525 
Dr. Hutton’s Course of Mathematics. 
teachers themselves, whilst they will form in the honA fide student 
a regard for good order, a judicious discrimination between different 
methods of operation, that cannot fail to be of the utmost future use 
to him. The almost universal use of Hutton’s Course both in pri- 
vate schools and by private students, therefore, will be rendered 
still more conducive to the general diffusion of good mathematical 
taste, by the publication of the present appendage to it. 
We have not space to enter into an analysis of the contents of the 
551 pages contained in Mr. Davies’s work — filled, as it is, with ori- 
ginal views on every branch of elementary mathematics. The author 
has even touched in various places on the matter of scientific history, 
and we value this innovation as much as any. How preposterous is 
it to despise the labours of our predecessors in whatever field of li- 
terature or science we are labouring ! As this portion of Mr. Davies’s 
work is more immediately open to criticism than any other, perhaps 
it will not be considered irrelevant if we devote a few lines to its 
consideration. 
The author’s observations on the middle-age abacus are sensible 
and valuable. The change between the manual abacus and the 
membranaceal tablets is, indeed, easily conceived ; and in all proba- 
bility was transferred in that manner to the Arabian system of com- 
putation. “ Though this mode of notation,” as Mr. Davies observes, 
may never have been necessary, and very rarely employed by chro- 
niclers and other persons merely literary, it would be of extreme 
value in the •performance of computations. Amongst these expedi- 
tion would be of great consequence, and this would often be facili- 
tated by writing the symbols in ruled columns, instead of placing 
the dice upon the abacus. This, again, would lead to running the 
several component letters of any one number into a single and con- 
tinuous figure, which would represent the number.” We must, 
however, observe, in all this, that we prefer facts to wholesale con- 
jecture, however pretty and ingenious this last may be. 
The derivations of the signs + and — as given at pp. 11, 13, 
are, we think, very improbable, and show that the late Professor 
Rigaud and Mr. Davies, who have worked together on this subject, 
are not well versed in ancient handwriting. On a point of this na- 
ture, where the subjects in dispute were introduced five centuries 
ago, it is necessary, we humbly submit, to take into consideration 
the mode of writing at the period, — ^if, indeed, the symbols are not 
altogether arbitrary, — -and not reason on the et and the P of the 
present day, as if our rough-Avriting were the same with that of the 
Italians in the fifteenth century. We are sorry to speak dispara- 
gingly of what we infer to be a favourite theory with our author, but 
its very improbability is quite sufficient to bring with it a condem- 
nation, and perhaps might eventually have done so from less mer- 
ciful critics. 
We beg our readers to study attentively the various remarks 
tending to the completion of the new method of solving numerical 
equations. The method of synthetic division, which forms the basis 
of that process, is here developed at length, and traced to the com- 
