Manahil al-Surur li-Mubtagha al-Hisab bil-Kusur
- Author died
- 1252 AH
- Editions
- T Istanbul
Manahil al-Surur li-Mubtagha al-Hisab bil-Kusur (The Springs of Delight for the Seeker of Calculation with Fractions) is a didactic poem on fractional arithmetic composed by the Damascene Hanafi jurist Ibn Abidin (d. 1252 AH / 1836 CE) .
Purpose and Composition
Ibn Abidin compiled the material for the poem from Nuzhat al-Hisab . In the introduction, he explains that he limited the treatise specifically to the study of fractions because whole numbers and other arithmetic rules were already well understood, and he rendered it in verse to make the rules straightforward and easily memorized by students . The entire poem consists of 117 verses .
Structure and Content
The poem systematically covers the fundamentals and practical applications of fractional arithmetic:
- Definitions and Classifications: It begins by defining a fraction in dust-board calculation (al-ghubar) as the ratio of one quantity to another, defining the numerator and the denominator (al-maqam or al-makhraj), and outlining the ten primary bases (halves through tenths, alongside the generic part) . It categorizes fractions into five types: simple (mufrad), related (muntasib), decomposed (muba‘‘ad), composite or disparate (mukhtalif), and excepted (mustathna) .
- Mixed Numbers and Fraction Reduction: It details how to expand mixed numbers containing whole integers alongside fractions . It also addresses the reduction and simplification of fractions based on the relationship between numerators and denominators, including coprime quantities (tabayin), commensurable quantities (tawafuq), and divisible/nested quantities (tadakhul) .
- Arithmetic Operations: The text outlines computational procedures for addition, subtraction, multiplication, and division involving fractions .
- Roots and Conversions: It covers the extraction of square roots (tajdhir) from fractions and methods for converting fractional expressions, including calculating rational approximations for surd or incommensurable fractions (al-asamm) .
- Determining Unknowns: The concluding sections explain methods for finding unknown quantities using four proportional numbers (al-a‘dad al-mutanasiba) and the method of scales / double false position (hisab al-kaffat or al-khata'ayn) .
Transmission and Publication
Manahil al-Surur was published in Damascus in 1301 AH and later included in Ibn Abidin's collected essays (Majmu‘at al-Rasa'il) published in Istanbul in 1325 AH . Manuscript copies of the poem are preserved in several libraries, including the Taymuriyya Library, the Cairo National Library, the Alexandria Municipal Library, and the Garrett Collection at Princeton University .
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