Historical Glossary of Important Terms in Hellenistic Astronomy

In: Hellenistic Astronomy
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This Glossary collects terms found in the texts and contexts of Hellenistic astronomy. In keeping with the conception of Hellenistic astronomy developed in the present volume, it aims not so much to understand these terms and their related concepts as they are understood today but, so far as possible, to decipher their sense as they were understood by those engaged in the various Hellenistic astronomies. Accordingly, this Glossary is historical, indeed philological, in nature and it assumes a geocentric cosmology.1

It is also incomplete in two senses: first, it does not collect all the terms used in Hellenistic astronomy and its diverse contexts but focuses mainly on those that figure in this particular volume; and second, most of the entries concern terms as they were used in only some of the relevant languages. There is, then, much work to be done before we have a proper historical Glossary of Hellenistic astronomy. The present offering is but a first step.

Anomaly (ἀνωμαλία, anomalia)

If a motion (κίνηϲιϲ) varies, that is, if it is not always the same (ὁμαλή: cf. ὁμή) and so is uneven, unsmooth, or irregular (ἀνωμάλη), it has anomaly. The angular motion of all the planetary bodies is anomalous because it is faster at perigee and slower at apogee.

  1. Moon
    1. first lunarThe periodic variation in the Moon’s velocity or daily progress in longitude, i.e., its variable angular velocity. The period of this anomaly is the anomalistic month [see Month, lunar: a].
    2. second lunarThis is the periodic variation in the Moon’s motion as its elongation from the Sun increases and decreases. This second lunar anomaly is also called evection.
  2. SunThe periodic variation in the Sun’s angular velocity or daily progress in longitude as it revolves around Earth. The period of this anomaly is the tropical year [see Year: b].
  3. Planets
    1. first or solarTo an observer on Earth, each of the five planets appears in the course of its direct motion eastward to vary in the amount and direction of its daily progress as it makes stations and retrogradations. Such periodic variation in eastward motion is an anomaly with respect to the Sun because it is a matter of the planet’s elongation from the Sun.
    2. second or zodiacalAgain, to an observer on Earth, the five planets make a periodic variation that correlates to the variation in the longitude where their stations and retrogradations are observed to occur as well as to a variation in the distance between their first and second stations. This variation is an anomaly with respect to the ecliptic or zodiacal circle [see Circle: k] because it relates to the planet’s longitude.

Ascendant. See Horoscopus

Aspect (aspectus, facies)

There are two ways of defining aspects. In the first, the aspects are defined in terms of how the seven planets—that is, the five planets (Saturn, Jupiter, Mars, Venus, Mercury) and the two luminaries (the Sun and Moon)—stand in relation to one another and thus look (aspicere) to one another. Thus,

  1. opposition (κατὰ διάμετρον)Two such planets standing at the ends of the same diameter of the zodiacal circle [see Circle: k], that is, 180° from one anther, are in opposition.
  2. quartile (κατὰ τετράγωνον)Two planets that are 90° from one another are in a quartile aspect and form a side or sides of tetragon (τετράγωνον, quadratum).
  3. sextile (κατὰ ἑξάγωνον)Planets that are 60° from one another are in a sextile aspect and form a side or sides of a hexagon (ἑξάγωνον, hexagonum).
  4. syzygy (κατὰ ϲυζυγίαν) or antiskian (κατ᾿ ἀντιϲκίαν)Two planets that are contained by the same parallel circles (defined by the rotation of the celestial sphere [see Circle: b]) and thus rise from the same place and set at the same place are in syzygy. Such planets “cast shadows” in opposite directions. They are also equidistant from Midheaven or Lower Midheaven.
  5. trine (κατὰ τρίγωνα)Planets that are 120° from one another are in a trine aspect and form a side or sides of a trigon (τρίγωνον, trigonum, trigon).

In the second, the aspects are relations between zodiacal signs [see Sign, zodiacal: b]. The definition of the particular aspects in this second sense are analogous to those above.

Astrology, Hellenistic: types

  1. catarchicThe determination of the astrological circumstances for or at the occurrence of some undertaking or event.
    1. electionThe determination of the best time to begin some undertaking.
    2. eventThe interpretation of an event that has occurred based on the time of its occurrence.
    3. decumbiture (κατάκλιϲιϲ)The determination of the course and outcome of an illness based on the time when the invalid took to his or her bed.
    4. interrogationThe determination of the outcome of an event such as a burglary or of a horoscope cast at the time when the question about the event was asked of the astrologer.
  2. general (universal, mundane)The prediction of events for countries, cities, states, and their populations based on periodic celestial phenomena. It may include the determination of the best time for founding a city or the interpretation of the horoscope cast at the time the city was founded.
  3. natal (genethlialogical)The interpretation of the native’s life based on the birth horoscope, which connects the time and place of birth to the positions of the Sun, Moon, and five planets as well as to the orientation of the zodiacal circle [see: Circle: k].
  4. hororary. See Astrology, Hellenistic: types a.4

Astronomy, Hellenistic: names

  1. BabylonianThere was no Akkadian term for either astronomy or astrology. Astronomy was subsumed under the scribal art (ṭupšarrūtu) and also classified with wisdom (nēmequ). Neither «ṭupšarrūtu» nor «nēmequ» should be translated by “astronomy”.Although there was no term for astronomy/astrology, the term for astronomer/astrologer was “ṭupšar Enūma Anu Enlil” (“scribe of [the celestial omen series] Enūma Anu Enlil”). This title has traditional roots going back centuries, at least to the seventh century bce in the celestial-divination advisers to the Neo-Assyrian royal court. However, the title itself, “ṭupšar Enūma Anu Enlil”, is much more frequently attested in the colophons of Seleucid astronomical texts that identify the scribal owner or copyists of astronomical tables (tērsītu).
  2. Early ChristianFor early Christians, astronomy and astrology were analogous terms, almost invariably considered negatively. Following Jewish apocryphal tradition, knowledge of the stars was taught to humans by fallen angels. Christians continued, in the main, to consider astronomy to be demonic. The Christian idea that astrology was demonic knowledge derives from two influential texts: 1 Enoch and the interpretation of Gen. 6:1–4 by Philo Judaeus (Alexandrinus). On the development of this claim by Christian writers to persuade one another and to separate themselves from non-believers, see Greenbaum 2009, app. 3A.
  3. EgyptianThe Egyptian language did not have a general term for either astronomy or astrology, though there is evidence that both subjects were known to them under some description and practiced.First is the documentary evidence of lunar omens and horoscopes in Demotic and belonging to that period from the sixth century bce onward in which Egyptian astronomy, while continuing a traditional interest in matters of timekeeping (divisions of the day or hours, lengths of daytime and nighttime, the risings and settings of fixed stars and planets, the lunar and solar calendars), acquired new practices and knowledge due to the influence of Babylonian astronomy.Next is the evidence of the titles of those who had knowledge of the heavens. In a linguistic tradition over four millennia, Egyptian vocabulary shifted considerably. Old Egypt records the words for “teach” and “star” as homophones («sbꜢ») but no astronomical texts have survived from this early era. In Middle Egyptian and Demotic, the phrase «imy-wnw.t» (“who is in the hour”) described a class of priests charged with a body of astronomical knowledge that was extended under the influence of Babylonian astronomy. An autobiographical inscription on the funerary statue of the imy-wnw.t priest Harkhebi lists his competencies. Although this list details a wide range of observations, calculations, and predictions, it does not record a lexical category analogous to astronomy. A similar list of astronomical skills appears in the Temple of Edfu. In some cases, the imy-wnw.t priest is expected to know (rḫ) astronomical topics that included astrological prognostication. The verb «rḫ» may be connected with calculations, especially those computed by tables; but the word has a wide semantic range. In Coptic, the most recent phase of the Egyptian language, two terms referred to practitioners of astral sciences. The first term, «ρεϥωπ μνϲιου» (“man who calculates the stars”), may be a calque for the Greek «μαϑηματικόϲ». The second term, «ρεϥκα ουνου» (“man who calls the hours”), represents an indigenous tradition with a long history.
  4. Greco-RomanThe three terms for astronomy—«ἀϲτρονομία», «ἀϲτρολογία», and «μαϑηματική»—were established in classical times, well before the question of horoscopic astrology arose in the Greco-Roman world. For Plato, the term of choice was «ἀϲτρονομία», a term which indicates by its formation the study of the grouping of fixed stars into constellations («ἄϲτρον + νέμω») or, more generally, the study of the temporal and spatial order governing the behavior displayed by the heavens («ἄϲτρον + νόμοϲ»).For Aristotle, however, the preferred term for astronomy is «ἀϲτρολογία», presumably because of its emphasis on theory or reasoning (λόγοϲ). (There is no occurrence of «ἀϲτρονομία» in the corpus of his writings.) As Aristotle uses it, «ἀϲτρολογία» should be rendered as “astronomy” and never by “astrology”. To emphasize that such theorizing may draw on mathematical argument, Aristotle often writes of astronomy as μαϑηματική and astronomers as μαϑηματικοί. In these contexts, it is an egregious mistake to render these terms by “mathematics” and “mathematicians”, since, for him, the mathematical science of astronomy is neither mathematics simpliciter nor a branch of mathematics like arithmetic and geometry nor applied mathematics. Depending on context, what Aristotle means by the former is either mathematical science or the particular science mathematical astronomy (ἀϲτρολογία); and by the latter, either mathematical scientists or the subset of mathematical astronomers (ἀϲτρολόγοι).In Hellenistic times, the term chosen for astronomy, that is, for the science that concerns timekeeping and the determination of the positions of the celestial bodies at any given moment, is significant insofar as it indicates an allegiance or bias and so affords a key to understanding an author. Thus, for Hipparchus, «μαϑηματικόϲ» signifies technical expertise in astronomy and so does not apply to the likes of Aratus, whom he regards as a mere ἀϲτρολόγοϲ at best. Again, although Philo uses «μαϑηματική» for astronomy, it is apparently not his own term: he more commonly calls it ἀϲτρονομία and thereby brings out a Platonic emphasis on celestial order. But whether it is ἀϲτρονομία or μαϑηματική, for Philo, astronomy includes the Chaldaean science (ἐπιϲτήμη) of astral divination. Thus, he puts predictive and prognosticatory astronomy under the same rubric and, by emphasizing the order disclosed by this science, he suggests a way to the abandonment of many of its key tenets, especially its astrology, in favor of an understanding of the cosmos that is in accord with Scripture as he interprets it.In the main, however, in Greek and Latin texts of the Hellenistic Period, the term for astronomy used by writers such as Strabo, Geminus, Vitruvius, and Pliny, who typically took a stand in favor of or against the inclusion of astrology in the traditional science, was «ἀϲτρολογία»/“astrologia”.Ptolemy’s usage merits special notice because, to judge from what has survived and is currently known, he redefined astronomy by synthesizing the projects of Babylonian mathematical astronomy with Greek descriptive astronomy to establish a unified predictive science that included horoscopic astrology. In positing a single science called ἀϲτρονομία in which predictions about Sun, Moon, and ἀϲτέρεϲ serve as the basis for prognostications about the impact of their motions and configurations on the sublunary realm, he did not assign a special term either to predictive astronomy or to prognosticatory astronomy. Indeed, in his works, the former is variously called ἀϲτρολογία and ἀϲτρονομία; and its practitioners are often called μαϑηματικοί—their discipline, though never identified simply as μαϑηματική, falls under τὸ μαϑηματικόν, i.e., that part of theoretical philosophy concerned with the heavens. The practitioners of the second, whom Ptolemy usually calls ἀϲτρολόγοι—their science being ἀϲτρονομία and, implicitly, ἀϲτρολογία as well as μαϑηματική—are often said by others to be Chaldaeans and μαϑηματικοί/mathematici.
  5. Judaic, Late Second TempleThere is no overall terminology for astronomical or astrological concepts in either the Hebrew or the Aramaic Jewish texts. Astronomically-related nouns appear across several genres of different origins in various forms related to the heavenly bodies. One Aramaic narrative refers collectively to “all the constellations of the heaven, the Sun, the Moon, and the stars” [The Genesis Apocryphon ar]. A Persian loan-word, «raz », understood as “mystery”, appears as an unknown quality in a number of Hebrew Wisdom-texts; some scholars relate it to the horoscope, depending on its context. It is also used poetically, for example, in The Thanksgiving Psalms: “…luminaries according to their mysteries, stars according to [their] paths…”. Some detailed Hebrew and Aramaic astronomical calendrical texts use vernacular language to describe lunisolar phenomena technically on certain days in the month. Thus, it is said that the Moon’s light is “completed” at the Full Moon (mid-month) and that the Moon’s disk is “obscured” [4QcryptA Lunisolar Calendar] or “empty of all light” [4QAstronomical Enochb ar] at conjunction (end of the month).
  6. MandaeanIn Mandaic, the term for astrologer is “kaldaia” (i.e., “Chaldean”), often used in a pejorative sense. The term “madna” is used for horoscope. The Mandaeans did not, so far as one can tell, have a general term for either astronomy or astrology. Yet, a Mandaean compendium of celestial knowledge is attested in the Book of the Zodiac (Aspar maluašia).

Band, zodiacal (ὁ τῶν ζῳδίων κύκλοϲ, ὁ ζῳδιακὸϲ κύκλοϲ; circulus zodiacus)

A band, otherwise known as the zodiac, that is equidistant above and below the zodiacal circle [see Circle: k]. Its width is set variously. The earliest specification comes from Geminus, who sets it at 12° without explanation. Pliny, like many others later, accepts this value; but, while he recognizes that this is just wide enough to accommodate the latitudinal motion of the Moon, he allows that it is not wide enough for Venus, which, as he says, can extend 2° on either side. Olympiodorus later gives the width of the zodiacal band as 20°, perhaps in aiming to buttress the theory that comets arise when planets approach fixed stars by accommodating the value of for Venus’ latitudinal motion given in Ptolemy’s Handy Tables and thus accounting for a comet observed in 565 ce. In PMich. 149, the width is given as 48° but this is perhaps a slip in which the zodiac is confused with the band about the celestial equator that is defined by the Sun’s oblique course.

The band is “zodiacal” because of its division into dodecatemoria [see Dodecatemorion: a] named after the zodiacal constellations [see Constellation: b].

It is clear in some Babylonian astronomical contexts that the lumāšū (written LU.MAŠ.MEŠ) represent the 12 zodiacal signs [see Sign, zodiacal: b] that the Sun traverses in its path. There is a phrase attested for the Sun’s “forward motion (progress) in longitude”, namely, «zi dšamaš ina LU.MAŠ.MEŠ» (“forward motion of the Sun through the zodiacal signs”).

Calendar

These instruments for regulating the activities of a community typically required identifying a lunisolar cycle in which some number of lunar months is identified with a number of years, and, sometimes, a number of days or a solar cycle in which one year is identified with a number of days. Thus, for example, the Metonic Cycle is a lunisolar cycle with , whereas the Babylonian 19-year cycle, from which it derives, has only . To understand an ancient calendar, it is important to know the epochs of the temporal units in the cycle [see Epoch]. In lunar-stellar and lunisolar calendars, it is also important to determine how the sequence of 29- and 30-day months—hollow and full months, respectively—was established in practice. If it was not by direct observation but by some scheme or calculation, one should determine whether it included intercalation. For example, in the Babylonian 19-year calendar of the Seleucid Era, there are 7 intercalary months inserted in years 1, 4, 7 9, 12, 15 (where the intercalary month is a second month XII or intercalary Addaru) and in year 18 (where the intercalary month is a second month VI or intercalary Ulūlu). In this way, the first month, Nisannu, is kept near the vernal equinox [see Table 1, p. 638].

Cardinal points

  1. equinoctialOne of two points (σημεῖα, puncta) in the Sun’s path or zodiacal circle [see Circle: k] defined by its intersection with the equinoctial circle [see Circle: c]. The point on the Sun’s course northward is the vernal equinoctial point; the point on its southward course, the autumnal equinoctial point.
  2. solstitialOne of two points on the Sun’s path or zodiacal circle where the Sun reaches its greatest distance from the equinoctial circle. The point where the Sun turns southward is the summer solstitial point; the point where it turns northward, the winter solstitial point.

Table 1

The epochs in select Hellenistic calendars

Babylonian

Greek

Egyptian

Roman

Judaean

Mandaean

calendar

lunisolar2

lunisolar

luni-stellar3

fixed 4

Julian5

lunisolar-zodiacal6

solar7

day

sunset

sunset

morning twilight

morning twilight

midnight

sunset

morning twilight

Table 1

The epochs in select Hellenistic calendars (cont.)

Babylonian

Greek

Egyptian

Roman

Judaean

Mandaean

month

day of Moon’s first visibility after conjunction

day of Moon’s first visibility after conjunction

first day of Moon’s invisibility before conjunction

morning twilight at the end of day 30 of a month or epagomenal day 5

midnight at the end of the last day of a month

lunar—day of Moon’s first visibility after conjunction in the zodiacal sign following the Sun’s sign [4Q318] or in the same sign [4Q208–209]

solar—the Sun’s entry into a zodiacal sign

morning twilight at the end of day 30 or epagomenal day 5

year

first lunar visibility at/after vernal equinox

8

heliacal rising of Sothis (Sirius)

heliacal rising of Sothis (Sirius)

various9

first lunar visibility at/after vernal equinox; the Sun is at Aries 0°

the first day of the first month (M awwal sitwa, Ar šabaṭ) of the winter season (months I–III)

Cardine (cardo). For Ascendant, see Horoscopus. See Midheaven, Descendant, Lower Midheaven.

Note that, the arcs from the Ascendant and Descendant to Midheaven and Lower Midheaven vary during the course of the year because of the different orientations of the zodiacal circle [see Circle: k].

The cardines are today often called angles.

Celestial sphere. See Sphere of fixed stars

Chronocrator or Time-Lord (χρονοκράτωρ)

A planet that rules a certain period of life.

Circle (κύκλοϲ; circulus, orbis)

  1. colure (ὁ κόλουροϲ [κύκλοϲ]; colurus)There are two colures: the equinoctial colure goes through the poles of the zodiacal circle and the two equinoctial points [see Cardinal points: a]; the solstitial colure, through these same poles and the two solstitial points [see Cardinal points: b].
  2. day-circleThe parallel circle that any celestial body describes from east to west as a result of the daily rotation of the celestial sphere.
  3. deferentA circle that has the center of another circle, an epicycle, on its circumference.
  4. dodecatropos (δωδεκάτροποϲ)The circle through the four cardines. Though this circle is thought to rotate, it is the zodiacal circle [see Circle: k] which rotates as its degrees coincide in succession with the cardines.
  5. eccentric (ὁ ἔκκεντροϲ [κύκλοϲ])A circle that does not have the Earth at its center. Martianus Capella does not write of the planet’s orbit being eccentric; instead, he prefers to say that the Earth is eccentric (telluris eccentros) to the orbit.
  6. epicyclic (ὁ ἐπίκυκλοϲ [κύκλοϲ]; epicyclus)A circle that has its center on the circumference of another circle, the deferent.
  7. equinoctial (ὁ ἰϲημερινὸϲ [κύκλοϲ], circulus aequinoctalis)The parallel circle that the Sun describes from east to west on the day of equinox as a result of the daily rotation of the celestial sphere.
  8. horizon circle (ὁ ὁρίζων [κύκλοϲ])The observer’s horizon construed as a circle projected onto the celestial sphere.
  9. hourOne of 24 meridians of longitude that divide the equinoctial circle into hours, viz. equal arcs of 15°.
  10. meridian (ὁ κατὰ κορυφὴν [κύκλοϲ], meridianus)The great circle though the poles of the sphere of the fixed stars and the observer’s zenith. This circle divides daytime and nighttime into two equal intervals.
  11. zodiacal (ὁ ζῳδιακὸϲ [κύκλοϲ], circulus/orbis zodiacus)The projection onto the celestial sphere of the path described by the Sun in its annual eastward motion. In Greek, it is sometimes designated as the circle through the middle of the zodiacal signs (ὁ διὰ μέϲων τῶν ζῳδίων) [see Sign, zodiacal: b], where the signs in question are the divisions of the zodiacal band, i.e., the dodecatemoria [see Dodecatemorion: a].

Colure. See Circle: a

Constellation ([κατηϲτεριϲμένα] ζῴδιον, ἄϲτρον; signum, stella, sidus, astrum)

  1. A grouping of fixed stars in a shape typically of a living creature and from the very beginning associated with myth. Note: though «ζῴδιον» originally designated the representation of a living creature or animal, it soon included the representation of any object.
  2. zodiacalA constellation through which the Sun passes on its annual course eastward.The Babylonian word for a zodiacal constellation was «lumāšu» and in Seleucid astronomical texts occasionally a zodiacal sign could be designated with the pseudo-logogram «LU.MAŠ».Though Greeks and Romans recognized 13 constellations on or near this path, it was from early on the custom to speak of 12. For their names, see Table 1, p. 12, Table 2, p. 47. The zodiacal constellations neither divide the path of Sun into equal arcs nor do they reach to the same distance above and below this path either severally or collectively.

Day (A ūmu, me; G ἡμέρα, νυχϑήμερον; L dies)

The interval from one epoch (e.g., the setting of the Sun) to the next. The length of the day actually varies throughout the course of the year. This variation, which is not the same as the annual variation in daytime, has a trigonometric component due to the inclination of the Sun’s path or zodiacal circle [see Circle: k] to the equinoctial circle [see Circle: c] and a physical component due to the variation in its speed along this path [see Equation of time].

Daylight

The interval from the start of morning twilight to the end of evening twilight.

Daytime (A me; G ἡμέρα; L dies)

The interval from one sunrise to the next sunset. This interval, i.e., daytime, increases and decreases throughout the year; it is longest on the day of summer solstice and shortest on the day of winter solstice.

Decan (E bꜣk.tjw, bꜢk.tı̓.w; G δεκανόϲ)

  1. One of 36 small groups of stars that rise consecutively every 10 days. They were used to mark divisions of nighttime into decanal hours [see Hour: c].
  2. A 21/2°-arc of a zodiacal sign [see Sign, zodiacal: b].
  3. A 10° arc of a zodiacal sign [see Sign, zodiacal: b].
  4. The divinity presiding over a decan [see Hour: c].

These assignments of divinities were made by taking the planets in their Chaldaean order [see Planets, order: b.1], beginning with Aries.

Depression (ταπείνωμα; deiectio)

The point in the zodiacal circle where a planet has its weakest influence. It is located 180° from the planet’s exaltation.

Descendant (δύϲιϲ)

The part of the zodiacal circle [see Circle: k] (specified either by zodiacal sign [see Sign, zodiacal: b] or by the degree of a zodiacal sign) that intersects the client’s horizon [see Circle: h] in the west at the occurrence of some event in question.

Dodecatemorion (δωδεκατεμόριον; dodecatemorium)

  1. One of the segments of the zodiacal band [see Band, zodiacal] when divided crosswise equally into 12. The dodecatemoria were given the names of the zodiacal constellations [see Constellation: b]. They were also called zodiacal signs [see Sign, zodiacal: a].
  2. One of the arcs of a zodiacal sign [see Sign, zodiacal: b] when divided equally into 12.

Dodecatropos. See Circle: d

Ecliptic. See Circle: k

Epoch (ἐποχή; epocha)

  1. In ancient astronomy, the position of a celestial body at a characteristic moment, e.g., a first appearance. Tables of the dates when the body has these positions are called epoch-tables.
  2. The fixed moment in time when some calendrical interval begins.

Equation of time

The difference between the local mean time (the time of day measured in equinoctial hours [see Hour: b]) and the local apparent time (as indicated by the Sun, say, on a sundial or by its position on its day-circle [see Circle: b]). This difference varies throughout the year. As Ptolemy realized, the key to its numerical quantification is to define the epoch of the day as the Sun’s crossing the observer’s meridian [see Circle: j]. (He chose the daytime crossing.) When plotted over the course of a solar year, this difference describes a closed figure-8 known as an analemma.

Equator, celestial. See Circle: g

Equinox (spring, fall: ἰϲημερία; aequinoctium)

One of two days of the solar year in which nighttime and daytime are equal in length. When the Sun is at the vernal equinoctial point, it produces the vernal or spring equinox; when it is at the autumnal equinoctial point, the autumnal or fall equinox [see Cardinal points].

Evection. See Anomaly, Moon: a.2

Exaltation (A bīt niṣirti; G ὕψωμα)

The zodiacal signs [see Sign, zodiacal: b] in which a planet has its most potent influence. The following are the Greek exaltations (ὑψώματα):

Sun

at

Aries 19°

Moon

Taurus 3°

Mercury

Virgo 15°

Venus

Pisces 27°

Mars

Capricorn 28°

Jupiter

Cancer 15°

Saturn

Libra 21°

The Babylonians (already prior to the invention of the zodiac) located a similar place in the heavens, a region called bīt niṣirti (house of the secret), where a planet had a particularly propitious significance. Obviously, these bīt niṣirti were not given as degrees within a zodiacal sign but simply as one or another region of the zodiacal constellations [see Constellation: b]. The locations of the Greek exaltations agree with the Babylonian assignments of the bīt niṣirti in all cases except that of Venus, which in the omen literature is in the constellation Leo and in the horoscopic literature, in the zodiacal sign Pisces.

Exeligmos (ἐξελιγμόϲ).

According to Ptolemy [Alm. 4.2], the exeligmos is an eclipse-cycle equal to three Saros-Cycles [see Saros: b] in which:

19,756 days

= 669 synodic months

= 717 anomalistic months

= 726 draconitic months

= 723 revolutions in longitude + 32°

≈ 54  years

This cycle was known earlier to Geminus [Intro. ast. c. 18], who does not mention the Saros-Cycle or the equation with 726 draconitic months.

Face (πρόϲωπον). See decan: c, d

For the faces, see Table 3, p. 465.

Horoscopus (ὡρόϲκοποϲ: horoscopus)

The part of the zodiacal circle [see Circle: k], specified either as a zodiacal sign [see Sign, zodiacal: b] or as a specific degree of a zodiacal sign, that intersects the client’s horizon circle in the east at the occurrence of birth or the event in question.

Babylonian horoscopes do not employ this concept.

Hour (G ὥρα; L hora)

  1. seasonal (A simanu)1/12 of daytime or of nighttime on any day but a day of equinox. On all such days, the lengths of daytime and nighttime are unequal for any observer who is not at the terrestrial equator. This means that seasonal hours of daytime are not equal to seasonal hours of nighttime either in the same day or in different days.
  2. equinoctial1/12 of daytime or of nighttime on the day of equinox. On these days, the length of daytime and nighttime are the same for any observer on Earth where the Sun rises and sets. Thus, equinoctial hours are equal throughout the day of equinox.
  3. decanalThe interval of nighttime delimited by the rising of two consecutive decans [see decan: a].

House (οἶκοϲ; domus)

The astrological houses constitute a system of rulership by which planets are assigned as rulers of zodiacal signs. According to Ptolemy [Tetr. 1.17], the houses divide the zodiacal circle [see Circle: k] into two halves, with six signs [see Sign, zodiacal: b] in each. One half spans the signs from Leo to Capricorn; the other, from Cancer to Aquarius. The Sun was assigned to Leo and the Moon to Cancer—the two signs associated with summer and heat. The remaining five signs in each semicircle became the houses of the five planets in order of their distance from Earth, i.e., Mercury, Venus, Mars, Jupiter, and Saturn. Thus, Saturn, for example, the farthest from the Sun and Moon, was assigned the two signs Capricorn and Aquarius as houses, both of which are associated with winter and cold. Each of the five planets had two houses assigned to it.

Hypsoma. See Exaltation

Lot (κλῆροϲ) or Part (pars)

A point on the zodiacal circle determined by adding the elongation of two planetary bodies, often the Sun and the Moon, to the Ascendant in one or the other direction. There are seven lots, though they need not all appear in a given horoscope.

Lower Midheaven or Underground (ὑπόγειον; imum coeli)

The point below the client’s horizon circle [see Circle: h] and 180° away from Midheaven, where the zodiacal circle [see Circle: k] intersects the client’s meridian circle [see Circle: j].

Mean Sun

In Antiquity, the mean Sun was an ideal body moving in the zodiacal circle with mean velocity [see Motion, mean]. It coincides with the true Sun at apogee and perigee.

Today, the mean Sun is said to move in the celestial equator and coincides with the true Sun at longitude 0° (the vernal equinox).

Meridian. See Circle: j

Midheaven or Culmination (μεϲουράνημα)

The intersection above the horizon at a given location of the meridian circle and the zodiacal circle [see Circle: j, k].

The point where the zodiacal circle intersects the client’s meridian circle [see Circle: j, k].

Month, lunar (A arhu; G μείϲ, μήν; L mensis)

  1. anomalisticThe interval of the Moon’s return to the same velocity or daily motion, e.g., of its return to its greatest velocity, which occurs at perigee, a point that completes a circuit of the zodiacal circle in the direction of increasing longitude in about 9 years.
  2. draconiticThe interval of the Moon’s return to the same node. Knowledge of the draconitic month is essential to the theory of eclipses.
  3. siderealThe interval of the Moon’s return (in longitude) to a fixed star.
  4. synodicThe interval of the Moon’s return (in longitude) to the Sun.

Month, solar (Egyptian)

The fixed interval of 30 days. Twelve of these months along with 5 additional or epagomenal days comprised the year-length of 365 days that is characteristic of the Egyptian wandering year. See Table 1, p. 638.

Motion, mean

A celestial body’s mean motion during some interval is its average daily angular displacement.

Given, a cycle of

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the mean daily motion m of the Sun is:

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For the Moon, one needs a cycle that includes the number of times that the Moon goes around the zodiacal circle, that is, its revolutions [see Saros: b]. Thus, given

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the Moon’s mean motion is:

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The fact that such cycles are known does not mean by itself that the mean motions were computed and known.

Night, Nighttime (νύξ; nox)

The interval from one sunset to the next sunrise. Nighttime is longest on the day of winter solstice and shortest on the day of summer solstice [see Solstice].

Node (ϲύνδεϲμοϲ, nodus), lunar

One of two points where the lunar orbit intersects the plane of the zodiacal circle. The node where the Moon rises north of the zodiacal circle is the Ascending Node; the node where it goes south, the Descending Node.

Normal Star. See Star: c

Oblique ascension. See Rising-time

Parallax

The shift in a celestial object’s position when it is observed from the Earth’s surface instead of from its center [Figure 1, p. 113]. The effect of this shift is to make the apparent position of the object lower than its true position (which is computed). Hellenistic astronomers were aware of parallax in the cases of the Moon and Sun only. It is important to allow for parallax in computing tables for solar eclipses, since the observer’s location on Earth affects or contributes to what is actually seen. (This is not so for lunar eclipses.)

Parapegma (παράπηγμα: parapegma, kalendarium)

A parapegma was a calendrical table based on the solar year. It was originally inscribed on stone with a hole for a peg that was moved from entry to entry as the year progressed but later written as a document. The tables themselves correlated dates in the year of phases of the fixed stars (usually first and last appearances) with seasonal changes in the weather. As Geminus notes, it was commonly supposed that parapegmata recorded causal connections between astronomical phenomena (including solar phenomena, such as solstices) and these changes in the weather. In any case, whether the astronomical phenomena are taken as causes or as signs (as Geminus insists), the parapegma belongs to the general practice of celestial prognostication (astrology).

Place (τόποϲ; locus)

In Hellenistic astrology, there are 12 places, each being an equal division of the chart [see p. 403] or dodecatropos [see Circle: d], that is made by starting at the Ascendant or from a point that is 5° or 15° ahead of it. The places are numbered in the direction opposite to the daily rotation. Since, at any given time, these places are of equal length, any given place will actually vary in length over the course of a day as Midheaven moves to and fro [see Beck 2007, 42–43] along the meridian [see Circle: i]. Nevertheless, in practice, the places are treated as though equal in length. Each place concerns a particular aspect of a person’s life. The first place, for example, is Life (ζωή). See Figure 3, p. 462.

Planet. See Star: d

Planets, order

Not every list of the planets implies a theory about their arrangement in space. Moreover, planetary lists are numerous and may vary when they share the same name. In fact, the assignment of a list to some person or culture may sometimes tell more about the source making the assignment than it does about the person or culture to which the list is assigned.

  1. non-spatial lists
    1. BabylonianThe order Jupiter, Venus, Mercury, Mars, Saturn is the standard enumeration of the five planets in cuneiform documents of the Seleucid Era. It is based on whether the planets are benefic, malefic, or ambiguous. In Babylonian horoscopes, the five planets are preceded in order by the Moon and Sun.
    2. DemoticThe sequence of the five planets in the Medinet Madi horoscopes is Saturn, Jupiter, Mars, Venus, Mercury, Sun, Moon.
  2. Greco-Roman lists with spatial commitments
    1. ChaldaeanThe order Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn attributed to the Chaldaeans is a Greco-Roman fiction.
    2. Greek (Platonic)The Greek order Moon, Sun, Venus, Mercury, Mars, Jupiter, Saturn is attributed to Plato. There were variants, however; thus, for some, the order was Moon, Sun, Mercury, Venus, Mars, Jupiter, Saturn (Venus and Mercury interchanged); whereas for still others it was Moon, Venus, Sun, Mercury, Mars, Jupiter, Saturn (Venus and Mercury re-positioned about the Sun).
    3. PythagoreanThe order ascribed to the Pythagoreans is Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn. This is the order adopted by Ptolemy.

Precession

  1. of the starsThe slow motion of the fixed stars eastward about the axis of the zodiacal circle [see Circle: k]. This is how Ptolemy understood precession. See Figure 5, p. 292.
  2. of the equinoxesThe slow motion of the equinoxes westward due to the revolution of the celestial poles about the poles of the zodiacal circle. This is, apparently, how Hipparchus, who discovered precession, understood it. See Figure 5, p. 292.Today, this motion is attributed to decay in the Earth’s rotation, that is, to a wobble consisting in the revolution of the axis of the Earth’s daily rotation from west to east, that maintains the Earth’s obliquity to the plane of its orbit about the Sun.

For Ptolemy, the rate of precession was 1° in 100 years, which implies a period of 36,000 years. The period is, in fact, roughly 25,800 years, which implies a rate of 1° in 712/3 years.

Rising-time

The time that it takes for an arc of the zodiacal circle [see Circle: k] to rise above the observer’s horizon circle [see Circle: h].

Saros (ϲάροϲ/ϲαρόϲ)

  1. the intervalThe term « ϲάροϲ» (or «/ϲαρόϲ») derives from the Babylonian word for 3,600, «šār». Its use to indicate an interval of 3,600 years is attested as early as the work of Berossus (flor. early third century bce), a scholar (possibly Babylonian) writing in Greek (or originally Aramaic), and is common in subsequent Greek historical literature.This interval is defined explicitly by Hesychius, the lexicographer (fifth century ce), in a report about Abydenus (second century ce?).
  2. the cycleUse of the term “Saros” for the eclipse-cycle of 223 lunar months was established by Edmond Halley in 1691, though even after then some continued to call it the Chaldean Period or Cycle. This eclipse-cycle, first evident in Babylonian texts where it is simply called “18 years”, roughly marks the return of a solar (or lunar) eclipse in type, time of year, location of the body eclipsed, magnitude, and direction. In this cycle, which sets
    65851/3

    = 223 synodic months

    = 239 anomalistic months

    = 242 draconitic months

    = 241 revolutions in longitude + 10°

    ≈ 18 years, 11 days, and 8 hours,

    the return in location and time, for example, is plainly approximate, not exact.The use of the term “Saros” in this sense is rare in Antiquity: for Ptolemy, e.g., this cycle is the Periodic Interval (περιοδικὸϲ χρόνοϲ). It is only in an entry found sub voce in the Suda (late tenth century ce) that this cycle is called a Saros. This entry is, however, incomplete, makes no mention of the use of the cycle for predicting eclipses, and is flawed by setting its length at 222 “lunar” months. Why the cycle was called a Saros is also unclear.

Science, celestial. See Astronomy, Hellenistic

Sign, zodiacal (A LU.MAŠ; G ζῴδιον; L signum)

  1. A dodecatemorion [a].
  2. A 30°-arc of the zodiacal circle [see Circle: k]. Each such sign got its name from the dodecatemorion [a] that delimited the arc in the zodiacal circle.

Solstice (summer, winter: A šamaš GUB; G τροπαί; L solstitium)

One of two days of the solar year in which either daytime or nighttime reaches its greatest or maximum length (for those not at the equator). When the Sun is at the summer solstitial point, it produces the summer solstice and the length of daytime is greatest; when it is at the winter solstitial point, the winter solstice and the length of nighttime is greatest [see Cardinal points]. The Latin “solstitium” derives from the observation that the Sun appears to stand still in the month or so preceding and following its arrival at the solstitial point itself.

Sphere of fixed stars

There is no evidence in cuneiform for the conception of a celestial sphere. It is found first in Greek literature.

It was generally assumed in Greco-Latin texts that the fixed stars [see Star: a] were equidistant from the center of the celestial sphere, i.e., the center of the Earth; but there were some who entertained the idea that this was not true.

Prior to Copernicus, this sphere was held to rotate, thus causing all those celestial bodies that rise and set for observers on Earth to rise in the east and set in the west and all other bodies to revolve in the same direction about the poles of this sphere. For observers north of the terrestrial equator, this was the original clockwise motion. After Copernicus, the rising and settings of the celestial bodies was attributed to the (counterclockwise) rotation of the Earth from west to east, a motion in the same direction as its annual revolution about the Sun.

Star (A MUL or MÚL, kakkabu; E sbꜢ; G ἀϲτήρ, ἄϲτρον; L stella, sidus, aster, astrum)

  1. fixed (ἀπλανήϲ -έϲ, inerrans)A star that remains in position relative to the other stars. Within the class of fixed stars, Aratus, for example, uses «ἀϲτήρ» for an individual star and «ἄϲτρον» for a constellation.
  2. counting [stars] (always in plural: MUL.ŠID.MEŠ, kakkabū minâti)The Babylonian term for the set of reference-stars near the zodiacal circle that serve in the Diaries to specify the positions of the Sun, Moon, and five planets.
  3. Normal. See Star: bA modern term for a star that was used by the Babylonians to specify the positions of the Sun, Moon, and five planets.
  4. wandering (πλανώμενοϲ -ον, πλανήτηϲ -εϲ, erratica -um, planeta [stella])A star that observably changes position in relation to the other stars. The Babylonians termed these bibbu (wild sheep), connoting the fact that they did not keep to their courses as did the fixed stars. There are seven wandering stars or planets: the Moon, Sun, Mercury Venus, Mars, Jupiter, and Saturn. Later, once it was recognized that the Sun and Moon do not make retrograde motions, there was a distinction between the seven and the five wandering stars.Some authors, such as Geminus, tend to use «ἀϲτήρ» for individual stars whether fixed or planetary and «ἄϲτρον» for the constellations as well as for celestial bodies in general; others are freer in their terminology. In Latin, “astrum” has all these meanings.

Systems A and B

Babylonian mathematical astronomy consists in the main of planetary and lunar tables—designated tērsītu (computed tables) in colophons—and a group of procedural texts stating the arithmetical rules (algorithms) used to calculate the various columns of the tables. Such tabular and procedural texts date to the period from the mid-fifth to the mid-first centuries bce, with the bulk of preserved tablets dating to the Hellenistic or Seleucid Period in the second century bce.

Characteristic of the table texts are parallel columns of numbers that represent dates or positions of the lunar and planetary appearances or other data relevant to calculating the synodic arc () of a planet or the Moon. These methods were based on recognition of period-relations (expressed in units of time such as the year, month, day, or degree) as well as two types of recursive mathematical steps (algorithms) now called Systems A and B. (There are variants and other, less well-attested systems too.) Their distinguishing signature was in the application of the step-function in System A and the zigzag-function in System B to the calculation of longitudes. The final construction of both systems took place early in the Seleucid Era.

Each scheme entailed an understanding of an intimate connection found between synodic arc (), or progress in sidereal longitude made by the planet or Moon from one synodic phenomenon to the next of the same kind (e.g., first visibility to the next first visibility), and synodic time (), or the time required for the body to complete a synodic cycle between successive phenomena of the same kind. Using step-functions, System A calculated progress in longitude as a function of longitude, that is, differences in longitude were treated as dependent on longitude itself. Thus, . System B derived longitudes of synodic arcs as a function of the serial number n of in the table. Thus, .

Zigzag- and step-functions, so called from modern graphical representations of the calculations in the columns of the Babylonian tables, were therefore used to account for the difference between a position or date and the next in sequence , reckoned as longitude in degrees or as time in tithis. Thus, . In System A, this difference d was variable in accordance with subdivisions of the zodiacal circle into zones of longitudinal progress, the simplest version consisting of two such zones of progress, one fast and the other slow, and more complicated versions consisting of four and six zones. In this way, System A described (mathematically) the synodic arc directly with a step-function of longitude, i.e., . In System B, on the other hand, the difference was constant and was applied not to phenomena (or synodic events) in the zodiacal circle but rather to the event-number in the table.

Tables of data organized in accordance with Systems A and B are also found in Greek and Latin during the Hellenistic Period.

Term (ὅριον; terminus)

The astrological doctrine of terms subdivided the zodiacal signs [see Sign, zodiacal: b] by certain numbers of degrees, the precise number of which was assigned differently in different systems (the so-called Egyptian system, which was originally Babylonian, and the so-called Chaldean system). The term or subdivision was assigned one of the five planets (or in some systems, additionally the Sun or both the Sun and Moon) as Lord, which therefore had particular influence in that segment (term) of the zodiac. For the cuneiform evidence of the terms, see Jones and Steele 2011.

Tithi

A Sanskrit term for 1/30 of a mean synodic month. Otto Neugebauer applied it to the same concept as it serves in Babylonian ephemerides, where the numbers of tithis are given without any accompanying term. This is now established usage in the study of Babylonian mathematical astronomy.

Triplicity. See Aspect: e

Year (A šattu; G ἐνιαυτόϲ; L annus)

  1. siderealThe time that it takes for the Sun to return to a fixed star.
  2. tropicalThe time that it takes for the Sun to return to an equinox or solstice (τροπαί).This difference in the sidereal and tropical year-lengths is due to precession. The Babylonians did not recognize the tropical year.
  3. Great Year (annus magnus)A period or cycle in which there is a whole number of days, lunar months, and solar years. (The Babylonians did not include days in such cycles.)

Zodiac. See Band, zodiacal

1

Terms given in italics are defined elsewhere in the Glossary. In lists of terms in more languages than Greek and Latin, the terms are preceded by letters as follows:

A

for Akkadian

Ar

for Aramaic

E

for Egyptian

G

for Greek

L

for Latin

2

Based on the cycle established in 475 bce.

3

Based on the cycle of with intercalations intended to keep its months in accord with those of the wandering calendar.

4

Based on the cycle with a sixth day added in every fourth year. The Egyptian wandering year, which is older—it was in use in the Old Kingdom (2664–2115 bce)—is the same but without the addition of the sixth day in the fourth year. This wandering year returns to synchrony with the Sun in 1,461 of its years = 1460 fixed years (the Sothic Period). Both calendars were used in civic life.

5

Based on the cycle with 1 day intercalated every 4 years. The names and lengths of the months varied throughout the Roman Empire.

6

As reconstructed, the schematic Aramaic calendars 4Q318 and 4Q208–4Q209 are based on a cycle in which . In 4Q208–4Q209, the zodiacal signs are represented by numbered “gates”. This 19-year cycle is determined mathematically: in 4Q318, and in 4Q209 fr. 7.col. 3, the same astronomical configuration of (a) solar and lunar positions in a zodiacal sign and (b) the lunar phase is repeated every 19 years on the same dates as they appear in the texts [Jacobus 2020a].

4Q318 lists day-by-day of each lunar month the Moon’s zodiacal sign in a cycle of . The zodiacal signs and Aramaic lunar month-names are explicit.

4Q208–4Q209, in a cycle in which , detailing the phases of the Moon, when it rises and sets, and its zodiacal sign by means of a “gate” number. This cycle is harmonized with a solar year of 360d. This solar year is inferred from the entrance of the Sun into a gate, based on the Sun’s passage through the 360° of the zodiacal circle and the solar year-length of 4Q318.

There is no historical data on how the Aramaic or Hebrew calendars from Qumran were intercalated. See Jacobus 2020a.

7

Based on the cycle, with 5 epagomenal days after month VIII.

8

The Athenian calendar is best known of the Greek calendars. Its record shows wildly variable month- and year-lengths.

9

E.g., the Julian year in Egypt (the Alexandrian year) began with Thoth 1 on Aug 29 of the Julian year in Rome; and in Asia, with Dystros 1 on Augustus’ birthday (Sep 23).