# 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**

I wish you well on this project. I would be one of the first to read the translations. The 2002 English translation of Leonardo of Pisa's "Liber abbaci" was extremely useful to me in writing my book The Man of Numbers, even though I can, with difficulty, read Latin. I was tempted to write a similar book about al-Khwarizmi, but was deterred by the lack of an English translation of his two greatest works. His texts deserve to be widely available today every bit as much as Leonardo's.