Dīwān al-‘adad al-wafq ديوان العدد الوفق Anonymous [‎45v] (38/187)

Content

Mathematical treatise on the construction of magic squares and triangles (العدد الوفق). The text is defective at the beginning and end so the author's name is unknown, but in what remains of the preface the author records the title of the work and says that his intention is to compile all that has been written on the subject up to date of the text's composition: 517/1123-4 (see f. 28r, lines 4-5). Seven authorities on magic squares are cited:

• al-Mufaḍḍal ibn Thābit al-Ḥarrānī (المفضل بن ثابت الحراني, d. before 978-79, see Ridwān 'Abū al-Khaṭṭāb al-Mufaḍḍal ibn Thābit al-Ṣābi’' [1990]): ff. 60v, 80v, 94r, 95v and 102r;
• Abū al-Wafā’ al-Būzjānī (أبو الوفاء البوزجاني, d. 997 or 998): ff. 64r, 87r, 91v, 94r, 95v;
• Ibn Haytham (ابن هيثم, d. ca 1040): f. 35v;
• Majd al-Dīn al-Amīr b. Abī Naṣr Manṣūr ibn Muḥammad ibn ‘Alī (مجد الدين الأمير بن أبي نصر منصور بن محمد بن علي): f. 51r;
• Abū Ḥātim al-Muẓaffar b. Ismā‘īl al-Isfizārī (أبو حاتم المظفر بن إسمعيل الإسفزاري, fl. late 5th/11th–early 6th/12th cent.): f. 41r;
• Abū al-Fatḥ ‘Abd al-Raḥmān al-Khāzinī (أبو الفتح عبد الرحمن الخازني, d. after 525): ff. 53v, 77v, 92r, 92v, 100v, 109v, f. 60v;
• Abū al-Ḥafṣ ‘Umar b. Ibrāhīm al-Khayyāmī (أبو حفص عمر بن إبراهيم الخيامي, d. ca 525): f.107v.

After a preface and table of contents (ff. 28r-29r), the treatise is divided into eight books (مقالات) each one further subdivided into parts (أقسام), chapters (أبواب) and sections (فصول), and sometimes even further into methods (وجوه). It is illustrated with 430 squares, triangles, tables and other diagrams.

• Maqālah One: Introductions (المقالة الأولى في المقدمة, ff. 29v-35v);
• Maqālah Two: The Simple Square (المقالة الثانية في الوفق الساذج, ff. 35v-58v);
• Maqālah Three: Bordered Squares (المقالة الثالثة في الوفق المحلّق, ff. 58v-80v);
• Maqālah Four: The Wonderful Bordered Odd Square (المقالة الرابعة في الوفق الفرد والغريب المحلّق, ff. 80v-93v);
• Maqālah Five: The Banded (?) Square (المقالة الخامسة في الوفق الموشّح, ff. 93v-99r);
• Maqālah Six: The Mixed Square (المقالة السادسة في الوفق الممتزج, ff. 99r-109v);
• Maqālah Seven: The Three-Dimensional Square (المقالة السابعة في الوفق المجسم, ff. 109v-116v);
• Maqālah Eight, which completes the Dīwān of Magic Squares with the Figure of the Triangle (المقالة البثامنة وهي المكمّلة لديوان العدد الوفق بالشكل المثلث, ff. 116v-119v, defective at end).

The third chapter (باب) of Maqālah Eight (المقالة البثامنة) is incomplete, and the final two chapters indicated in the table of contents (f. 29r) are missing.

The date of the copy is not known, but it appears to have been produced in the 15th or 16th century, and is at least earlier than 1037/1627-8, the date of the earliest seal in the manuscript (f. 28r).

Begins (f. 28r, lines 1-4, defective at beginning):

الساذج ثم بعده المحلق ثم الوفق الغريب ثم الموشح والممتزج وبعد جميعها المركب بعضها مع بعض

ونختمه بالوفق المجسم العجيب ووفق الشكل المثلث ونشير إلى النوادر واختلاف والوقوع في

مواضعها على أوجز ما يمكن من غير إخلال بأصل من أصول من ها بل نسهّل فيه الغامض ونبيّن الخفي ...

Ends (f. 119v, lines 21-24, defective at end):

الفصل الثاني

في الموشح المهمل من الثلاثيات

وهو الذي يبتدئ أقسام ضلعة منالواحد وتزايد ثلثة ثلثة مثل واحد أربعة سبعة عشرة

إلى حيث أريد من أقسام أضلاع المثلثيات

Extent and format

Ff. 28a-r-119v

Physical characteristics

Material: Eastern laid paper

Dimensions: 270 x 180 mm leaf [210 x 140 mm written]

Foliation: 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. foliation in pencil, also foliated in black ink in Eastern Arabic numerals

Ruling: No ruling visible; 25 lines per page; vertical spacing 12 lines per 10 cm

Script: Nasta‘līq

Ink: Black ink with rubricated headings and diagrams in red, light red and two other colours (blue and yellow?) that have corroded and damaged the paper (see ff. 58 and 101)

Binding: Full cloth case binding

Condition: Extensive insect damage and water stains; many folios torn and repaired

Marginalia: Very few; catchwords added by later hand

Seals: Ff. 28a-r (was two fragments that were rejoined, supported and bound into volume during conservation work), 28r (seal covered with thin sheet of paper removed during conservation work) and 119v

Written in

Arabic in Arabic script

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