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	827H/1424J
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_576

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

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.

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.

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.

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

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

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

Hogendijk, Jan. 2009. “Al-Kāshī's Determination Of Pi To 16 Decimals In An Old Manuscript”. Zeitschrift Für Geschichte Der Arabisch-Islamischen Wissenschaften 19.