles.

Hipparchus also attempted to precisely measure the length of the tropical year (the period for the Sun to complete one passage through the ecliptic).

Hipparchus calculated the length of the year to within 6.5 minutes and discovered the precession of the equinoxes, which is due to the slow change in direction of the axis of rotation of the earth. This work came from Hipparchus' attempts to calculate the length of the year with a high degree of accuracy.

Hipparchus' most important astronomical work concerned solar and lunar theory, the orbits of the Sun and Moon, a determination of their sizes and distances from the Earth, and the study of eclipses. Hipparchus analysed the complicated motion of the Moon in order to construct a theory of eclipses.

Hipparchus made use of Babylonian astronomical material, including methods/procedures as well as observations. Gerald Toomer has argued that Hipparchus was responsible for the direct transmission of both Babylonian observations and procedures and for the successful synthesis of Babylonian and Greek astronomy. The discovery of Hipparchus’ dependence on Babylonian sources raises the question of what material was available to him, and in what form. The Babylonian astronomical material must have been excerpted and translated by someone in Mesopotamia who was well acquainted with Babylonian astronomical methods. When and how the transmission occurred is unknown. Hipparchus is the first Greek known to have used the highly technical Babylonian astronomical material comprising the lunar and planetary ephemerides. Without it his lunar theory, and hence his eclipse theory, would not have been possible. Ptolemy states in the Almagest) that Hipparchus renounced any attempt to devise a theory to explain the motions of the 5 planets.

Hipparchus is also credited with the production of the first known catalogue of fixed stars (and Catasterisms). According to some science historians Hipparchus made a catalogue of the sky providing the positions of 1080 stars by stating their precise celestial latitude and longitude. However, the number is thought to be approximately 850.

The only work by Hipparchus which has survived is his Commentary on the Phaenomena of Aratus and Eudoxus written in 3 books as a commentary on 3 different writings. Firstly, the treatise by Eudoxus on in the names and descriptions of the Greek constellations. Secondly, the astronomical poem Phaenomena by Aratus which was based on the constellation treatise by Eudoxus. Thirdly, the commentary on Aratus by Attalus of Rhodes, written shortly before the time of Hipparchus.

Appendix 5: Claudius Ptolemy

Claudius Ptolemy (circa 90 CE to circa 170 CE) was a Greco-Egyptian mathematician, astronomer, astrologer, and geographer of Alexandria. He was the greatest and most influential of Greek astronomers and geographer of his time. Our view of Greek astronomy tends to formed by the accomplishments of Ptolemy. By his time, however, sophisticated late Babylonian arithmetical methods had been effectively joined with native Greek geometrical astronomy. This fact tends to obscure just how casual the first great Greek astronomers were concerning observational data - Eudoxus included.

Most of the traditional Greek constellation descriptions derive from Ptolemy's descriptions. The basic patterns of the older Greek constellations were firmly established by the star catalogue in Ptolemy's Almagest, his great handbook of mathematical astronomy written circa 120 CE. Ptolemy described 48 constellations comprising the Greek sphere. These included the 12 zodiacal constellations/signs. A few individual stars were also named including: Arcturus, Capella, Antares, Procyon, and Canopus. Ptolemy also carefully designated each star by describing its position within the constellation to which it belonged. Thus the most conspicuous star in Cygnus, known today as Alpha Cygni, was designated by Ptolemy "the bright star in the tail" of the bird. Later additions of constellations over the entire sky expanded the 48 constellations of Ptolemy to 88 constellations.

Appendix 6: Greek Star Catalogues

A star catalogue essentially comprises a list of stars, usually according to position and magnitude (brightness). There were 3 substantial ancient Greek star catalogues. A "star catalogue" by Erastosthenes of Cyrene (3rd-century BCE) was a constellation description and catasterism and did not include any numerical data (coordinates) on the positions of stars. Previously, Eudoxus of Cnidus in the 4th century BCE had described the stars and constellations in 2 books called Phaenomena and Entropon. Aratus of Cnidus wrote a poem called Phaenomena based on Eudoxus's work.

The first Greek catalogue of stars giving accurate positions (coordinates) for single stars was by Hipparchus (2nd-century BCE). It contained some 850 stars. The next star catalogue was by Ptolemy (included as part of his Almagest) 2nd-century CE. It was a larger and improved star catalogue than Hipparchus' Catalogue of stars (having more exact coordinates). In his star catalogue, Ptolemy listed 1,028 stars/objects forming the classical 48 constellations. The star catalogue in Ptolemy's Almagest is the only extent star catalogue from ancient Greece. Hipparchus' Catalogue of stars has not survived as an independent work. It is thought likely that a substantial part of it is preserved in the large number of observational data (stellar coordinates) of his Commentary on Aratus. Hipparchus' Commentary contains many stellar positions and times for rising, culmination, and setting of the constellations.

Ptolemy's star catalogue in his Almagest was much later updated by the Persian astronomer al Sufi in the 10th-century. It was the 1st medieval star catalogue. No other star catalogues are known to have appeared until the 10th-century. Next, Ulugh Beg (a Timurid ruler (sultan) and astronomer, and mathematician), in the 15th-century, working in his own observatory in the years 1420–1437, reobserved all the stars in Ptolemy's star catalogue that he could see from Samarkand, Uzbekistan. The star catalogue that he compiled became known in Europe in the 1500s and was printed there in 1665. This star catalogue was superseded only in the late 16th-century by the star catalogue of the Danish nobleman Tycho Brahe and the Hessian star catalogue of Landgrave (Count) Wilhelm IV of Hesse-Kassel via their use of superior ruled instruments and spherical trigonometry, which greatly improved accuracy. The star catalogue made by the skilled Danish observer Tycho Brahe (1546–1601) was the last and finest star catalogue of the pre-telescope era . It was included in expanded form in the Rudolphine Tables of the early 17th-century German mathematical astronomer Johannes Kepler.

Appendix 7: Stellar Coordinate System

Our modern astronomical coordinate system originated in ancient Greek astronomy. The first coordinate system preserved is the star catalogue data in ecliptical coordinates (featuring longitude and latitude for each star) in Ptolemy’s Almagest (circa 150 CE). Both Mesopotamian and Greek astronomers made use of time to measure the positions/distances of objects on the celestial sphere.

In early texts in Greek and Mesopotamian mathematical astronomy there are different positioning systems used for stars; including (1) use of the horizon as frame of reference, and (2) use of the shapes of constellations to describe the location of stars. What is evident is the development from what may be approximated as a Mesopotamian rather basic equatorial system (i.e., the Astrolabe genre and the Mul.Apin series, 2nd-millennium BCE) to the Hellenistic period use of a detailed ecliptical system in Ptolemy’s Almagest (circa 150 CE).

It is indicated that the system of geographical coordinates were derived from the system of celestial coordinates (probably by Ptolemy).

There were several "ecliptical longitude" systems used in antiquity: (1) simply the division of the ecliptic, (2) the notion of zodiacal sign X, degree Y, and (3) the use of a spherical orthogonal coordinate system.

In Greek observational astronomy a 360° division of the ecliptic was in use as least as early as Eudoxos. The original works by Eudoxus have not come down to the present-day but Hipparchus cites Eudoxus' ecliptical longitudes in his Commentary on Aratus and Eudoxus. Hipparchus refers to certain longitudes of stars and judges whether Eudoxus was accurate, and occasionally corrects him. This shows that Eudoxos must have given definite longitudes (in terms like "Leo 3°"). However it is uncertain if the described format "star X holds its place on a parallel circle at about 3° of the Lion" really reflects a concept of longitudes as lines perpendicular to the ecliptic in an orthogonal coordinate systems (a longitude in our sense of a longitude). Unfortunately, still unpublished is: Hipparchus' Commentary on the Phaenomena of Aratus and Eudoxus by Roger Macfarlane and Paul Mills; comprising the first English-language translation. The German-language translation, Hipparchi in Arati et Eudoxi phaenomena commentariorum libri tres by Carolus Manitius (1894) is full of errors.

The question of the coordinate system of Hipparchus has been frequently discussed. It is thought likely that the original frame of reference of Hipparchus was probably not ecliptical longitude but right ascension. The astronomer and researcher Susanne Hoffmann does not agree concerning the term "coordinate system" when discussing Hipparchus and his predecessors, and suggests it is better speak of "frames of reference."

Susanne Hoffmann writes (Hastro-L, 1-July-2016): "I do not agree concerning the term "coordinate system" and suggest to better speak of "frames of reference" because (1) It is sure that Hipparchus and his predecessors divided the ecliptic in 360 degrees but (2) the "parallel circles" are parallel to the equator and not parallel to the ecliptic. Hence, they certainly did not use latitudes, but declinations. (3) the way Hipparchus describes positions of stars at a distance to the ecliptic is - translated to our mathematical language - something like "star X is at the same right ascension as 3° of the Lion", i.e. the same RA as a certain point on the ecliptic (is that a longitude???). Concluding, Hipparchus (and maybe/ probably earlier astronomers?) did not really use our concept of coordinates but a pre-stage. Concerning Greek mathematical astronomy even earlier texts are preserved: Autolykos of Pitane, Euklid's Phainomena, Hypsikles, and others discuss sections of circles rising or setting and - in a way - try to transform of coordinates. Unfortunately, we know only few [details] about their coordinate systems: are they only operating with great circles or also considering the grid of coordinates on the sphere? The zodiac as a band of constellations as well as a division of the ecliptic in twelve equal parts named after constellations in Mesopotamia preceeded (sic) the Greek zodiac by maybe one or two hundred years (unsure, ongoing research and depends on how "zodiac" is defined). In the Babylonian astronomical diaries (earliest preserved, -7th century) and procedure texts to compute positions of planets, moon etc. (See Ossendrijver, 2012, p.32-34) we find orthogonal coordinates, i.e. longitudes and latitudes - but only in a certain band (c. 10° width?) around the ecliptic where the planets move. AFAIK- we do not know anything about a Babylonian concept of giving celestial coordinates somewhere else (like used in the Almagest, e.g. "star at the tip of tail of Ursa Maior at longitude X, latitude Y")."

Appendix 8: Parapegmata and Paranatéllonta

Parapegmata star calendars were an important part of the popular and practical astronomy of the Greeks. A star calendar (parapegma) listed the phases (heliacal risings and settings) of important stars and constellations. In the astrometeorological parapegmata, weather phenomena were correlated to astronomical phenomena, namely, the risings and settings of bright stars. It is thought unlikely that the use of lunar parapegmata served only astrological purposes and not the more general function of time-reckoning. Parapegmata in the Latin West are known to have been used as calendars. The survival of lunar calendar reckoning in the culture of the Latin West is also evident in the well-attested lunar parapegmata.

The term "paranatellonta" is well-known in Greek astrological literature. Paranatéllonta, stars 'rising alongside' designates stars either rising together with the sun or being in other conspicuous positions to it. Paranatéllonta (or synanatéllonta, 'rising simultaneously'), are constellations, parts thereof (also of the signs of the zodiac) or especially bright individual stars, which become visible or invisible at the same time as certain degrees or decanal sections (segments of 10 degrees) of the ecliptic. They were first described by Aratus who description was later criticised by Hipparchus. In antiquity, "paranatellonta" (or synanatéllonta) were used for determining the seasons and for distinguishing zodiacal prognoses by astrologers. Tentatively, a forerunner of this conception has been identified in an Egyptian depiction attested several times from the 13th-century BCE onwards. There, "gods" are depicted who are defined by their positions in regard to the Sun-god. It seems possible to connect their positions with the typical meanings of the word "paranatellonta." Some contributions of Egypt to Hellenistic astrology are found in the (largely unpublished) corpus of demotic Egyptian astrological texts.


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