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THE BOOK OF INSTRUCTION

Written in Ghaznah, 1029A.D.

46 Great Russell Street

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CONTENTS

The numbered sections (abwab) below are referred to in the Arabic text by numbers alone.

GEOMETRY

1-28. Deal with definitions and propositions of Euclid's Geometry, Book I.
29-32. Of Euclid Book II.
33-36. Of Euclid Books III and IV.
37. Ratio of diameter to circumference.
38-51 & 55. Definitions of Euclid Book V.
52-54. Of Euclid Book VI.
56-71. Definitions from Euclid Books XI & XII.

ARITHMETIC

72-95. Names and properties of the various kinds of numbers.
96-108. Arithmetical Operations. Decimal Notation.
109-115. Algebra.
116-119. Representation of numbers by letters of the alphabet.

ASTRONOMY

120-124. The Spheres.
125. Stars and Planets.
126-131. Celestial Movements. Horizon. Meridian. Cardinal points. Indian Circle.
132-137. Day and Night. Dawn and Twilight. Hours.
138-143. Equinoctial. Ecliptic. Parallels of Declination and of Latitude. Muqantarahs, Equinoxes. Solstices.
144-145. Subdivision of the circumference of the circle. Relation to it of the diameter.
146. THE SIGNS.
147. Declination and Latitude of Stars.
148. Degree of a Star.
149. Latitude and Declination of Planets.
150-152. THE PLANETS. Superior and Inferior. The Epicycle.
153-154. Combustion and Conjunction with the Sun.
155-156. Waxing and Waning of the Moon. Phases peculiar to the Moon?
157-162. The Fixed Stars. Their arrangement in Constellations, Zodiacal, Northern and Southern. Tables of these.
163-166. Star names. MANSIONS OF THE MOON. Their Ascension.
167-169. The Galaxy. Order of succession of Signs. Northern and Southern Signs and Mansions.
170-175. Mumaththal Orbit or Parecliptic. Apogee of Sun. Its Excentric Orbit. Its Mean Movement, Mean Argument and Equation. The amount of its movement in the Ecliptic.
176-185. Inclined orbits of planets, their Nodes. Epicycle; Deferent; Equant. Apogee of Epicycle, Mean rate of planet, Mean and True Anomaly. Mean and Corrected Longitude. Equation of Anomaly. True Position among the stars.
186-190. Orbits of the Moon. Its Movements. Those of the Planets. Revolution of the Planets.
191. The Trepidation Theory.
192-196. Latitude of the Moon and of the Planets. Position of their Apogees and of their Nodes.
197-198. Daily rate of movement of Planet, BUHT.
199-201. Maqamat, Ribatat, Nitaqat.
202. Planets. Ascending and Descending.
203. Increase and Decrease of the Planets.
204. World-Days and World-Years.
205-209. Size of Planets. Distance from the Earth. Size of the Earth and surrounding Elements.
210-213. Distribution of Land and Water. Equator. Erect posture.
214-219. Latitude and Longitude of Locality.
220-222. Ortive Amplitude. Day and Night. Diurnal Arc.
223-224. Stars of Perpetual Apparition and Occultation.
225-226. Altitude and Zenith Distance.
227-229. Gnomon and Shadow.
230-235. Azimuth. Meridian Altitude and Shadow. Relation to time of prayer. Azimuth of Qiblah. Direction of Mecca.

GEOGRAPHY

236-240. The Seven Climates. Their Extent and Characteristics. Qubbat al-ard. Other Methods of dividing the Earth.
241. Cities in the Seven Climates.

ASTRONOMY

242. Co-ascensions of Equinoctial and Ecliptic.
243. 'Epoch' of star with Latitude. Degree with which it rises, sets and crosses the Meridian.
244. Da'ir. Arc of parallel of a star traversed from the horizon at a given time.
245-248. Ascendant. Houses. Cadent and Succeedent. Their Angles.
249. Anniversary.
250. CONJUNCTIONS of Saturn and Jupiter.
251. Transit in Conjunctions.
252-254. Conjunction and Opposition of Moon. Phases (Fasisat) at which forecasts are made, Athazer (al-tasyirat).
255-267. Eclipses of Moon. Eclipses of Sun. Parallaxis.
268. Mean Day.

CHRONOLOGY

269-272. Months. Solar and Lunar Years. Leapyear. Intercalation.
272a. Hindu Names for Days of the Week.
273-279. Months of the Various Nations.
280-281. Dates. Cycles. Eras.
282. Feasts and Fasts of the Nations.
283-290. Jewish.
291-300. Christian.
301. Muslim.
302-310. Persian.
311-315. Days in Greek Calendar.
316-320. Soghdian and Khwarizmian.
321-323. THE CALENDAR. Page of a Persian Calendar.

THE ASTROLABE

324-346. The Astrolabe. Its Parts. Various Kinds. Uses.

ASTROLOGY

347-358. The Signs. Their Nature and Characteristics. Relation to points of the Compass and to the Winds.
359-371. Tables giving Indications as to their influence on Character, Figure and Face, Profession, Disease. Crops. Animals.
372. Years of the Signs.
373-376. Signs and Planets in Aspect and Inconjunct.
377. Relations other than Aspect.
378. Ascending and Descending halves of the Zodiac.
379-380. Triplicities and Quadrants of the Zodiac.

THE PLANETS

381-393. Their Nature and Characteristics. Relation to points of the Compass. AS Lords of Hours and Days of the Week. Relation to Climates and Cities.
394-395. Their YEARS. Periods (FIRDARIA) of control of Human Life.
396-435. TABLES giVing Indications as to Soils. BUildings. Countries. Jewels. Foods. Drugs. Animals. Crops. Parts of the Body. Disposition and Manners. Disease. Professions &c.
436-439. ORBS and YEARS. Details of Firdaria.
440-444. Domiciles and Detriments. Exaltation and Fall.
445. As Lords of the Triplicities.
446-447. Planets in Aspect. Friendship and Enmity of Planets.

DIVISIONS OF THE SIGNS

448-452. Halves. Faces. Paranatellonta. Decanates. Ptolemy's thirds.
453-454. TERMS and their Lords.
455-456. Ninths and Twelfths.
457-460. Characteristics of DEGREES of the Signs.

THE HOUSES

461-474. TABLES of Indications at NatiVities, at Horary Questions, as to Organs, Powers, Joys and Powers of the Planets. Sex. Characteristics of Groups of Houses in Threes and Sixes.

THE PART OF FORTUNE

475-480. Tables of other LOTS cast in a similar way.
481-488. Relative Position of Planets and Sun. Cazimi. Orientality. Influence changed under certain conditions. TABLES.
489-490. APPLICATION and SEPARATION.
491. DEAD DEGREES.
492. Conjunction in longitude and in latitude.
493-505. DIGNITIES. Order of precedence. Favourable and unfavourable situations of the Planets in the Signs and Houses.
506-509. Interference with their conjunctions, Reception &c.
510. Substitutes for conjunction and aspect.
511. Opening the doors.
512-513. Strength and Weakness of Planets.
514. The Combust Way.

JUDICIAL ASTROLOGY

515-519. The Five Divisions and the astrological principles on which inquiries are to be based in each.
520. The Lord of the Year. Salkhuda.
521-523. The determining conditions at a nativity, Hyleg, Kadkhuda, Ascendant, Horoscope, Figure of the Heavens. Direction or Aphesis (Tasyir) Janbakhtar. Gifts of length of life. Position ot the malefics (qawati') which terminate it.
524-526. Procedure at birth. Use of Numuder. A similar substitute for Ascendant (Rectification).
527. 'Elections'. Selecting suitable time for action.
528-530. General Questions. Thought reading. Danger of hasty conclusions.

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From the PREFACE

Dr. Singer ... kindly placed a rotograph of the Persian version (PL) at my disposal. It was from this that the translation was made in the first instance.

... Professor Wiedemann of Erlangen ... had translated various passages from the Tafhim in his "Beitraege zur Geschichte der Naturwissenschaften" communicated to the Physico-Medical society of Erlangen, and was good enough to look over my translation of this work and to make a number of valuable suggestions which have been incorporated into it. He advised that the Arabic versions should be collated with the Persian, lending me with this object photographs of the two Berlin MSS. (AB.AB'.) and presenting me with copies of his numerous papers on Arabic science. He was about to write at my request a short Introduction to this work, which he did not live to complete, in which he proposed to compare the life and works of Al-Biruni in the East with those of his contemporary Ibn al-Haitham, better known in the west as Alhazen, so distinguished for his researches in Optics.

... The Tafhim is a Book of Instruction on the Principles of the Art of Astrology (Kitab al-tafhim li awa'il sina'at al-tanjim) but may be regarded as a primer of eleventh century science, because apart from the elements of Geometry and Astronomy (ilm al-nujum, ilm al-falak) and the use of the Astrolabe for astronomical and astrological purposes (Astrology is differentiated as ilm al-tanjim, ilm ahkam al-nujum) it has sections on Geography and Chronology both favourite topics at this period. It is, therefore, often classified with other works designated aS cosmographies but the author places it at the head of his list of works on Astrology. Al-Biruni insists that no one is entitled to call himself an Astrologer unless he possesses a thorough knowledge of these ancillary sciences.

The author, Abu'l-Rayhan Muhammad ibn Ahmad Al-Biruni (Al-Khwarizmi) generally known by his nisbah, which means that he belonged to the suburbs, outside (birun) the walls of the Khwarizmian capital, but also often referred to by his kunyah, which is occasionally written Abu Rayhan. No mention is made of Al-Biruni's offspring nor is there any indication why ‘rayhan’ (literally sweet-basil, but also a not uncommon name) should have been seleoted as his kunyah. Sprigs of this fragrant plant are often worn by Arabs, and it may have been as characteristic for him as an orchid for a distinguished politician. In its feminine form, Rayhanah, it is a woman's name like any other taken from flower or plant like Myrtle. It is also the name of the lady, Rayhanah the Khwarizmian, daughter of Al-Hasan, to whom this book is dedicated and at whose request, indeed, it was written.

The Tafhim occurs in both Arabic and Persian versions, neither of which according to Rieu purports to haye been translated the one from the other. Browne speaks of the bilingual Tafhim ... and of its having been composed simultaneously in both languages ... while a Paris MS (AP) has been regarded on inadequate grounds as favouring the view that it had been translated from the Persian by the author. (p. XIV under AP.)

Rayhanah being a native of Khwarizm would necessarily be more familiar with Persian than with Arabic, which would account for the Persian version. Al-Biruni wrote in Arabic and was accustomed to make use of assistants in his literary output. There are some indications that the translator into Persian was less familiar with Arabic than Al-Biruni. (v. note p. 81)

... In one of his verses Al-Biruni says Mahmud [the Ghaznavid Sultan] did not cease to load him with benefits; he may have occupied an official position as Astrologer; but many of the twelve years between 406 and the completion of his second great work "India" (Ta'rikh al-Hind) in 421/1030 must have been spent in travel and study in India, as well as in the extraordinary and encyclopædic literary activity, including the Tafhim in 420/1029, which may be gathered from his own bibliography of his writings up to 427, contained in the Leiden MS. Golius 133, printed by Sachau in his Preface, and translated by Wiedemann, with the appendix of Al-Ghadanfar (630-692 AH) who is responsible for the details on which the figure of Al-Biruni's horoscope p. 191 is founded.

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Peculiarities

Biruni dedicated this book to Lady Rayhanah, about whom virtually nothing is known. She was a member of the Khwarizmian court, and one of those carried off to Ghazna by Sultan Mahmud. According to Hajji Khalifa (Ta'rikh-i Rashidi, p. 45), oneedition of the Tafhim (421 H) was dedicated to one Abu'l-Hasan Ali ibn Abi al-Fadl Al-Khassi. Al-Khass was a village near the ancient Capital of Khwarizm and Abu’l-Hasan was evidently another of the Khwarizmian exiles in Ghaznah. Biruni occupied such a prominent position in Gurganj, it is possible that Rayhanah was a namesake (samiyyah), daughter of some friend at Ma'mun’s court.

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QUOTES

p. 5:

A versed sine is the sagitta at the doubled arc or the line from one end of the arc to the extremity of the sine opposite it. The greatest of all versed sines is a diameter, as that of all natural sines is a radius.

p. 86-97:

The expression ascension of the mansions does not mean their rising above the horizon, which occurs once every day, but this ascension is like the condition of orientality, tashriq, which we considered in connection with the three superior planets. Because when the sun is near one of the fixed stars it conceals it by its radiance; the star rises by day and sets before the disappearance of the twilight. This condition is described as its ghaibah, time of invisibility in the west. This persists until the sun moves away somewhat, so that when the star rises before the sun, the pale light of the dawn is not sufficient to overcome it. The beginning of visibility in the east in the morning, this is the real ascension (heliacal rising) and is known as nau' as if the star were rising with difficulty. Just about the time we have described when the mansion has arisen, its nadir, the fourteenth from it. sets. This nadir is also called raqib, and its setting suqut. Between the ascension at two adjacent mansions there is an interval of approximately thirteen days, not exactly, because of the difference in magnitude of the stars concerned and their divergence to the north or south.

The term anwa' is associated with the rains, because the times of their occurrence are related to the setting of the mansions in the morning in the west, while that of bawarih refers to the winds and is related to other times of rain on the ascent of a mansion escaping from beneath the rays in the morning.

What has been said with regard to rain and other atmospherical phenomena refers to Arabia, for these differ very much in places distant from each other, indeed, in places quite near it their situation with regard to heat, low-lying or elevated ground, alkaline desert (or bodies of water), differs.

p. 98:

The milky way, kahkashan, is a collection of countless fragments of the nature of nebulous stars. They form a nearly complete great circle which passes between Gemini and Sagittarius, the stars densely-packed in some places, more scattered in others, the way sometimes narrow, sometimes broad, and occasionally breaking up into three or four branches. Aristotle considered that it is formed by an enormous assemblage of stars screened by smoky vapours in front of them, and compared it to haloes and nebulæ.

p. 144:

The fifth climate begins with the country of the Eastern Turks, and the territories of Gog and Magog, Yajuj and Majuj, with the surrounding wall, passes the mountains of the Turks with their well-known tribes, and arrives at Kashgar, Balasaghun, Thasht, Ferghana, Isbijab, Al-Shash, Ushrushna, Samarqand, Bukhara, Khwarizm, and the Sea of the Khazars (known also as Abiskun) [the Caspian] and passes Bab al-abwab (Derbend of the Khazars), Barda'a, Maiyafarqin, Armenia, the Passes into Asia Minor, the cities there, then crosses over Rumiya the Great, the country of the Galicians and the cities of Andalus to end in the encircling Ocean.

The sixth climate begins among the dwelling places of the Eastern Turks with the Qay and Qun, the Khirkhiz and Kamak and Taghazghaz towards the Turcoman country and Farab, the city of the Khazars (Itil) to the north of their Sea and the Alans [and As] who occupy the country between that sea and the Sea Of Trebizond which leads to Constantinople, Burjan, France and Northern Spain where it ends in the Western Ocean.

The seventh climate contains little habitable land; however in the east there are forests and mountains which shelter groups of Turks in a miserable condition, then the Bashkhirt mountains are reached and the boundaries of the Ghuzz and Pechenegs, the two cities of Suwar and Bulghar, Russia, Slavonia, Bulghariya and Maj'ar, and finally the Western Ocean. Beyond this climate there are few people living, except groups like the Ansu, the Varangians, the Bardah and the like.

p. 146:

At the equator the ascensions being vertical are said to occur in the erect sphere, and there the ascensions of sets of four signs are equal if the signs are equidistant north or south of the equinoctial points. Thus Aries and Pisces which are at the same distance from the vernal equinox as Libra and Virgo from the autumnal, have all equal ascensions. The same is true of Taurus and Aquarius and Leo and Scorpius, as well as of the four other signs. Again the descensions of these signs are equal to their ascensions.

p. 154-155:

The word nasi' means intercalating or postponing, and is used in connection with the fact that the lunar year finishes about 11 days before the solar, and consequently the Arabic months change through all the seasons in about 33 years, any month you name occurring in any season or part of a season. The Jews are commanded by the torah (the Mosaic law) to keep both sun and moon natural; this they did by arranging a leap-year containing an additional month made up by accumulating (for 3 or 2 years) the difference between lunar and solar years, so that the year returned to its proper position after having been too far in advance; their leap-year is called in Hebrew 'ibbur i.e. pregnant, because they compare that 13th month which is added to the year to the fruit which a pregnant woman bears in her womb.

The Jews were neighbours of the Arabs in Yathrib the city of the Prophet. Now the Arabs not only wanted their pilgrimage to occur in the proper month (dhu'l-hijjat) but also that it should be fixed at the pleasantest time of the year, so that they might set out and find travelling and commerce easy. They acquired the Jewish method of intercalation not in any learned way, but in one suited to the people generally. It was communicated to the public by the voice of the qalammas or intercalator, a hereditary office (before the new moon, and, the calculation of the period when it was desirable to intercalate the kabisah having been carefully attended to, announcement would be made trom the pulpit that such and such a month would be postponed.) Supposing that were a sacred month, e.g. Muharram, the intercalator would say "I postpone Muharram and make this month free from obligations" so there would be two Muharrams in the year, the first free from restrictions and from war, while the second (in reality Safar) would be observed as the real Muharram. This practice was adhered to till Islam put an end to it in the 9th year of the Hijra, known as the year of the farewell Pilgrimage, when the Prophet (on whom be peace) bade farewell to the world and to his own people.

Whoever desires to associate lunar months with some years cannot dispense with the kabisah; the Harranians of Harran and of Baghdad, known as Sabians, who are a remnant of the Greek pagans, also employ it, although we are insufficiently acquainted with their methods and opinions.

The Hindus also duplicate any month when necessary to complete the reckoning, calling the year in question 'am malmasa, which means a year with a month to be discarded. This word is, however, replaced in the literary language by adhimasa.

p. 175:

Kippur is the tenth day of Tishrin, it is sometimes on this account called 'ashura ('assor). The word kippur in Hebrew means expiation of sins or atonement; fasting is obligatory on this day and non-compliance is punishable by death. The fast lasts for 25 hours beginning (half an hour) before sunset on the 9th and ending half an hour after sunset on the 10th when fast is broken. Kippur must not fall on Sunday, Tuesday or Friday.

p. 177:

The fast of Nineveh is called from the Syrian town of that name, which is also the town of the prophet Jonah (May God bless him). The name Jonah is a Greek one; according to the Christians he spent three days and three nights in a fish's belly, and this is regarded as a sign that Jesus would remain three days and three nights under the earth. This fast lasts for three days and precedes the great fast by three weeks beginning on a Monday.

p. 179:

As regards special days in the Muslim months, the tenth of Muharram is called 'Ashura; it was appointed as a fast in the first year of the Hijra but was afterwards abrogated by the setting apart of the month ot Ramadan. It remains, however, a very advantageous day for voluntary religious acts, and then it coincides with the date of the murder of Husayn bin 'Ali, so that the Shi'ites of Baghdad mourn for him on that day.

The fifteenth night of Sha'ban is much esteemed; it is known as the night of exemption, barat, and I think that barat in this case means delivery from the fire.

In Ramadan is the night of power, qadr, mentioned in the Qur'an [the majesty of which is apparent from the Qur'an] (XCVII: 1-3). It is said that it must be sought among the last ten days, and indeed among the odd days of these ten; the opinion of the majority is in favour of the 27th.
 

p. 181:

The last five days of the month Aban are called Parvardagan (nourishing) because the Magians [Zoroastrians] on these days set out food and drink for the spirits of the dead, which it is said is all taken and consumed.

p. 211:

All the hot signs are male and the cold female. The planets are powerful in those signs which resemble them in nature and sex, but they partake of the nature of the signs in which they are situated so that a planet obviously male shows a tendency to femaleness by being in a female sign. The Hindus say that all the odd, i.e. male signs are unlucky and the female signs lucky.

p. 214:

Indications of the signs as to families. The watery signs Cancer, Scorpius, Pisces and the hinder half of Capricorn favour large families; Aries, Taurus, Libra, Sagittarius and Aquarius small ones, while the first part of Taurus, Leo, Virgo and the first part or Capricorn indicate sterility. The production of twins is specially in charge of Gemini, but also is favoured by Virgo, Sagittarius and Pisces, and sometimes by Aries and Libra and the last part of Capricorn. (The fore parts of Capricorn and Scorpius indicate hermaphroditism) In consequence of what we have said Aries and Libra are described as being of two natures, as are also Capricorn and Sagittarius. Virgo is called mistress of three forms, and Gemini as many-faced, because they denote not only twins but three or more children.

With regard to marriage, Aries, Taurus, Leo, Capricorn indicate eagerness therefor, for Libra and Sagittarius much the same can be said. With regard to the conduct of women, Taurus, Leo, Scorpius and Aquarius denote reserve and abstinence; Aries, Cancer, Libra and Capricorn corruption and bad conduct, while Gemini, Virgo, Sagittarius and Pisces denote a mean in this regard; of the four Virgo is the most virtuous.

p. 232:

The influence of Venus is towards moderate cold and moisture, the latter predominant, of Mercury towards cold and dryness, the latter rather stronger, which influence however may be altered by association with another star. The moon tends to moderate cold and moisture, the one sometimes dominating the other. For the moon alters in each quarter in accordance with the extrinsic heat it is receiving from the rays of the sun. Comparing it with the seasons of the year, the first week has a spring-like character tending towards warmth and moisture, the second summer-like, warmth and dryness, the third after opposition, autumnal towards cold and dryness, and the fourth winter-like towards cold and moisture.

p. 234:

All the three superior planets and the sun are male, Saturn, among them, being like a eunuch (has no influence on birth). Venus and the moon are female, and Mercury hermaphrodite, being male when associated with the male planets, and female when with the female; when alone it is male in its nature. Some people say that Mars is female, but this opinion is not received.

p. 236:

Similarly the various organs of a plant are distributed to different planets. Thus the stem of a tree is appropriated to Sun, the roots to Saturn, the thorns, twigs and bark to Mars, the flowers to Venus, the fruit to Jupiter, the leaves to the moon, and the seed to Mercury. Even in the fruit of a plant like a melon the constituent parts are divided among several planets, the plant itself and the flesh of the fruit belong to the sun, its moisture to the moon, its rind to Saturn, smell and colour to Venus, taste to Jupiter, seed to Mercury and the skin of the seed and its shape to Mars.

p. 238:

With regard to the seven climates the first from the equator to its boundary is given to Saturn the first and highest planet and the one with the widest orbit, because the first climate is the longest of all, the most generous in yielding the necessities of life, and its inhabitants resemble Saturn in colour and disposition. The second climate belongs to Jupiter and so on to the seventh Which is allotted to the moon. Abu Ma'shar regards this as a Persian view, and says that the Greeks give the first climate to Saturn, the second to the sun, the third to Mercury, the fourth to Jupiter, the fifth to Venus, the sixth to Mars and the seventh to the moon.

p. 239:

To find an association between a particular place and a sign or planet is a matter for investigation and research, but how are we to draw a horoscope or ascertain the lord of the hour for a place, unless we know accurately the time of the beginning of its construction? And what city is there of which such a recollection is preserved? Even if a religious ceremony be associated with the foundation of a city, the history of its early conditions has passed into oblivion. Even suppose that is not so, and that we assume a certain date of its foundation, and draw a horoscope and calculate the lords of the hours in accordance therewith, how are we to do so for a well-known stream or a great river, since we can know nothing as to when water began to flow in it and excavate its channel? These questions are futile and their absurdity is obvious to the intelligent.

p. 243:

Saturn: Litharge, iron slag, hard stones. Lead. Pepper, belleric myrobalan, olives, medlars, bitter pomegranate, lentils, linseed, hempseed.

Jupiter: Marcasite, tutty, sulphur, red arsenic, all white and yellow stones, stones found in ox-gall. Tin, white lead, fine brass, diamond, all jewels worn by man. Wild pomegranate, apple, wheat, barley, rice, durra, chickpeas, sesame.

p. 246:

Sun: Sheep, mountain goat, deer, Arab horse, lion, crocodile, nocturnal animals which remain concealed during the day.

Venus: All those wild animals which have white or yellow hoofs such as gazelle, wild ass, mountain goat also large fish.

p. 251:

Venus: Lazy, laughing, jesting, dancing, fond of wine, chess, draughts, cheating, takes pleasure in every thing, not quarrelsome, a sodomite or given to excessive venery, well-spoken, fond of ornaments, perfume, song, gold, silver, fine clothes.

p. 273:

The water under Aquarius is composed of four small stars near each other situated below the point where the beginning of the flow of water is pictured. Some people call this place the urn of Aquarius, but there are no stars here, and so an urn is assumed in the hand of the man from which the water flows, just as a sword is assumed in the right hand of Perseus.

p. 279:

The Part at Fortune is a point of the zodiac, the distance of which from the degree of the ascendant in the direction at the succession of signs is equal to the distance of the moon from the sun in the opposite direction. The method of determining this is to find the place of the sun (Place 1), then that of the moon (Place 2); the ascendant is Place 3. Then ...

p. 289:

Again in the case of the lot for grandparents, if the sun is in Leo, they take from the beginning of Leo to Saturn by day, and by night in the opposite direction. And if it is in the domicile of Saturn then from the Sun to Saturn by day, and vice versa by night, in both cases cast from the ascendant even if Saturn is under the rays or otherwise afflicted.

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