Miftāḥ al-ḥisāb مفتاح الحساب Kāshī, Jamshīd ibn Masʿūd كاشي، جمشيد بن مسعود [‎107r] (226/240)

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. 3v, line 3). The text is known by both the short title Key to Calculation (مفتاح الحساب, see ff. 2r, line 8 and 3v, line 18) 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). In this copy the text begins on folio 3v, but a longer version of the introduction is found on folios 1v-2v, which includes the dedication to the sultan Ulugh Beg (ألغ بك, d. 1449, see f. 2r, lines 4-5) and a list of the divisions of the text and their titles (f. 2r-2v).

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. 1v-2v and 3v);
• Chapter One: Calculation with Integers (المقالة الأولى في حساب الصحاح, ff. 4v-12r);
• Chapter Two: Calculation with Fractions (المقالة الثانية في حساب الكسور, ff. 12r-18v);
• Chapter Three: The Astronomers' Method of Calculation (المقالة الثالثة في طريقة حساب المنجمين, ff. 18v-28v);
• Chapter Four: Mensuration (المقالة الرابعة في المساحة, ff. 28v-61r);
• 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. 61r-110r).

Contains numerous diagrams.

The copy was completed on 2 Shawwāl 997/14 August 1589 by ‘Abd al-Razzāq ibn ‘Abd Allāh ibn ‘Abd al-Razzāq ibn Jamshīd ibn Mas‘ūd ibn Jamshīd (عبد الرزاق بن عبد الله بن عبد الرزاق بن جمشيد بن مسعود بن جمشيد), who it is claimed in the colophon Section at the end of a manuscript text. was the great-great-great-grandson of the author Jamshīd ibn Masʿūd ibn Maḥmūd al-Kāshī (see colophon Section at the end of a manuscript text. , f. 110r, lines 2-11, transcribed below).

Begins (f. 1v, lines 1-6, folio mutilated at head [cf. f. 3v, lines 1-6]):

الحمد لله الذي توحد بإبد[اع] ...

الشافعين يوم التنا[د]...

الله تعالى إلى عفوانـ[ـه] ...

أحواله يقول لما مار[ست]...

في دقائقها وكشت غوامضها وحللت مشكلاتها واستنبطت كشيرًا من ...

والضوابط فيها واستخرجت ما صعب استخراجه على كثير من مباشريها كما استأنفت ...

Ends (ff. 109v, line 19-110r, line 2):

... وهذا آخر ما

أردنا إيراده في هذا الكتاب والحمد لله على

نعمائه والصلوة والسلام

والسلام (!) على خير خلقه محمد وآله الطاهرين وأصحابه

الهادين المهتدين ...

Colophon Section at the end of a manuscript text. (f. 110r, lines 2-11):

... قد فرغت من انتساخ

هذه النسخة الشريفة ليوم الأثنين

من شهر شوال سنة 997

حرره الفقير إلى الله

عبد الرزاق بن عبد الله

بن عبد الرزاق

بن جمشيد بن

مسعود بن جمشيد

مصنف هذا الكتاب

الشريف

Extent and format

Codex A collection of pages, usually gathered into quires, and bound between covers. ; ff. ii+110+iii

Physical characteristics

Material: Eastern laid paper

Dimensions: 243 x 170 mm leaf [written: 180 x 115 mm (ff. 1v-2v), 175 x 115 (f. 8v-12v), 175 x 110 (ff. 3v-7v), 175 x 110 (ff. 13v-21r), and 175 x 110 (ff. 21v-110r)]

Foliation: British Museum foliation in pencil / 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. Library foliation stamped in black ink

Ruling: Misṭarah ; average lines per page: 27 (ff. 1v-2v and f. 8v-12v), 27 (ff. 3v-7v), 27 (ff. 13v-21r), and 21 (ff.21v-110r); vertical spacing (lines per 10 cm): 16 (ff. 1v-2v and f. 8v-12v), 16 (ff. 3v-7v), 16 (ff. 13v-21r), and 12 (ff. 21v-110r)

Script: Naskh ; the colophon Section at the end of a manuscript text. is signed by ‘Abd al-Razzāq ibn ‘Abd Allāh ibn ‘Abd al-Razzāq ibn Jamshīd ibn Mas‘ūd ibn Jamshīd (عبد الرزاق بن عبد الله بن عبد الرزاق بن جمشيد بن مسعود بن جمشيد, f. 110r, lines 6-9); at least four hands appear to be distinguishable: (a) ff. 1v-2v and f. 8r, line 11-f. 13r, line 9; (b) ff. 3v-8r, line 10; (c) f. 13r, line 10-f. 21r; and (d) the hand of ‘Abd al-Razzāq ibn ‘Abd Allāh on ff. 21v-110r

Ink: Black ink, with rubricated headings and diagrams, numerals, overlinings in red; at least one use of blue ink (f. 20r)

Binding: British Museum half-leather binding

Condition: Tidemarks at head and tail; f. 1 mutilated and repaired at head and lower text block towards gutter with loss of text block; ff. 2-6 mutilated at upper edge corner and f. 3 also along edge and repaired without loss of text block

Marginalia: Many on ff. 4r-8r (by hand of scribe who begins on f. 8r); very few after f. 8r

Seal: f. 3r

Written in

Arabic in Arabic script

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