Miftāḥ al-ḥisāb مفتاح الحساب Kāshī, Jamshīd ibn Masʿūd كاشي، جمشيد بن مسعود

Content

Compendium of mathematics by Ghiyāth al-Dīn Jamshīd ibn Masʿūd ibn Maḥmūd al-Kāshī (غياث الدين جمشيد بن مسعود بن محمود الكاشي, d. 1429 or 1436) or al-Kāshānī (الكاشاني, see f. 15v, line 5). The text is known by both the short title Key to Calculation (مفتاح الحساب, see f. 16v, line 3) and the long title The Calculators' Key to Arithmetic (مفتاح الحسّاب في علم الحساب).

The work is divided into an introduction (مقدمة) and five treatises (مقالات) each subdivided into chapters (أبواب). The introduction includes a dedication to the sultan Ulugh Beg (ألغ بك, d. 1449, see f. 16v, line 1) and a list of the divisions of the text and their titles (f. 16v, line 6-17v, line 14).

Contents:

• Introduction: Definition of Arithmetic, Explanation of the Subject and Definition of Number and its Parts (المقدمة في تعريف الحساب وبيان الموضوع وتعريف العدد وأقسامها, ff. 17v-18r);
• Chapter One: Calculation with Integers (المقالة الأولى في حساب الصحاح, ff. 18r-31r);
• Chapter Two: Calculation with Fractions (المقالة الثانية في حساب الكسور, ff. 31r-41v);
• Chapter Three: The Astronomers' Method of Calculation (المقالة الثالثة في طريقة حساب المنجمين, ff. 41v-52v);
• Chapter Four: Mensuration (المقالة الرابعة في المساحة, ff. 52v-85v);
• Chapter Five: Deriving Unknowns by Means of Algebra, Muqābalah , the Two Errors and Other Rules of Calculation (المقالة الخامسة في استخراج المجهولات بالجبر والمقابلة والخطائين وغيرها من القواعد الحسابية, ff. 85v-122r).

The treatise contains numerous diagrams.

Begins (f. 15v, lines 2-6):

وتوفيقك تعتصم ياكريم الحمد لله الذي يوحد بإبداع الأحاد وتفرد بتأليف

صنوف الأعداد والصلوة على خير خلقه أشفع الشافعين يوم التناد وعلى

آله وأولاده الهادين سبيل النجاة والرشاد فإن أحوج خلق الله تعالى إلى غفران

جمشيد بن مسعود بن محمود الطبيب الكاشاني الملقب بغياث أحسن الله أحواله يقول لما مارست

الأعمال الحسابية والقوانين الهندسية حتى بلغت إلى حقائقها وبالغت في دقائقها

Ends (f. 122r, lines 3-5):

... وهذا آخر ما أردنا إيراده في هذا الكتاب و

الحمد لله تعالى على نعمائه والصلوة والسلام على خير محمد وآله الطاهرين

وأصحابه الهادين والمهتدين

Extent and format

Ff. 15v-122r

It is part of

Anonymous treatise on mathematics and Miftāḥ al-ḥisāb مفتاح الحساب Kāshī, Jamshīd ibn Masʿūd كاشي، جمشيد بن مسعود

290 images

Ref: IO Islamic 1039

Written in

Arabic in Arabic script

Type

Manuscript item

Access & Reference

Original held at

British Library: Oriental Manuscripts

Access conditions

Unrestricted

Archive reference

IO Islamic 1039, ff 15v-122r

History of this record

Date(s)

1041 (AH, Hijri qamari)

Related material

Finding aids

• Loth, Otto, A Catalogue of the Arabic Manuscripts in the Library of the India Office The department of the British Government to which the Government of India reported between 1858 and 1947. The successor to the Court of Directors. (London: Printed by order of the Secretary of State for India in Council, 1877), Item 756, p. 220
• Stewart, Charles, A Descriptive Catalogue of the Oriental Library of the Late Tippoo Sultan of Mysore. To which are Prefixed, Memoirs of Hyder Aly Khan, and his son Tippoo Sultan (Cambridge: Cambridge University Press, 1809), p. 100, nos. vi and vii

Select Bibliography

Edition:

• Kāshī, Jamshīd ibn Masʿūd, Miftāḥ al-ḥisāb , ed. by Muḥammad Ḥamdī al-Ḥifnī Shaykh, Aḥmad Saʿīd Dimirdāsh, and ʿAbd al-Ḥamīd Luṭfī (al-Qāhirah: Dār al-Kātib al-ʿArabī lil-Ṭibāʿah wa al-Nashr, 1967)

Partial facsimile edition and translation:

• Kāshī, Jamshīd ibn Masʿūd, The Extraction of the n-th Root in the Sexagesimal N otation ... Chapter 5, Treatise III, of Miftāḥ al-ḥisāb , ed. and trans. by Abdul-Kader Dakhel (Beirut: American University of Beirut, 1960)

Studies:

• Rosenfeld, B. A. and Ekmeleddin Ihsanoğlu, Mathematicians, Astronomers, and Other Scholars of Islamic Civilization and Their Works (7th-19th c.) , (Istanbul: IRCICA, 2003), no. 802, pp. 269-71
• 'Kāshī: Ghiyāth (al-Milla wa-) al-Dīn Jamshīd ibn Mas‘ūd ibn Maḥmūd al-Kāshī [al-Kashānī]', in The Biographical Encyclopedia of Astronomers , ed. by Thomas Hockey et al. (New York: Springer, 2007) pp. 613-15

People & organisations

Jamshīd ibn Masʻūd Kāshī

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Miftāḥ al-ḥisāb مفتاح الحساب Kāshī, Jamshīd ibn Masʿūd كاشي، جمشيد بن مسعود, British Library: Oriental Manuscripts, IO Islamic 1039, ff 15v-122r, in Qatar Digital Library <https://www.qdl.qa/archive/81055/vdc_100048818589.0x000002> [accessed 13 March 2025]

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