Workshop oriental sine tables/Workshop Oosterse Sinustabellen

Workshop oriental Sine Tables, English version (January 2022) as well as Dutch version (November 2021).

Introduction to the abjad-system for writing numbers


The word abjad refers to the system a = 1, b = 2, j (jim) = 3, d = 4 etc.
We assume that the participants have studied the workshop on abjad numbers which can be found on the special page (this includes extra information in English and in Dutch)

Sine tables

Workshop: English version   Dutch version

Afghanistan: al-Biruni   Uzbekistan/Iran: Ulugh Beg   Morocco: al-Marrakushi   Syria: al-Battani   Turkey: Taqi al-Din

Afghanistan: al-Biruni (ca. 1030)

Arabic manuscript of sine table
Transcription of sine table
Biography
German translation of the explanation by al-Biruni how he computed his table, in C. Schoy, Die trigonometrischen Lehren des Persischen astronomen Abu'l-Raihan Muh. ibn Ahmad al-Biruni dargestellt nach al-Qanun al-Mas`udi. Nach dem Tode des Verfassers herausgegeben von Julius Ruska und Heinrich Wieleitner. Hannover 1927. Scans: deel 1,   deel 2.
The entire Arabic manuscript (of the Qanun Mas`udi) is available online (Qatar Digital Library).
See also the website www.albiruni.nl

Uzbekistan/Iran: Ulugh Beg (ca. 1440)

Persian manuscript of sine tablel
Transcription of sine table (between 0 and 45 degrees) taken from the work by C. Schoy mentioned above (see al-Biruni).
Biography
Explanation by Miram Chelebi (ca. 1500, Turkey) on the computation of the table by Ulugh Beg, in pp. 69-83 of L. P. E. A. Sédillot, Prolégomènes des Tables Astronomiques d'Oloug-Beg, Paris 1853. Download (archive.org). Biography of Miram Chelebi.
A Turkish manuscript of the astronomical work of Ulugh Beg was published in facsimile with Turkish translation in:
Atilla Bir, Mustafa Kacar, Ulugh Bey'in Astronomi Cetvelleri, Zic-i Ulug Bey, Ankara: Kültür ve Turizm Bakanligi, 2012, in two parts. ISBN 978-975-17-3593-5.
For the sine table see part 1 (facsimile part), 27a-35b, part 2 (translation), pp. 88-105.

Morocco: al-Marrakushi (ca. 1280)

Arabic manuscript sine tablel
Transcription of sine tabel from J.J. Sédillot, see below.
Biography
French translation of the first part of the work by al-Marrakushi, which contains the sine table: J.J. Sédillot, L.-A. Sédillot, Traité des instruments astronomiques des Arabes, Paris 1834, available online (archive.org). For the transcribed sine table see pp. 103-114.

Syria: al-Battani (ca. 900)

Arabic manuscript of sine table
Transcription of sine table taken from C. A. Nallino, Al-Battani sive Albatenii Opus Astronomicum, Pars Secunda, Versio tabularum omnium cum animadversiones, glossario, indicibus, Milaan (Mediolanum) 1907, herdrukt Frankfurt, Institut für Geschichte der arabisch-islamischen Wissenschaften 1997, pp. 55-56.
Biography

Turkey: Taqi al-Din (ca. 1580)

Arabic manuscript of sine table
Transcription of sine table, taken from Remzi Demir, Takiyüddin'de Matematik ve Astronomi, Ankara 2000, pp. 67-69.
Biography. See also the website on Taqi al-Din by Huseyin Sen.

General literature on history of trigonometry:
Introductory: Glen van Brummelen, The mathematics of the heavens and the earth: the early history of trigonometry, Princeton, Princeton University Press, 2009.
Older and more comprehensive: A. Von Braunmühl, Vorlesungen über Geschichte der Trigonometrie, Erster Teil: Von den Ältesten Zeiten bis zur Erfindung der Logarithmen, Leipzig 1900, online version (archive.org), another online version (gallica.fr)
(The second part of this work is: A. von Braunmühl, Vorlesungen über Geschichte der Trigonometrie, Zweiter Teil: von der Erfindung der Logarithmen bis auf die Gegenwart, Leipzig 1903, online version, (gallica.fr)
For more information please send me an email.


Jan Hogendijk <J.P.Hogendijk_at_gmail.com>

2022