Astronomy in the work of Ab¯uRayh.¯anB¯ır¯un¯ı

Jan P. Hogendijk

Department of Mathematics, Utrecht University, Netherlands

2018 Ab¯uRayh.¯anB¯ır¯un¯ı

Born: K¯ath,Khw¯arizm,362 H./973 CE Forced to move to Afghanistan: 407 H./1017 CE Died: ca. 442 H./1051 CE. Biruni listed 113 of his works (manuscript in Leiden, Netherlands)

See www.albiruni.nl Biruni’s existing works: approximate number of pages if printed

Introductory 250 Astronomy 750 Geodesy 150 Bibliography 30 Astron. Instruments 400 Mineralogy 200 Mathematics 200 Physics 20 Pharmacology 300 Chronology 300 Astrology 150 Indian science 500 Biruni’s didactical principle (Chronology, Chapter 6)

Q    h. Qk @X@ ð .’Ë@ éʯð ÈCÓB @ úÍ@ A«X Yg@ð ᯠú ¯ Ð@X @X@ Q¢JË@ àA ¯ È      Q    QªJK ð B @ AîE Yg@ úΫ ú GAK B ‡K@Yg ú ¯ XX Ó éKA¾¯ ᯠúÍ@ ᯠáÓ       èYË YK Yg. É¾Ë ÉJ ¯ AÒ» AîD Ë@ Q¢JË@ ú æîD‚ ð AîD Ê« QjJ ¯ øQk@ éË “If the mind is constantly busy with one single science, it gets bored and distracted; but if the mind changes from one science to another, it is as if you are going around through gardens: if you enter one of them, you already see the next one. Then you feel a longing and you like what you see, as people say: everything new is enjoyable.” The observational basis of medieval Islamic astronomy

(1) Observations of solar (noon) altitude =⇒ theory of solar motion in ecliptic.

(2) Observations of lunar eclipses + theory of solar motion =⇒ theory of lunar motion (only conjunctions and oppositions) =⇒ theory of lunar motion in general. Distances of sun and moon to earth. Lunar parallax.

(3) Observations of fixed stars with respect to moon =⇒ positions of the fixed stars, value of precession of the equinoxes (which was interpreted as “motion of the fixed stars”)

(4) Positions of fixed stars =⇒ theory of planetary motions. Observations by B¯ır¯un¯ı(Q¯an¯unMasc ¯ud¯ı),see website: albiruni.nl). Al-B¯ır¯un¯ımeasured the meridian altitude of the sun using a quadrant.

“In Jurj¯aniyya, in the house of the Am¯ır, on monday 11 Rab¯ıc II, 407 Hijra = Mihr 10, 385 Yazdgerd = Aylul 17, 1327 Alexander the noon altitude of the sun was 47o440.”

Quadrant (reconstruction) More observations by B¯ır¯un¯ıin Jurjaniyya: beginning of autumn

Maximum noon altitude of the sun is: 71o180 (beginning of the summer) Minimum noon altitude of the sun is: 24o80 (beginning of the winter) Average is the noon altitude at the beginning of autumn, that is 47o430 (so geographical latitude of Jurjaniyya is 90o − 47o430 = 42o170) Monday 11 Rab¯ıc II, 407 H: noon altitude was 47o440. Noon altitude next day was 47o200.

B¯ir¯un¯ıconcludes (linear interpolation): autumn began Monday 11 Rab¯ıc II, 407 H, one hour after noon. Solar orbit, as computed by B¯ır¯un¯ıfrom the observed lengths of the seasons

beginning M B 25;3,5,24 Gemini summer

Center of solar orbit

G A beginning of beginning Earth spring autumn sun

3 27 EC/CM = 2 + 60 + 602 + ... Solar apogee had changed since Ptolemy

Ptolemy (150 CE): Solar Apogee in 5o300 Gemini B¯ir¯un¯ı(ca. 1016 CE): Solar Apogee in 25o30 Gemini

Is the difference (19o300) due to the precession of the equinoxes? (value in Islamic astronomy 1 degree per 66 years). That is to say: is the solar apogee fixed with respect to the fixed stars?

B¯ir¯un¯ıargues that observations of solstices are inaccurate. He concluded that difference between motion of apogee and precession is not significant; but perhaps it can be significant in future. Islamic astronomers were able:

* to predict positions of sun, moon, planets, accurate to naked-eye astronomy

* to predict lunar and also solar (!) eclipses.

* to determine accurate values of the solar year, precession, etc.

* for predict the time of beginning of dawn, visibility of lunar crescent, etc.

* philosophical discussions produced a better model of lunar motion than ancient Greeks Popular astronomy:     Õæ j. JJË@ é«AJ“ ÉK@ðB Õæ ê®JË@ H. AJ»

Book of the Instruction in the First Principles of the Art of Astrology for Rayh.¯ana[teenage daughter of some important person of Khw¯arizmiandescent] The best introduction to medieval Islamic mathematics, astronomy, (and astrology). Also in Persian. Written in the form of ca. 500 questions and answers. Pictures on eclipses from the book for Rayhana

Good (although necessarily superficial) source to become acquainted with medieval Islamic mathematics and astronomy! Rayhana saw a lot of numbers:

World map Distances of planets to the earth, etc. Application of astronomical methods: Biruni’s work on coordinates (Tah.d¯ıdnih¯ay¯atal-am¯akinf¯ıtas.h.¯ıh. mas¯af¯at al-mas¯akin):Hard applied science! One of its purposes: Determination of the qibla at Ghazni (Afghanistan). Basis: spherical earth.

1. Determination of geographical coordinates: latitude of Mecca is 21o400, latitude of Ghazni is 33o350, longitude difference between Mecca and Ghazni is 27o2202400

2. Computation of the qibla (four times in four different but equivalent ways): South-West, and the distance to the south is 70o4801500, 70o4701300, 70o4901600, or 70o4605600

3. approximate construction for architects (who were not astronomers and therefore did not understand degrees and minutes). Comparison by E.S. Kennedy of B¯ır¯un¯ı’sco¨ordinateswith modern values. Comparison by E.S. Kennedy of B¯ır¯un¯ı’sco¨ordinateswith modern values. Text: computation in the manuscript

o 0 00 o 0 o 0 He assumes λ = 27 22 24 φ = 33 35 φM = 21 40 . He finds

(1) cos φ sin λ = sin a a = 22o3101900 (2) sin φ/ cos a = sin φ o 0 00 1 φ1 = 36 46 48 (3) f = φ1 − φM f = 15o604800 (4) cos f cos a = sin d. d = 63o505400 (5) sin q = cos φM sin λ/ cos d. q = 70o470600 Text: beginning of computation in the manuscript:

Numbers are Hindu-Arabic (integers > 1000) and Abjad (small integers and sexagesimal fractions). Longitude Ghazni is 94o2202400 from the West, Mecca 67o from the West, Text: beginning of computation in the manuscript:

Geographical longitude of Ghazni (measured from Canary Islands) 9402202400, geographical latitude of Ghazni 33o350 so its complement 56o250, longitude difference with Mecca 26o2202400 60 cos(33o350) × 60 sin(27o220240) = 49; 59; 5 × 27; 35, 14 = 1378; 56, 22, 42, 10. Then 1378; 56, 22, 42, 10/60 = 22; 58, 56, which is found in the sine table to be 60 sin(2203101900). Then 90o − 22o3101900 = 67o2804100 and 60 cos(2203101900) = 60 sin(67o2804100) = 55; 25, 26 etc. etc. etc. Approximate construction for architects: divide radius to South into 3 equal parts or to West into 18 equal parts

Explanation: arccos(1/3) = 70o3104300 and arcsin(17/18) = 70o4804300. Biruni and the astrolabe

Common astrolabe, made by H. ¯amidKhujand¯ıin 374 H / A.D. 985 (when Biruni was a young boy). Astrolabe made in Lahore by Allahdad (ca. 1567), based in part on Biruni’s methods Some of Biruni’s works on the astrolabe (numbers in the list on www.albiruni.nl)

For readers who do not know anything: the chapter in 1. Introduction to Astrology, kit¯abal-tafh¯ımli-aw¯a’ils.in¯ac at al-tanj¯ım,in Arabic and Persian (ca. 30 manuscripts). Published in Arabic, English, Persian, Russian, Uzbek.

For users with limited knowledge: 5. Operations with the common astrolabe, a user manual in 68 chapters [10 manuscripts, edited by Pouyan Rezvani] Drawing of the astrolabe, from the introduction to Astrology Biruni’s works on the astrolabe (numbers in the list on www.albiruni.nl)

For readers with an intermediate knowledge: 4. Exhaustive discussion of all possibilities in the (practical) construction of the astrolabes, in 78 chapters [ed. Seyyed Mohammad Akbar Jawadi al-Hosseini, Meshed 1380 A.H. Shamsi]: common, mixed, zawraqi, others Construction drawing of the astrolabe, from the “Exhaustive discussion” Zawraqi astrolabe by al-Sijz¯ı

On the standard astrolabe, the stars move and the horizon is fixed. On the Zawraqi (boat) astrolabe, the horizon moves and the stars are fixed. Picture in manuscript of text by B¯ır¯un¯ı. Connection with Rotation of the Earth

B¯ır¯un¯ısays on the Zawraqi astrolabe:

“I I liked it immensely because he developed it on an independent principle, which is derived from some people’s belief that the observed (daily) motion of the Universe from East (to West) is due to the Earth and not to the Sky. By my life, it is an uncertainty, extremely difficult to resolve or verify. . . . the geometers and astronomers, have no means to contradict this (idea). Whether the movement is ascribed to the Earth or the Heavens, in either case it does not affect their arts. If it is possible to contradict this belief and resolve the uncertainty, then this is the task of the natural philosophers (i.e., not the astronomers).” Istic ¯ab,ed. Husseini, p. 128 Only extant Zawraqi astrolabes made in Lahore, 17th c. CE Website www.albiruni.nl

Dedicated to the memory of E.S. Kennedy (1912-2009), B.A. Rosenfeld (1917-2008), and A. Rasulov (1888-1977)

E.S. Kennedy B.A. Rosenfeld Thank You!

Download the presentation at www.jphogendijk.nl/talks/Biruni1.pdf

Download a written form of the talk with references at www.jphogendijk.nl/talks/Biruni2.pdf