# Al-Khwārizmī, who wrote first on algebra, then on India's arithmetic*, is one of the greatest mathematicians to have lived.

*So why hasn't 40% of his book on arithmetic been translated into English?*

A few years AFTER writing his book on what we now call algebra, al-Khwārizmī wrote a book on Indian arithmetic. (*AK refers to his earlier algebra book in his arithmetic book.*) And the rest, as they say, became history: *or did it?*

Only about 60% of al-Khwārizmī's book on arithmetic has ever been translated into English. [1] That means there might be hidden gold in that remaining 40%.

One of my dream projects is to have al-Khwārizmī's complete text available in English. As a stepping stone towards this goal, my father, Peter Crabtree, (a polymath, fluent in 16 languages), translated the section on the multiplication of fractions. [2] Yet my father passed away just before Christmas (cancer).

I don't know how it might happen, but it will be wonderful if the complete work of al-Khwārizmī on arithmetic was available in English by 2025. That would mark (approximately) the 1200 year anniversary of al-Khwārizmī's book. In the meantime, I hope you enjoy my Dad's translation. **Just click the blue links below for the PDFs**.

# How al-Khwarizmi multiplied fractions

*If you care... please share! *

# How al-Khwarizmi divided fractions (new!)

[1] *Thus Spake al-Khwarizmi: A Translation of the Text of Cambridge University Library Ms. Ii.vi.5*, John N. Crossley and Alan S. Henry, Historia Mathematica, 17 (1990), 103-131. NOTE: This Latin manuscript cuts off at the start of al-Khwārizmī's explanation of fraction multiplication.

[2] To help with this project, Dr. Menso Folkerts kindly mailed and emailed me, the complete paper and digital editions of the following. *Die älteste lateinische Schrift über das indische Rechnen nach al-Ḫwārizmī*, (Latin & German) Menso Folkerts; Paul Kunitzsch; Hispanic Society of America, München : Verlag der Bayerischen Akademie der Wissenschaften, 1997.

* Al-Khwarizmi did not consider either zero or one numbers and he never dealt with negative numbers. For details on my new research watch the video at **www.j.mp/Arith2Podo**