The Moon and the Planets in Classical Greece and Rome (original) (raw)
The roles of observational astronomy in ancient Greece
2015
This paper offers an investigation into the interface between science, in the form of astronomy, and culture, in the form of religion and the calendar. Early societies made use of a variety of mechanisms to mark time, based on the cycles of the sun, moon and stars, whether separately or in combination. In this paper I provide a survey of the use of one of these cycles, namely that of the stars, in one ancient culture, that of the Greeks. I show how gradually the night sky was mapped out with a number of distinct constellations, the number increasing over time. The Greeks used the first and last visible risings and settings of these stars at dawn and dusk as ‘event markers’, in order to signal the appropriate time for pivotal activities, especially in the agricultural sphere, such as ploughing, sowing and harvesting. At the same time, Greek societies used the moon as the basis for their civil and religious calendar, and within the lunar months were situated regular festivals of an ag...
Early Greek Astrophysics: The Foundations of Modern Science and Technology
American Journal of Space Science, 2013
The foundations of modern science and technology, metrology, experimental physics, theoretical physics, theoretical mathematics, astrophysics, including applied optics and spectroscopy go back to the Prehistoric, Presocratic, Classical and Hellenistic Greece. This tradition is well deep rooted in time, going back mainly to the epoch of the prehistoric Aegean sea, the mainland of Greece and the Islands, Cycladic, Euboea, as well as Crete, at the late Neolithic period, probably starting back at 4400 BC. Humans observe the sky before the prehistoric era and wonder and as even Plato declares, these observations that lead us to try and understand the Cosmos make us humans as well, since the actual meaning and etymology of this term human in Greek, the word ANTHROPOS, is the one that looks up, observes the ordered Universe and tries to understand its nature and its hidden Laws which govern it. Science and Philosophy emerged as a result of the human efforts to live even more successfully within a hostile environment. Humanity eventually manages to understand Nature and especially the Cosmos, using the Pythagorean principle: "Nature can only be understood accurately by the use of Mathematics, which expresses the underlying Laws of Nature and which explain all natural phenomena based on the Principe of Causality.
ANCIENT GREEK HELIOCENTRIC VIEWS HIDDEN FROM PREVAILING BELIEFS?
We put forward the working hypothesis that the heliocentric, rather than the geocentric view, of the Solar System was the essential belief of the early Greek philosophers and astronomers. Although most of them referred to the geocentric view, it is plausible that the prevalent religious beliefs about the sacred character of the Earth as well as the fear of prosecution for impiety (asebeia) prevented them from expressing the heliocentric view, even though they were fully aware of it. Moreover, putting the geocentric view forward, instead, would have facilitated the reception of the surrounding world and the understanding of everyday celestial phenomena, much like the modern presentation of the celestial sphere and the zodiac, where the Earth is at the centre and the Sun makes an apparent orbit on the ecliptic. Such an ingenious stance would have set these early astronomers in harmony with the dominant religious beliefs and, at the same time, would have helped them to 'save the appearances', without sacrificing the essence of their ideas.
Astronomical Basis of Hellenistic Planetary Order in Astrology
The structure of astrological sign rulership from the Hellenistic Egyptian period around 150-200 BCE was based on observational astronomy. This structure of Hellenistic planetary order has been maintained for over 2,000 years yet the reason for it’s order has been forgotten. This article is a culmination of 20 years of research to find the artifacts and astronomical verification for this ordering of planetary rulership of zodiacal signs.
Ancient Greece and origins of the Heliocentric theory
Since early antiquity, the important question of philosophy and astronomy was, what occupies the center of the known world. According to the geocentric system, in accordance with the anthropocentric view, the Earth lies at the center of the world. For centuries this was the dominant theory, supported by the majority of philosophers and astronomers. However, the Ancient Greek world was also the cradle of the opposite view, the heliocentric theory of Aristarchus of Samos (c.310 -230 BC), which is generally credited to be the first to postulate a non-geocentric system. But, centuries before him, seeds of the heliocentric theory can be traced back to the Orphic Hymns and to the teachings of Anaximander and the Pythagoreans. Here, the evolution of the heliocentric theory of Antiquity will be analyzed and discussed from the first mention of it in the Orphic Hymns. The theory was further advanced by the Pythagoreans, especially the “pyrocentric” system with a central fire, of Philolaus of Croton. Also contributing to the heliocentric theory were the views and ideas of Icetas, Ecphantus, Heraclides of Pontos, Anaximander, Seleucus of Seleucia, and finaly of Aristarchus of Samos. Unfortunately, the heliocentric theory did not prevail over the geocentric view, which gained wide recognition due to the weight of Aristotle’s support, and later on due to the theories of the great astronomer Claudius Ptolemy (2nd century AD).
In this article we consider the role of the three principal celestial bodies, the Earth (Gaia), the Sun (Helios) and the Moon (Selene), as well as the Sky (Ouranos) in the ancient Greek cosmogony. This is done by the analysis of antique Greek texts like Orphic Hymns and the literary remains of the writers and philosophers like Aeschylus, (Pseudo) Apollodorus, Apollonius Rhodius, Aristotle, Euripides, Hesiod, Homer, Hyginus, Nonnus, Pausanias, Pindar and Sophocles, as well as by the analysis of texts of Roman writers like Cicero, Ovid and Pliny.
Hellenistic Astronomy: The Science in Its Contexts edited by Alan C. Bowen and Francesca Rochberg
Aestimatio: Sources and Studies in the History of Science, 2021
One of the daunting challenges involved in reviewing a 750-page standard tome on a subject like astronomy is being able to evaluate all aspects of the volume, covering technical data as well as any possible impact of subject matter on other disciplines. The editors, mindful of their readership consisting of both “insiders” and “outsiders”, have taken decisive steps towards making Hellenistic astronomy accessible and comprehensible, with an appropriate balance between complex graphs and arithmetic equations and more general topics, as well as a glossary of technical terminology. The present reviewer, an unrepentant “outsider”, will attempt to focus on some key issues involving the connections between Babylonian and Greek astronomy in the period in question, as well as the impact of astronomy as a whole. Reviewed by: M. J. Geller, Published Online (2021-08-31)Copyright © 2021 by M. J. GellerThis open access publication is distributed under a Creative Commons Attribution-NonCommercial-...
Putting the astronomy back into Greek calendrics: the parapegma of Euctemon
Instruments – Observations – Theories: Studies in the History of Astronomy in Honor of James Evans, ed. Alexander Jones and Christián Carman, 2020
It is a pleasure to be able to offer a paper to our honorand. Many years ago James Evans established himself as a great teacher of the history of ancient Greek astronomy to many beyond the confines of his own lecture room through his book, The History and Practice of Ancient Astronomy. While in more recent years he has provided us with sophisticated papers on the more technical aspects of astronomy, especially as they pertain to the Antikythera Mechanism, it is to that earlier monograph, and its impact on myself and my own students, that I wish to pay homage in this small offering on ancient "observational" astronomy.
The New Alexandria Library of Texas + it's old Publisher London : Hunt and Clarke, 10 Tavistock Street, Covent Garden - , 1827
This extremely rare book that was almost destroyed from being worn from the weather that was buried under mountains of junk is a comprehensive and esoteric work that explores the connections between mythology, ancient astronomical knowledge, and the origins of religious traditions. Published in 1827, the book is divided into three parts, each delving deeply into the symbolic and mythological significance of celestial bodies and their role in shaping human history, culture, and belief systems. Mackey’s approach combines speculative interpretations, historical analysis, and his unique worldview, which draws heavily on astrology, alchemy, and early theories of the cosmos. Part I: The Origins of Mythological Astronomy The first part lays the groundwork for Mackey’s thesis, asserting that ancient civilizations encoded astronomical knowledge in their myths, legends, and religious practices. He posits that early societies, especially those of Egypt, Mesopotamia, and Greece, personified celestial phenomena (such as planets, stars, and constellations) into deities and heroes. These myths served not only as religious narratives but also as complex astronomical texts. Key points include: • The Primordial Sky Religion: Mackey claims that early humans worshipped the heavens, interpreting celestial movements as divine will. • Zodiacal Symbolism: He analyzes the twelve signs of the zodiac and their connections to seasonal cycles, agricultural practices, and mythological archetypes. • The Great Year: Drawing from theories of precession, Mackey discusses the concept of the "Great Year," a vast cosmic cycle that underpins mythological timekeeping systems. Part II: The Influence of Celestial Bodies on History and Religion In the second part, Mackey expands on how ancient knowledge of the heavens influenced religious doctrines and historical events. He argues that many key religious symbols, such as crosses, circles, and serpents, are rooted in astronomical observations. This section also delves into the syncretism between different cultures’ mythologies, particularly how Egyptian, Greek, and Roman traditions absorbed and adapted astronomical lore. Notable themes include: • The Sun and the Solar Deities: A detailed examination of solar worship across cultures, with a focus on Ra (Egyptian), Apollo (Greek), and Mithras (Persian). • Planetary Worship: The veneration of planets as gods, exploring how Venus, Mars, and Saturn were mythologized. • The Role of Eclipses and Alignments: Mackey discusses how eclipses and planetary conjunctions were interpreted as omens or divine interventions in human affairs. Part III: Mythological Astronomy as a Key to Unlocking the Past The final part is the most speculative, as Mackey presents his vision of mythological astronomy as a tool for understanding the ancient world. He suggests that much of human history can be reinterpreted through the lens of celestial symbolism. Mackey also critiques contemporary scholars for failing to recognize the astronomical underpinnings of ancient myths, calling for a revival of what he terms "astro-theology." Highlights include: • Astronomical Codes in Sacred Texts: Mackey asserts that texts like the Bible, the Rigveda, and Homeric epics are encoded with astronomical knowledge. • Astrological Determinism: He explores how ancient societies believed their destinies were shaped by the stars. • The Lost Knowledge of Antiquity: Mackey laments the loss of ancient astronomical wisdom, which he believes is essential for understanding human origins and spiritual evolution. Style and Influence Mackey’s work is written in an enthusiastic and often polemical style, blending historical research with bold conjectures. His ideas reflect the intellectual milieu of the early 19th century, a time when Romanticism, esotericism, and an interest in ancient wisdom flourished. While not widely recognized in mainstream academia, The Mythological Astronomy has influenced later occultists, astrologers, and esoteric thinkers who see the cosmos as a mirror of human existence. Conclusion The Mythological Astronomy is a thought-provoking and ambitious attempt to unify mythology, astronomy, and religion. Though speculative and occasionally anachronistic, Mackey’s work provides valuable insights into how ancient civilizations viewed the heavens and their place in the cosmos. It invites readers to reconsider the mythologies of the past as profound repositories of astronomical and spiritual knowledge. Tags-Mythological astronomy, Sampson Arnold Mackey, ancient astronomy, celestial mythology, astrology, alchemy, ancient wisdom, zodiac signs, precession of the equinoxes, Great Year, sacred geometry, astro-theology, celestial deities, planetary worship, solar deities, lunar symbolism, eclipses, planetary conjunctions, astrological determinism, star lore, ancient religions, Egyptian mythology, Greek mythology, Roman mythology, Mesopotamian astronomy, cosmic cycles, astronomical symbolism, mythological archetypes, solar worship, lunar worship, Venus in mythology, Mars in mythology, Saturn in mythology, constellations, sacred texts, Bible and astronomy, Rigveda, Homeric epics, astronomical codes, cultural syncretism, serpent symbolism, circle symbolism, cross symbolism, celestial phenomena, divine interventions, sacred calendars, astronomical alignments, esoteric knowledge, lost knowledge, human origins, spiritual evolution, astro-mythology, cosmic symbolism, ancient cosmology, star worship, sky religion, primordial religion, astrological symbols, religious symbols, cosmological theories, cosmic narratives, ancient manuscripts, historical astrology, symbolic cosmology, mythological cycles, celestial movements, sacred astronomy, astro-archetypes, mythical narratives, sky deities, ancient cultures, astro-mysticism, archeoastronomy, astro-histories, stargazing, celestial omens, cosmological interpretations, zodiacal archetypes, astrological myths, esoteric cosmology, mythological studies, astro-chronology, solar myths, lunar myths, planetary cycles, skywatching, stellar symbolism, astronomical lore, heavenly bodies, celestial codes, cosmic order, astro-anthropology, mythology and religion, sun myths, moon myths, astrological prophecy, sacred traditions, cultural astronomy, star cycles, divine cosmology, astro-symbology, planetary archetypes, celestial divination, symbolic narratives, astro-histories, zodiac traditions, cultural syncretism, astro-interpretations, stellar deities, moon goddesses, sun gods, planetary gods, cosmic revelations, ancient astrology, astro-rituals, cosmic mythology, astrological systems, sky symbolism, astro-legends, religious cosmology, star mysteries, cosmic legends, astral worship, sacred constellations, mythic astronomy, celestial chronology, planetary alignments, astro-literature, stellar myths, sacred texts and stars, mythic deities, celestial theology, astral science, star prophecies, astro-history, symbolic archetypes, cosmic myths, stellar cycles, astro-traditions, ancient calendars, star divination, mythical figures, solar-lunar myths, planetary symbolism, cosmic beliefs, zodiac mythology, cosmological legends, sacred myths, astro-mythology studies, astro-religions, cosmic reflections, star traditions, sacred geometry in mythology, astral myths, zodiac legends, heavenly myths, cosmic theology, astro-spirituality, planetary worship traditions, divine constellations, astral codes, celestial legends, sacred zodiac, symbolic heavens, ancient heavenly lore, stellar archetypes, star prophecies, astronomical myths, sacred star knowledge, cosmological myths, star symbolism, celestial history, planetary worship symbols, sacred rituals, solar-lunar cycles, star wisdom, astral cosmology, sacred astro-myths, planetary gods myths, heavenly stories, astro-heritage, cosmic divination, mythological stars, symbolic planets, sacred archetypes, astro-histories of myths, ancient star maps, mythic star lore, ancient astro-theology, zodiacal stories, stellar prophecies, cosmic mysteries, celestial worship, astro-codes, astral narratives, sacred astronomy traditions, stellar interpretations, planetary cycles in mythology, astronomical symbols in religion, celestial myths and legends, astro-philosophy, cosmic archetypes in myths, astro-syncretism, celestial wisdom traditions, symbolic cosmic cycles, heavenly symbols, stellar astrology, sacred cosmic knowledge, astro-systems, celestial mysteries in texts, star-based myths, planetary patterns in religion, ancient cosmic wisdom, cosmic signs, mythological sky lore, celestial order in myths, astro-secrets, stellar theology, planetary lore, divine astrological knowledge, symbolic myths, star religions, sacred texts and cosmology, celestial myths in sacred literature, divine star worship, symbolic constellations, zodiac lore, celestial imagery, heavenly archetypes, mythical cycles in the cosmos, astro-inspired myths, celestial motifs, sacred cosmic archetypes, astro-allegories, ancient star myths, cosmic wisdom traditions, sacred planetary cycles, mythic astronomical systems, zodiac myths, sacred astro-symbolism, astronomical deities, mythical heavens, astro-cultural traditions, cosmic storytelling, stellar mythos, astro-lore studies, ancient astro-legends, celestial beings, sacred sun myths, astro-traditions of the zodiac, stellar imagery, sacred astrological cycles, astro-symbolic traditions, planetary myths, heavenly lore, divine astronomical traditions, ancient sky worship, sacred astronomy rituals, cosmic astro-lore, zodiac figures in myths, star-lore in sacred texts, planetary deities, ancient cosmic cycles, astro-allegorical systems, symbolic constellations, celestial prophecies, astro-mythic wisdom, zodiac archetypes in ancient myths, cosmic patterns in mythology, astro-symbols in religion, sacred astro-lore, divine solar myths, celestial wisdom in myths, zodiacal codes in mythology, astro-philosophical studies, cosmic symbolic systems, s...
Two cosmic routes for Night and Day in greek archaic thought ?
My aim is to show that there are at least two routes for Day and Night in archaic thought, or at least that Hesiod – or the author of Theog. 744-761 – invented a new route, as a result of a new interrogation of a probably previous route or maybe several previous routes that can still be observed in later authors. The variety of these routes is a testimony of the ongoing interrogation, within archaic poetry, on the best way to represent cosmic phenomena. And Hesiod's innovation shows an attempt to clarify this representation through the use of explicit criteria and the appeal to symmetry. This give us a sense of the scientific debate before and outside the rise of ionian thought.
Astronomy in the Odyssey: The Status Quaestionis
Homeric poems, other than being the first literary record of the ancient Greek civilization, represent a rich source of information about the " scientific " knowledge of Greeks during the Archaic period. In the Iliad and in the Odyssey, whose redaction dates back to the VIII century BC, there are mentions of several heavenly bodies: the Sun and the Moon, the planet Venus, some stars, constellations (Boötes, Ursa Major and Orion) and asterisms (Pleiades and Hyades). Hence, the Homeric epos is an important evidence for archaeoastronomical studies dealing with civilizations that arose in the Mediterranean basin, in particular ancient Greece. However, few scholars have addressed so far a systematic review of the Homeric passages that include astronomical references, on the one hand because of little interest in such kind of problems in philological studies, on the other hand since astronomical expertise is required to support the analysis. By virtue of the subject matter of the story itself—the nostos of Odysseus back to Ithaca—the Odyssey contains the majority of the passages concerning the description of celestial bodies and phenomena. This supports indications, obtained independently, that during the pre-Homeric period stars had already been extensively used as a reference for navigation, in order to find and follow the route during the long crossings of the Mediterranean sea. In the present contribution we describe the state of the art of scientific and philological research concerning the passages of the Odyssey where astronomical knowledge of that time is reflected. Some of them have been interpreted as the description of celestial events that really occurred. This has given rise to a lively discussion among the scientific community on the possibility to assign a date to the historical facts
The cultural relevance of astronomy in classical Antiquity
Studies in History and Philosophy of Science II, 2021
Nowadays we understand 'astronomy' as the study of celestial bodies. However, astronomical knowledge in classical Greece and Rome cannot be reduced to the study of the sky. Of course, it did include the study of stars and planets, but this knowledge was intimately linked to many other subjects, such as religion, geography, meteorology, mythology, medicine, etc. Acquaintance with many celestial phenomena and the constellations and their lore was part of ancient culture. Remove from the classical Antiquity its astronomical knowledge, and many of its features and activities would become impossible or meaningless. Astronomy was deeply implanted in ancient culture, as will be shown in this paper, and that was the reason underlying its very high status in Antiquity.
Colloquium 2: Two Stages Of Early Greek Cosmology
Proceedings of the Boston Area Colloquium of Ancient Philosophy, 2013
It is generally held that Presocratic cosmologies are sui generis and unique to their authors. If, however, a division is made between sixth-century and fifthcentury BC cosmologies, some salient differences emerge. For instance, heavenly bodies in sixth-century cosmologies tend to be light, ephemeral, fed by vapors, and located above the earth; those in fifth-century cosmologies tend to be heavy, permanent, heated by friction, and to travel below the earth. The earlier cosmologies seem to embody a meteorological model of astronomy, the latter a lithic model. The change in models can be accounted for on the basis of Parmenides’ discovery that the moon is illuminated by the sun and hence is a spherical, permanent, opaque or earthy body. This insight generated empirical evidence to confirm itself and rendered obsolete earlier cosmologies.
ANCIENT CELESTIAL SPHERES FROM GREECE
We present several ancient celestial spheres from the 8th century B.C. found throughout Greece, mainly in Thessaly, at the temple of Itonia Athena, but also in Olympia and other places. These celestial spheres have an axis, equator and several meridians and they have several markings with the symbol of stars (today's symbol for the Sun) odot\odotodot. Such instruments could have been used to measure the time, the latitude of a location, or the coordinates of stars. By the 8th century BC, the transition from the Geometric to the Archaic Age was producing the first signs of a renaissance of Greek civilization, after the collapse of the Mycenaean order and the subsequent wars that left Greece depopulated. The Olympic Games were revived in 776 BC, the Homeric epics were becoming popular throughout the Hellenic world, and Hesiod produced the first detailed Theogony, as well as his Works and Days, that contained a repository of the cosmological (and meteorological) knowledge of that era. The accepted wisdom of those days only dimly foreshadowed the amazing series of scientific and philosophical revolutions that were to occur only a couple of centuries later. At that time, as we know from Hesiod, the earth was considered to be flat, possibly disk shaped, while the heavens were spherical, endlessly revolving around the still Earth. Many of the constellations catalogued in antiquity had been named by the early Archaic age, as had many of the brightest stars (Orion, Ursa Major, Ursa Minor, Bootes, Sirius, Arcturus, the Pleiades and Hyades). The colonization of the Mediterranean and the Black Sea had boosted the mercantile and navigational experience of those early Greeks, who, venturing far from their native ports, had almost certainly used the position of fixed stars for navigational purposes. Aratus mentions (although some centuries later) that Greek seamen used the constellation of Ursa Major for navigational purposes, while the Phoenecians relied on Ursa Minor to chart their courses on the sea. The sphere of the heavens had already been incorporated in mythology, with the titan Atlas holding it on his shoulders. In later ages, a variety of devices were invented to calculate the time or latitude of a place, by comparing the position of the Sun or another star with respect to the horizon. Those devises ranged from the simple casting of the Sun's shadow on a graduated quadrant pitch circle, to elaborate astrolabes and celestial spheres crafted during the Hellenistic Age. In earlier ages, sundials (dating from the 15th century BC in Egypt, and possibly the Aegean region as well) had provided the first small scale application of astronomical observations for the practical needs of people (large scale applications consisted of the study of yearly and monthly variations of the Sun, Moon and stars, for the creation of farming calendars,
Aristotle on the “Great Year”, Eudoxus, and Mesopotamian “Goal Year” Astronomy
« Aristotle on the “Great Year”, Eudoxus, and Mesopotamian “Goal Year” Astronomy », A.I.O.N. Annali dell’Università degli Studi di Napoli L’Orientale. Dipartimento di studi del mondo antico e del Mediterraneo antico. Sezione filologico-letteraria XXXV, 2013, p. 111-123. Abstract. - Aristotle’s annus maximus is shown to have been a supposed period of 12 960 years between two returns of the sky and the planets to the same configuration. It is likely that Plato and Eudoxus of Cnidus also investigated this period, but arrived at different results. The planetary periods used in Aristotle’s calculation are of Mesopotamian origin and were probably borrowed by Eudoxus in Egypt. This file contains an important Corrigendum.
Greek Astromythology: intersections between mythology history and modern Astronomy Education
Frontiers in Education, 2025
This article provides a comparative assessment of the intersection between Greek Astromythology and Astronomy Education, as an interdisciplinary and intercultural contribution. The research is based on a qualitative assessment of narratives and concepts, using a brief systematic literature review to compile related academic production, with the objective of providing critical discussions on this intersection. The findings show that there is a broad diversity of themes in Astronomy that have their roots in Greek Astromythology: 174 items in total. Most stars related to Greek Astromythology, about 63%, were named in tribute to Greek culture, whereas approximately 36% of the findings correspond to elements belonging to the daily life of the Hellenic people. This shows that the Greeks’ efforts to catalog various stars and think about the multiple aspects involving Astronomy resonate contemporarily and, therefore, it is imperative to contextualize the historical and cultural aspects involved in modern Astronomy science. In addition, the results identified a broad range of myths related to Astronomy, which demonstrate the significant contribution of Greek Astromythology to this science area. Hence, the use of mythology as a historical and cultural aspect of the visible constellations and planets can play a relevant contribution to scientific literacy and teaching, particularly in introductory courses of Astronomy, which are commonly developed in primary and secondary schools. Exploring this intersection at the school level can also enable the reflection, implementation, and evaluation of consistent teaching and learning indicators toward a critical education.
The dichotomy between 'practical' and 'theoretical' astronomy in ancient and late antique literature
In Plato's dialogues Republic and Laws, the most important disciplines for the best education of the rulers of the city are identified with arithmetic, geometry and astronomy. Those disciplines, however, are not intended for practical applications, but to reach the truth and see the form of good. In particular, another dialogue, Epinomis, stresses on the relevance of astronomy itself as main discipline, since it coincides with the study of the gods, that is, the planets and the heaven. According to Epinomis, the wise astronomer does not observe the risings and settings of stars for practical applications such as the farmer calendar, but he studies the orbits of the planets. Therefore, the 'practical' astronomy of farmers appears intrinsically less important than the 'theoretical' astronomy, i.e. the study of the planetary motions. We discuss the possibly far-reaching negative implications of such a specific discrimination. We report some examples taken from Greek and Latin literature illustrating the difficulties of a coherent description of the risings and settings of stars that had been attempted by scholars, and probably had been of little help for farming. We conclude by pointing out the practical importance of astronomy (intended in a broad sense) even today, and of the dangers of the separation or discrimination of disciplines and sub-disciplines for the culture during the present global economic crisis.
Putting the astronomy back into Greek calendrics: the parapegma of Euktemon
arXiv: History and Philosophy of Physics, 2018
A re-investigation of the parapegma of Euktemon (5th century BC, Athens), based on the assumption that some star observations may in fact have been calculated rather than directly observed. The calculation follows Pliny, Natural History 18.218, where he states that the sun should be at least three-quarters of an hour below the horizon. So 'observations' were based on time, rather than on star magnitude.