al-Risālaẗ al-Muḥīṭiyyaẗ

TEXT

al-Risālah al-Muḥīṭiyyah

Title (arabic)	الرسالة المحيطيّة
Title (translit)	al-Risālah al-Muḥīṭiyyah
Alias	al-Muḥīṭiyya
Author	Ghiyāth al-Dīn Jamshīd ibn Masʿūd ibn Maḥmūd al-Kāshī [al-Kāshānī]
Created	1424 CE/ 0827 AH
Language	Arabic
Subject	Arithmetic: Practical/ḥisāb
Notes	A treatise on the circumference that determines the parameters of successively inscribed and circumscribed polygons inside and around a circle, in order to calculate the value of Pi to 16 decimal fractional units. Kāšī's calculations are performed in sexagesimal numberation for a circle with a radius of 60. The results are expressed in sexagesimal and decimal fractions.
ismi_id	499858

Manuscript Witnesses

9 witnesses:

al-Risālah al-Muḥīṭiyyah_Istanbul_Askeri Müze_Military Museum Library_756

al-Risālah al-Muḥīṭiyyah_Mashhad_Kitābkhāna-yi Markazī-yi Āstān-i Quds-i Riḍawī_NONE_12145

al-Risālah al-Muḥīṭiyyah_Mashhad_Kitābkhāna-yi Markazī-yi Āstān-i Quds-i Riḍawī_NONE_12235

al-Risālah al-Muḥīṭiyyah_Mashhad_Kitābkhāna-yi Markazī-yi Āstān-i Quds-i Riḍawī_NONE_5389

al-Risālah al-Muḥīṭiyyah_Tehran_Majlis shūrā_NONE (Majlis shūrā, Tehran)_642

al-Risālah al-Muḥīṭiyyah_Tehran_Milli (Kitabkhana-yi Milli)_NONE (Tehran-National Library)_1146

al-Risālah al-Muḥīṭiyyah_Tehran_Milli (Kitabkhana-yi Milli)_NONE (Tehran-National Library)_1428

al-Risālah al-Muḥīṭiyyah_Tehran_Tehran University_unknown collection_Tehran University_5499

al-Risālah al-Muḥīṭiyyah_Toronto_Andrews Engineering Collection_2002

Literature References

al-Kāshī, Jamshīd ibn Mas‘ūd. 2013. A Facsimile Edition of the Autograph Manuscript (MS 5389, Holy Shrine Library, Mashhad, Iran). Tehran: Mīrāth Maktūb.

Saliba, George. 2012. “KĀŠI, ḠIĀṮ-AL-DIN”. In Encyclopaedia Iranica, 64-67. New York: Encyclopaedia Iranica Foundation, Inc.

DENA: Fihristwāra-Yi Dastniwishthā-Yi Īrān. 2010. 12 vol. Tehran: Muṣṭafā Dirāyatī.

9:197. There are 7 witnesses listed for this work in repositories in Mashhad, Shiraz, and Tehran.

Azarian, Mohammad K. 2010. “Al-Risāla Al-Muhītīyya: A Summary”. Missouri Journal of Mathematical Sciences 22 (2): 64-85.

Hogendijk, Jan. 2009. “Al-Kāshī’s Determination of Pi to 16 Decimals in an Old Manuscript”. Zeitschrift für Geschichte Der Arabisch-Islamischen Wissenschaften 19.

Rozenfeld, Boris, and Ekmeleddin İhsanoğlu. 2003. Mathematicians, Astronomers and Other Scholars of Islamic Civilisation and Their Works (7th-19th c.). Istanbul: Research Centre for Islamic History, Art, and Culture.

P. 270 (no. 802), M3.

Youschkevitch, A. P., and B. A. Rosenfeld. 1973. “Al-Kāshī”. In Dictionary of Scientific Biography, 7:255-62. New York: Charles Scribner’s Sons.

Luckey, Paul L. 1953. Der Lehrbrief Über Den Kreisumfang (ar-Risāla Al-Muhītīya) [Jamshīd Ibn Masʻūd Al-Kāshī]. Abhandlungen Der Deutschen Akademie Der Wissenschaften Zu Berlin. Klasse Für Mathematik Und Allgemeine Naturwissenschaften. Jahrgang 1950 Nor. 6. Berlin: Akademie-Verlag.

German translation.