556 Analysis of Books. {Ocr. 
2r 
this kind, hit upon a convenient formula such as m +igias Though the 
m+ 1 
formula, when found, appears simple, yet the difficulty of actually finding it, with 
their limited means, must have been very great. It was like the Druids elevating 
the immense blocks of Stonehenge without mechanics. Most probably it was 
discovered by long and laborious tentation. 
The author then discusses the effects of assuming as the approximate square 
re% 
2mz2+1 
to the Arabs, we omit, and shall sum up the whole in his words— 
“We may hence form some judgment how much the old arithmeticians must have 
been perplexed and retarded by the labour of long multiplication. We, who enjoy the 
benefits of the great discovery of Logarithms, can now scarcely form an estimate of the 
difficulties with which they had to conteud from this want, and the facilities which we 
enjoy from their use. While, therefore, the Arabian method of extraction may inspire us 
with more gratitude to Lord Narrer, we must not too hastily condemn it as uselessly 
laborious, till we can show that, without a knowledge of his discovery, we could have 
more happily succeeded in the facilitating and abbreviation of calculation. Should, after 
all these considerations, the intention of the Arabian operation be thought of little value, 
and the labour employed to accomplish it misused, yet the artful contrivances by which 
it is attained, and the skilful adaptation for this purpose of the simple principle of the 
variation of the signification of symbols from the variation of their situation, must, I 
think, in justice, always cause the Pulpit Diagram to be considered a deserving monu- 
ment of Arabic ingenuity.” 
The Author concludes his essay— 
“With an acknowledgment of my obligations to my very intelligent friend Dewan 
Kanu JzEE of Patna ; by him I was furnished with the extract of the Ayoun-ool-Hisab. 
His treatise of Arithmetic formerly mentioned*, and his oral explanations enabled me 
to comprehend the obscure and studied brevity of the Arabian Author ; and from the 
same sources I derived those observations on the fractional part of the root which form 
the basis of the concluding paragraphs of the present Essay.” 
The treatise of Arithmetic here alluded to, and named by its author, the Khiza- 
nut-ool-Ilm, is described in vol. xiii. of the Researches, p. 466. It is avery large 
work, consisting of three parts : first, anaccount of Arabian Mathematical Science ; 
next, of that of the Hindus, and lastly, as much of the European as the author was 
acquainted with. The whole, we are happy to say, is in the course of printing by the 
Committee of Public Instruction, and will, when complete, form an invaluable store 
of information respecting Oriental Mathematics. 
The European part of the Khizanut-ool-Ilm consists of two sections: first, a 
complete translation by the Dewan of Bonnycastle’s Algebra; secondly, an extract 
consisting of acollection of Geometrical Problems from the papers of the celebrated 
Turuzzoou Hosain Kuaun of Delhi. This person during his life, was considered 
we believe, the best Mohammadan mathematician in India, and he appears to have 
employed his time in translating European mathematical works into Arabic ; after 
his death, which took place some years ago, Government, we are told, made strong 
efforts to obtain his MSS. but in consequence of legal disputes between his rela- 
tions these were unsuccessful, and the fate of the papersis probably not known. It 
is much to be wished that they could be procured. 
* See Essay on the Binomial Theorem, vol. xiii. of the Researches, p. 466. The Dewan here men. 
tioned is since dead. 
root the formula m + in which z is indefinite ; but this, as foreign 
