AS PRACTISED BY THE ARABS. 53 



(6.) I am induced to hope that this enquiry may be the more interest- 

 ing, from not having been able to find it undertaken any where else ; it is 

 neither mentioned in Mr. Colebrooke's elaborate translations of Sanscrit 

 Algebra and Arithmetic, nor in Dr. Taylor's Lilawati. In the Researches 

 vol. XII. Mr. Strachey gives from the Kholasut-ul-Hisab, a full and 

 accurate account of Arabian Arithmetic, as far as Multiplication, but is 

 silent respecting the extraction of Roots. He observes, p. 171 — •" On the 

 other Rules nothing is delivered differing so much from those contained 

 in our common books of Arithmetic, as to require specific mention." Mr. 

 Strachey was probably led into this opinion from his having only consult- 

 ed the Kholasut-ul-Hisab, a work far inferior, as I have reason to believe, 

 either to the Ayoun-ul-Hisab, or its predecessor, the Miftah-ul-Hisab, and 

 which contains no more than the extraction of the Square Root. To that 

 edition of the Kholasut-ul-Hisab, which was printed at Calcutta in 1812, 

 with a Persian translation, by Mouluvee Itoshuu Alee, (I presume the 

 same mentioned by Mr. Strachey at p. 167, ibid.) there is indeed added an 

 Appendix, containing the extraction the Cube Root, by Nujm- Uddeen Alee 

 Khan; but this last contains no more than the bare rule, goes to no higher 

 powers, and sets out by declaring, \^^\ cjL> ^5 ^jA&L*j\ <_**£ ~\j*r?\ 

 p. 466. " The extraction of the Cube is one of the greatest difficulties in 

 the science of Arithmetic." And even this rule, as far as I can find, has 

 never been translated into English. 



(7.) In the 35th number of the Edinburgh Review, Professor Play- 

 fair (I suppose) employs pages 201 and 202 in explaining the method 

 used by the Greeks, for the extraction of the Square Root : and this pre- 

 cedent will, I hope, be a sufficient justification of me for employing so 

 much time upon the present subject. 



(8.) For this purpose it will be necessary to have a general demon- 

 stration of the extraction of the Roots of all powers, and as it would 



