The length of life problem: why ancient astrologers could not agree

Ptolemy opens his treatment of length of life by saying the inquiry "takes the leading place" among questions about events after birth.¹ His next sentence attributes an older argument to "the ancient": it is ridiculous to attach predictions to a person who will not live to experience them. Firmicus, writing two centuries later in Latin, says nothing matters more at the start of natal work than establishing the span of life, because an early death cancels every other promise in the chart.² Valens calls the topic essential.³ Demetra George, surveying the whole tradition, concludes that nearly every ancient astrologer attempted some version of it.⁴

That consensus about priority is where the agreement ends. Read the surviving procedures side by side and they diverge at every joint: which point in the chart carries the life, which planet can allot years, which houses qualify a candidate, and which clock converts a chart position into a number of years. Dorotheus, Ptolemy, Valens, Firmicus, and Paulus each preserve a different answer. The Persian and Arabic astrologers who inherited the material translated and reorganized it, and in places visibly struggled to reconcile sources that had never agreed in the first place.

This article is a history of that disagreement. It explains what each authority said, where the texts contradict each other, and how the Greek doctrine became the medieval Hyleg and Alcocoden. It does not offer a method for predicting anyone's lifespan, and it will not pretend the historical record contains one agreed procedure waiting to be recovered.

One editorial boundary, stated plainly at the outset: nothing here is a death date, an estimate of anyone's years, or an endorsement of the practice. George, whose two-volume Ancient Astrology in Theory and Practice reconstructs this doctrine chapter by chapter, calls it "a highly controversial topic," declines to advocate its use with clients, and openly questions whether the procedures are feasible or accurate.⁴ That is the posture this article takes.

The offices, before the Latin names

The medieval Latin terms Hyleg and Alcocoden are late arrivals. The Greek sources behind them use a small vocabulary of offices, and the offices have to come first, because the later confusion largely consists of putting one name over several different jobs.

The Predominator (epikratētōr) is the point judged able to carry the signification of life. Depending on the author, the candidates include the Sun, the Moon, the Ascendant, the Lot of Fortune, and the degree of the new or full Moon before birth. Each author tests these candidates against eligibility rules, and the rules differ.⁵

The releaser (aphetēs) is the name the significator takes in motion. When a selected life significator serves as the point from which a release or direction begins, Greek authors call it the aphetēs, from a verb meaning to send forth.

The Master of the Nativity (oikodespotēs) is, in several of the longevity procedures, a planet selected from among the Predominator's rulers that can grant a base allotment of years, usually drawn from the traditional planetary periods. The office is not universal: Firmicus selects his ruler without any Predominator, and Ptolemy's lifespan procedure installs no separate year-giver at all. The word itself is unstable. Dorian Greenbaum's study of the terminology distinguishes at least four distinct uses of oikodespotēs in the Greek material: an ordinary sign ruler, the dominant planet over a place, the bound lord of a Predominator, and the overall ruler of a chart.⁶ A sentence that says "the Master" means something precise only once you know whose text it comes from.

The Lord of the Nativity (kurios) is a separate office again. The Introduction to the Tetrabiblos transmitted under Porphyry's name distinguishes the Lord from the Master and compares their roles to different officers of a ship.⁷ The attribution is contested: Greenbaum defends Porphyry's authorship of most of the text, while a 2021 study by Levente László rejects it, which is why recent scholarship often cites the work as Pseudo-Porphyry.⁸ George treats the Kurios as an overall ruler connected with the native's actions rather than a longevity planet, and later syntheses blur the line.

The destroyer (anairetēs) is the destructive planet, ray, degree, bound, or contact that can interrupt the releaser's course. Its identity and its effective conditions also vary by author, and in several procedures a well-placed benefic can blunt or cancel the effect.

The offices were being distinguished early. Paulus cites a treatise by Apollinarius titled "On Releaser and Master and Destroyer," which shows that at least one earlier author already treated the three as distinguishable parts of one inquiry.⁹ Our hyleg calculator works with the first of these offices, the selection of a releaser, and the history below is the reason any honest implementation has to name whose selection rules it follows.

Dorotheus: the releaser walks through the bounds

The earliest layered witness is Dorotheus of Sidon, a first-century poet whose Carmen Astrologicum survives mainly through a chain of translations: Greek to Middle Persian in the Sasanian period (no Pahlavi copy survives), then Persian to Arabic around 800 CE by 'Umar al-Tabari. David Pingree's critical edition demonstrates that the transmitted text is not an untouched original. One chart embedded in Book III dates to 381 CE, three centuries after Dorotheus, which securely establishes later material in that chapter, though it dates only the passage that contains it. Pingree dated a second example to 281 CE; Benjamin Dykes disputes that reading and reconstructs the same chart to 44 CE, so the age of that passage remains contested.¹⁰ When this article says "the transmitted Dorotheus," the hedge is deliberate.

We are lucky to have a control. Hephaistio of Thebes, a Greek author of the early fifth century, summarized the Dorothean procedure in Greek (Apotelesmatics II.26), independently of the Persian and Arabic chain. His summary gives a candidate order for the releaser in a day birth: the Sun, then the Moon, then the Lot of Fortune, then the degree of the prenatal new or full Moon, and finally the Ascendant. At night the luminaries trade places, and the editors infer rather than read that the remaining fallbacks repeat in the same order; Dykes marks that step "presumably."¹¹ A candidate qualifies only in a strong place and only when one of its dignity lords witnesses it by aspect.

The transmitted Arabic text of the same doctrine (Carmen III.2) opens with a different order, placing the degrees of the Ascendant's bound immediately after the sect light, and it adds the decan lord to the list of qualifying witnesses, a lord absent from Hephaistio. Robert Schmidt judged the decan an Arabic addition. The chapter's worked example then departs from its own opening list and follows Hephaistio's order instead: the Sun, Moon, Fortune, and prenatal full Moon are all cadent, so the example settles on the Ascendant as releaser, exactly where the Greek summary would have landed.¹² The Greek and Arabic witnesses disagree with each other, and the Arabic chapter's opening list conflicts with its own worked example.

The Dorothean clock is the most distinctive part. Once selected, the releaser is moved forward through the bounds, the unequal divisions of each sign that each belong to one of the five non-luminary planets, at the rate of the local rising times of the signs. Each bound lord governs the period during which the releaser crosses its bound, and any planet or ray encountered inside a bound participates in that period. The Greek name for the procedure is peripatos, commonly rendered circumambulation, a walking around; Arabic authors write qisma, translated both as division and as distribution.¹³ The technique matters for the history because a Dorothean procedure of this shape is attested in Greek by the early fifth century, well before the Arabic translations, so the familiar description of distribution as an Arabic invention reverses the chronology. What cannot be shown is that every surviving detail goes back to the first-century poem. You can explore the mechanism itself with our distribution through bounds calculator.

Ptolemy: one releaser and a geometric clock

Ptolemy's treatment (Tetrabiblos III.10 in the Robbins translation; the Hübner critical edition numbers the same chapter III.11, and the manuscripts carry both numerals) is the most mathematically ambitious of the Greek procedures and among the most frequently misdescribed.

Ptolemy first restricts the search to specific regions of the chart, the prorogative places, and ranks them. He then tests the luminaries, the Ascendant, the Lot of Fortune, and the planets holding rulership over those places, with different hierarchies for day and night births. The winner is a single prorogator, his releaser, for the length of life inquiry; destructive and protective contacts enter afterward, once the direction is under way, to modify or terminate its course.¹⁴ What his procedure lacks is a separate fixed-year Master: no planet steps forward to grant its greater years as a base allotment, the way it does in Paulus or Firmicus. Rulers participate in electing the releaser; none of them is installed as a year-giver.

The clock is primary directions, built from the daily rotation of the heavens. After birth the whole celestial sphere appears to turn, carrying every chart point with it. Ptolemy measures that turning on the celestial equator rather than along the zodiac, and takes one equatorial degree, one "equinoctial time," to stand for one year of life. He directs the releaser toward destructive contacts, weighs benefic intervention, and converts the arcs with proportional semiarcs and ascensional times.¹⁵ His treatment shaped later practice without founding it: directed longevity procedures existed before him, and later authors built competing geometries on the same idea. Even his ancient readers disagreed about his instructions, which is one reason a primary directions calculator has to state which geometry and which time key it uses. Which house framework Ptolemy intended has also been disputed since antiquity, read by some as an equal house construction and by others as a quadrant one, and Chris Brennan shows the dispute began among Ptolemy's ancient readers, long before modern software gave it a settings menu.¹⁶

A popular summary has Ptolemy refusing to name a single ruler of the nativity because no one planet could govern contradictory fortunes. That argument exists, but it lives in a different chapter doing a different job. In Tetrabiblos IV.10, on the division of times, Ptolemy assigns separate prorogations to separate topics: the Ascendant for the body and travel, the Lot of Fortune for property, the Moon for the soul and marriage, the Sun for dignity, and the Midheaven for actions, friendships, and children.¹⁷ His stated reason is that a person can prosper in one department of life while suffering in another, so general timing needs several releasers running at once. George reads this as evidence that Ptolemy never sought one universal Master of the Nativity, and as a synthesis that is reasonable. But it is a modern synthesis, and it cannot be read backwards into the length of life chapter, where Ptolemy plainly selects one releaser and directs it.

Valens: a working astrologer's case files

Vettius Valens shows the doctrine in the hands of a practicing astrologer, and his Anthology (second century CE) is direct evidence that no standard procedure existed. He opens Book III by saying that earlier writers "handed down the tradition in different ways."¹⁸ He also criticizes inherited doctrine directly, rejecting a maximum-years rule associated with the Nechepso and Petosiris literature because charts in his own files had outlived it.¹⁹

His central method runs two calculations against each other. Select a releaser (the sect light where possible, with the Ascendant or Midheaven as fallbacks when both luminaries are poorly placed), and find its ruler, normally the lord of the bound the releaser occupies. Then compute two numbers: the releaser's directed arc to a destructive point, converted by rising times, and the planetary years of the ruler. Valens generally takes the smaller.²⁰ The ruler must be fit to give its years: witnessing the releaser, well placed, and not disqualified by its position at the western horizon. The translations differ over that last condition, Schmidt rendering it as the ruler not setting, Riley as the ruler not being at the Descendant.

Valens also documents the charts where the machinery jams. In one example the Moon's bound lord Venus has set, and the text calls the nativity one "without a house ruler"; in the same chart the Ascendant serves as releaser, and the destructive and protective rays are judged from it. In another, both luminaries are cadent, the Ascendant becomes releaser, and its bound lord Jupiter is too badly placed to serve, so the chart lacks a usable ruler twice over.²¹ Elsewhere he allows that a provisionally identified ruler can still fail to control the allotment. The translations disagree about what to call these cases (Schmidt writes "without a predominant planet," Riley "without a houseruler" or "without a controller"), and this article follows George in regularizing them as charts without an Oikodespotes, with the caveat that the regularization is modern.

Around the central method the Anthology collects alternatives: a numerical lot projected from the prenatal lunation, a fallback from the prenatal syzygy and the lunar nodes for charts with no ruler at all, chains built on the Lot of Fortune and its rulers, crisis periods built on sevens and nines, Moon-based sign periods, and gnomon tables.²² One late stretch of the transmitted text is identified by Riley as a fifth-century addition, so even "Valens says" sometimes needs a footnote.²³ His own position on this plurality is on record: he calls the methods practicable both by themselves and in combination, and recommends combining and testing them against one another.²⁴ He accepted individual procedures while wanting corroboration.

Firmicus: a rule from outside the Predominator family

Julius Firmicus Maternus, writing in Latin in the fourth century, preserves the clearest evidence that "the ruler of the nativity" was never one algorithm, because his preferred selection procedure does not begin by identifying a Predominator. His lifespan judgment still weighs the Sun, the Moon, the Ascendant, and the ruler's power; the selection of the ruler itself simply starts somewhere else.

In Mathesis IV.19 he surveys four competing views on finding the dominus geniturae, then endorses this: take the sign the Moon occupies at birth, and the ruler of the nativity is the domicile lord of the next sign the Moon enters, skipping Cancer and Leo, because in his doctrine the Sun and Moon cannot hold this office. Moon in Aries gives Venus, because Taurus follows. Moon in Gemini skips Cancer and Leo and lands on Virgo, giving Mercury.²⁵ No Predominator, no eligibility testing of luminaries in strong places, no directed arc in this treatment. The selected planet is then read through its condition and its planetary periods.

Two source cautions belong in the main text rather than in fine print. First, the Latin of the luminary exclusion is damaged: the coherent main sentence clearly excludes both luminaries, but a corrupt, bracketed continuation that follows has been read as granting them a narrow share under restrictive bound conditions, and Jean Rhys Bram's English translation omits the continuation. Second, Firmicus is inconsistent with his own vocabulary, equating the giver of life with the ruler of the nativity in one book and listing them as separate offices in another.²⁶ A modern proposal from the Project Hindsight circle conjectures that the "next sign" rule may itself be a corrupted survival of a Moon-related bound lord doctrine; that is a conjecture rather than an edition-backed correction, and the transmitted rule stands in the meantime.²⁷

For the priority of the question itself, Firmicus is emphatic, and the statement sits outside the damaged passage: establish the span of life first, because everything else depends on it. He refers readers to a dedicated work of his own on the ruler of the nativity and the chronocrator. It does not survive.²

Paulus: the best-conditioned lord

Paulus Alexandrinus (fourth century) gives the procedure that most resembles the later medieval workflow.

In chapter 36 of his Introductory Matters, Paulus finds the qualified luminary for the sect, or falls back through the prenatal lunation, the Lots of Fortune and Spirit, and finally the Ascendant. He then compares the lords with a claim on that point. By day he names the Sun's bound, exaltation, and triplicity lords; by night, the Moon's bound and domicile lords, with the remainder "as above." The candidate with the strongest rulership claim wins, strengthened by morning rising ahead of the Sun, by angularity, by standing on its own throne, and by testimony to the sect light.²⁸ The victorious Master can award its greater years as a base. The adjustments around that base are not symmetrical: benefics in good condition add their lesser years, while Saturn and Mars can add when well situated and subtract when badly situated. The arithmetic scale behind this, the lesser, mean, and greater periods of each planet, is the subject of our planetary years calculator; Paulus assigns a qualified Sun up to 120 years and a qualified Moon 108, figures he gives in his chapter on the bounds rather than in the selection chapter itself.²⁹

The caution is that the tidy modern sequence, "find the Predominator, then choose the best of its four dignity lords," is a reconstruction, and it should be credited as one. It is George's synthesis of a compressed and asymmetrical chapter.³⁰ Paulus's day list and night list name different dignities, the mandatory or merely strengthening status of witnessing is unclear in the Greek, and Greenbaum's notes on her own translation concede that the exact dignity behind one key term (idiothroneō, being on one's own throne) cannot be pinned down. There is no points table in Paulus. Any calculator that scores his conditions numerically is making modern decisions on his behalf, and should say so. That reconstruction gap is precisely why our Master of the Nativity calculator treats the competing selection procedures as named methods rather than one merged score.

Into Persian and Arabic: hīlāj, kadkhudāh, and the distributor

The Greek doctrine crossed into Middle Persian under the Sasanians and into Arabic in eighth and ninth century Baghdad, and the crossing renamed the offices. The Greek aphetēs became Middle Persian hīlāg, then Arabic hīlāj or haylāj, then the Latin hyleg. The Oikodespotes corresponds to the Pahlavi kadag xwadāy, the master of the house, which became Arabic al-kadkhudāh and then the Latin alcocoden.³¹ The terms began as close lexical and functional correspondences and accumulated new meanings on the way: Giuseppe Bezza documents later readings of the pair as wife and husband, mother and father, body and soul, while Dykes cautions that the "wife" etymology of hīlāj is probably a medieval misunderstanding rather than the word's actual history.³²

What the Persian and Arabic authors inherited was the disagreement documented above, and their compilations show the seams. The longevity chapters attributed to Masha'allah, in the Book of Aristotle, a work that survives only in Latin translation and whose attribution Dykes argues on internal evidence, combine instructions recognizably descended from Dorotheus, Ptolemy, and Valens, and Dykes's notes repeatedly catch the compilation conflating sources that had never agreed.³³ 'Umar al-Tabari's procedure is the most explicit surviving manual of the mature system, though it too reaches us through Latin transmission, in an edition Dykes has rearranged and annotated: test the Sun, Moon, Fortune, Ascendant, and prenatal lunation in a sect-specific order for the hīlāj; require one of its dignity lords to witness it; choose the kadkhudāh from the lords with a claim on it, a step the chapter points two ways, by the count of dignities each holds and by preference for the bound lord; grade the kadkhudāh's grant of greater, middle, or lesser years by its angularity and condition, with a later passage in the same chapter still allotting a band to a year giver holding no dignity at its own degree; let benefics add and malefics subtract; then direct the hīlāj and compare.³⁴ At one point the text attributes a rule to Ptolemy that, on Dykes's diagnosis, is a Persian reinterpretation of a chapter that installs no kadkhudāh at all.³⁵ Even the tradition's own citations of its Greek sources are part of the disagreement.

The later tradition also kept the failure cases. 'Umar describes the nativity that has neither hīlāj nor kadkhudāh and reroutes judgment through other significators.³⁶ Al-Biruni, cataloguing the technique in the eleventh century, states outright that some nativities have no hīlāj.³⁷ The indeterminate chart is an attested outcome in Valens, in 'Umar, and in al-Biruni alike. That is why our alcocoden calculator has to be able to return no qualified year-giver: several of the historical procedures behind it allow exactly that.

One office in this layer is the most commonly garbled. The jārbakhtār, the "distributor of time," is the lord of the bound through which the directed hīlāj is currently passing. It changes whenever the direction crosses into a new bound. It is a time lord (Martin Gansten notes that the Persian element means time, not life, and matches the office to the Greek chronocrator), and it is distinct from the natal kadkhudāh even though the same planet can hold both offices at a birth, a coincidence Dykes identifies as a running source of textual confusion.³⁸ Arabic authors call the active bound the division and its lord the divisor; the body or ray the direction encounters along the way is the promissor of primary-directions vocabulary, and the sources describe it as partnering with the divisor for that stretch of the direction. This is Dorotheus's circumambulation, preserved and systematized. In Abu Ma'shar's annual system distribution is applied broadly, with almost any significator, never only the hyleg, directed through the bounds.³⁹

A note on firdaria

Firdaria, the fixed sequence of planetary periods and subperiods of probable Persian origin, is regularly described as a stage bolted onto the Hyleg and Alcocoden procedure. It is a separate engine. It allots its own fixed periods and subperiods to every life, but it selects no hīlāj and plays no part in the kadkhudāh's lifespan grant, and it appears in the sources (Abu Ma'shar, al-Qabisi, Al-Biruni) in its own chapters with its own tables, next to the planetary years and explicitly distinguished from them.⁴⁰ What a later practitioner could do is read the current fardar lord as corroborating testimony alongside distributions, profections, and revolutions, and Abu Ma'shar's annual method does exactly that.⁴¹ Adjacent and combinable, then, rather than one calculation. Gansten documents both the separation and the later confusion between division and firdaria that helped create the modern muddle.⁴²

Why no calculator can return "the ancient method"

Stack the procedures side by side and the disagreement sorts into four levels, each sufficient on its own to change the answer.

The first is vocabulary. The same Greek word covers an ordinary sign lord, the ruler of a place, the bound lord of a Predominator, and an overall chart ruler; the Latin and English traditions then flattened several offices into "the Hyleg" and "the Alcocoden." Al-Qabisi reports that certain people substituted the general victor of the chart, the mubtazz, for the kadkhudāh.⁴³ A calculator that prints "your Hyleg" without naming a source has already made an unmarked historical decision.

The second is the candidate list. Hephaistio's Dorotheus, the Arabic Dorotheus, Ptolemy, Valens, Paulus, and the Persian manuals overlap around the luminaries and the Ascendant, but they agree neither on the order, nor on the fallbacks, nor on Fortune's rank, and Firmicus selects his ruler without a Predominator at all.

House division is the third level, and it changes eligibility before any candidate is weighed. These chapters are among the first places degree-based divisions appear beside whole sign places: Valens introduces quadrant divisions to judge operative strength, and Ptolemy's prorogative places were read both ways in antiquity.¹⁶ George's worked charts show how much all of this moves the result. In her Picasso example, Valens's procedure names the Moon as Predominator, then rejects its bound lord Jupiter, which is in aversion, leaving no Valens Oikodespotes under either house framework she tests. Paulus reaches the same Moon and allows Jupiter as Master only with explicit uncertainty. Dorotheus's procedure selects the Ascendant as Predominator, with the Sun confirming it. Firmicus's rule returns Saturn as Master. The Pseudo-Porphyrian procedure returns Jupiter as Master, and Ptolemy's names Jupiter as Predominator with no separate Master to name.⁴⁴ One birth, and the authorities disagree about the office as well as the planet.

The clocks are the fourth level, and they are different machines. A directed arc to a destructive contact, a base grant of planetary years modified by condition, a walk through the bounds at the pace of rising times, and a comparison that takes the smaller of two results do not return the same number for the same chart, even when the same planet is selected.

So the six calculators this article links are presented as separate historical components rather than as six steps of one recipe: selection of a releaser, selection and evaluation of a year-giver, the comparison of author procedures, the direction of a significator, the distribution through bounds, and the planetary year tables those procedures draw on. Connecting them into a single automated lifespan verdict would misrepresent every author it cited.

What the argument teaches

The length of life problem shows ancient astrology developing the way long technical traditions develop: by argument among practitioners, carried on through Greek, Middle Persian, Arabic, and Latin, with the losing positions preserved alongside the winning ones. George's conclusion after a hundred pages of reconstruction is that there was "no single, standard procedure."⁴⁵ Valens had already conceded the plurality in the second century, and his advice was to test the methods against each other.

Abu Ma'shar can have the last word. Writing at the head of the chapter that coordinates the lifespan indicators, he warns the practitioner against anxious curiosity about the end of life, and he declines to judge a cutting year from one indicator alone, requiring at least a second in agreement before anything is ventured.⁴⁶

The surviving texts hand us a record of argument and transmission, and that record rewards study on its own terms. It does not hand us anyone's death date, and this article has no interest in manufacturing one.

Sources

Primary texts, in the translations and editions used here: Ptolemy, Tetrabiblos, trans. F. E. Robbins (Loeb, 1940), with the Greek from Wolfgang Hübner's critical edition (Teubner, 1998); Vettius Valens, Anthology, trans. Mark Riley (2010) and Robert Schmidt (Books II and III, 1994); Dorotheus of Sidon, Carmen Astrologicum, ed. David Pingree (Teubner, 1976) and trans. Benjamin Dykes (2019); Hephaistio of Thebes, Apotelesmatics Book II, trans. Robert Schmidt (1998); Firmicus Maternus, Mathesis, ed. Kroll, Skutsch, and Ziegler (1897 to 1913), trans. Jean Rhys Bram (1975); Paulus Alexandrinus, Introductory Matters, trans. Robert Schmidt (1993) and Dorian Gieseler Greenbaum (2001); Pseudo-Porphyry, Introduction to the Tetrabiblos, in Catalogus Codicum Astrologorum Graecorum V.4; Masha'allah, Book of Aristotle, and Abu 'Ali, in Benjamin Dykes, Persian Nativities I (2009), a Latin transmission witness with the Masha'allah attribution argued by Dykes; 'Umar al-Tabari and Abu Bakr in Dykes, Persian Nativities II (2010), likewise edited from the Latin transmission; Abu Ma'shar in Dykes, Persian Nativities IV (2019) and The Great Introduction (2021); Abu Ma'shar and al-Qabisi in Dykes, Introductions to Traditional Astrology (2010); Al-Biruni, The Book of Instruction, trans. R. Ramsay Wright (1934).

Modern scholarship: Demetra George, Ancient Astrology in Theory and Practice, Volume II (2022), chapters 90 to 98; Dorian Gieseler Greenbaum, The Daimon in Hellenistic Astrology (2016); Levente László, "Revisiting the Authenticity of Porphyry's Introduction to Ptolemy's Apotelesmatics," Classical Philology 116 (2021), pages 392 to 411; Chris Brennan, Hellenistic Astrology (2017); Martin Gansten, Annual Predictive Techniques of the Greek, Arabic and Indian Astrologers (2020); Giuseppe Bezza, "Astrological Considerations on the Length of Life in Hellenistic, Persian and Arabic Astrology," Culture and Cosmos 2.2 (1998), pages 3 to 15.

Footnotes

1. Ptolemy, Tetrabiblos III.10, trans. Robbins, printed page 271. Hübner's critical edition numbers the chapter III.11 (critical page 202); the manuscript witnesses carry both numerals. ↩

2. Firmicus, Mathesis IV.20.1 to 2; Bram, printed page 144; Kroll, Skutsch, and Ziegler, printed page 258. ↩ ↩²

3. Valens, Anthology VI.8; Riley, printed pages 120 to 121. ↩

4. George, Ancient Astrology in Theory and Practice, Volume II, printed page 1123. ↩ ↩²

5. George, Volume II, printed pages 1035 to 1064. ↩

6. Greenbaum, The Daimon in Hellenistic Astrology, printed pages 255 to 261. ↩

7. Pseudo-Porphyry, Introduction to the Tetrabiblos 30, in CCAG V.4, 206.3 to 8; Brennan, Hellenistic Astrology, printed page 419. ↩

8. László, "Revisiting the Authenticity of Porphyry's Introduction," Classical Philology 116 (2021), pages 392 to 411; see also the Ptolemaeus Arabus et Latinus catalogue record. Greenbaum (2016) defends Porphyrian authorship for most of the text. ↩

9. Paulus, Introductory Matters, preface; Schmidt, printed page 1. ↩

10. Pingree, Dorotheus, preface, printed pages VII and XIV to XVI; Dykes, Carmen Astrologicum, introduction, printed pages 5 to 6. ↩

11. Hephaistio, Apotelesmatics II.26; Schmidt, printed pages 78 to 79; the "presumably" on the nocturnal fallbacks is Dykes, Carmen Astrologicum, printed pages 189 to 190. ↩

12. Dorotheus, Carmen III.2; Pingree, printed pages 242 to 245; Dykes, printed pages 189 to 196. Schmidt's judgment on the decan lord is at Hephaistio II.26, note 199, printed page 79. ↩

13. George, Volume II, printed pages 1132 to 1135; Gansten, Annual Predictive Techniques, printed pages 28 to 33. ↩

14. Ptolemy, Tetrabiblos III.10; Robbins, printed pages 273 to 279 for the candidate places and rulers, 281 to 307 for the direction procedure. ↩

15. Robbins, printed pages 281 to 307; Hübner, critical pages 208 to 223. ↩

16. Brennan, Hellenistic Astrology, printed pages 388 to 392. ↩ ↩²

17. Ptolemy, Tetrabiblos IV.10; Robbins, printed pages 449 to 451. ↩

18. Valens, Anthology III.1; Schmidt, printed page 27; Riley, printed page 58. ↩

19. Brennan, printed page 391, with Pliny's attribution of the maximum doctrine to Nechepso and Petosiris and Valens's criticism of it. ↩

20. Valens, Anthology III.1 to III.3; Schmidt, printed pages 27 to 41; Riley, printed pages 58 to 62. ↩

21. Schmidt, printed pages 46 to 47; Riley, printed page 62. ↩

22. Schmidt, printed pages 53 to 73; Riley, printed pages 63 to 70. ↩

23. Riley, printed pages 167 to 172, labeled a fifth-century addition. ↩

24. Riley, printed page 68, where each method is called practicable "both by itself and when combined with another"; Anthology VI.8, Riley, printed pages 120 to 121, on combining and testing methods. ↩

25. Firmicus, Mathesis IV.19.1 to 4; Bram, printed page 138; Kroll and Skutsch, printed pages 243 to 244. ↩

26. Bram II.25, printed pages 56 to 57, equates the giver of life with the ruler of the nativity; IV.1.8 lists them separately. ↩

27. Project Hindsight, Mathesis summary, presented there as a modern conjecture. ↩

28. Paulus, Introductory Matters 36; Schmidt, printed pages 75 to 77; Greenbaum, printed pages 74 to 76. ↩

29. Paulus, Introductory Matters 3; Schmidt, printed pages 8 to 9. ↩

30. George, Volume II, printed pages 1068 and 1145. ↩

31. Pingree, preface, printed pages XV to XVI; Dykes, Persian Nativities I, introduction, printed pages xl to xli; Bezza, pages 5 to 7. ↩

32. Bezza, pages 5 to 7; Dykes, Carmen Astrologicum, introduction, printed page 49, on the "wife" etymology. ↩

33. Masha'allah, Book of Aristotle III.1.5 to III.1.10, in Dykes, Persian Nativities I, printed pages 53 to 66. ↩

34. 'Umar al-Tabari, Three Books on Nativities I.4, in Dykes, Persian Nativities II, printed pages 7 to 22. ↩

35. Dykes, Persian Nativities II, printed page 12, note 71. ↩

36. 'Umar, Three Books I.3.3, in Dykes, Persian Nativities II, printed page 6. ↩

37. Al-Biruni, Book of Instruction, section 522, printed page 118. ↩

38. Gansten, printed pages 32 to 33; Dykes, Persian Nativities I, introduction, printed page xli. ↩

39. Gansten, printed pages 28 to 31; Dykes, Persian Nativities IV, introduction section 7, printed pages 61 to 65. ↩

40. Al-Biruni, Book of Instruction, section 395, printed page 32, for the firdaria sequence, and sections 438 to 439, printed page 48, for the firdaria tables. The planetary years sit immediately alongside in both places, at section 394 on printed page 32 and section 437 on printed page 48, and each passage cross-references the other. Abu Ma'shar and al-Qabisi, in Dykes, Introductions to Traditional Astrology VII.1 to VII.2, printed pages 330 to 332. ↩

41. Abu Ma'shar, in Dykes, Persian Nativities IV, IX.8, printed page 661. ↩

42. Gansten, printed pages 37 and 73, and glossary, printed page 194. ↩

43. Al-Qabisi, in Dykes, Introductions to Traditional Astrology VIII.1.4, printed page 357. ↩

44. George, Volume II, printed pages 1079 to 1080. ↩

45. George, Volume II, printed page 1146. ↩

46. Abu Ma'shar, in Dykes, Persian Nativities IV, IX.8, printed pages 645 to 646. ↩