820 
to the monks, and proofs of the obliga- 
tions we are under to the religious orders, 
ought not to be passed over in silence. 
«* T wish not,” he says, ‘* to shock the pre- 
sent manner of thinking on this subject, nor 
to undertake the defence of monkery. There 
were, it. must be allowed, abuses in the 
monasteries; but what human institution, 
even those of philosophical or literary socie- 
ties, is always freed from them? Abuses are 
like the ivy, which will at last cover old build- 
fngs, or diseases which destroy the human 
body. Tallow it to be right and necessary to 
reduce these institutions extremely, and to al- 
low in them only an easy and honourable sub- 
sistence, and by public authority the chains 
of the unhappy victims of ignorance, of youth, 
of family ambition, might have been broken. 
But was it necessary to drive back into the 
world, with a pitiful pension, cut to pieces a 
thousand ways, and oftentimes refused, a 
erowd of old men who, on entering into the 
world, must be a prey to misery or death? A 
few years would have put an end to their con- 
vents, and the reservation of twenty or thirty 
houses, as asylums for them, in such an im- 
mense territory, could not have been an ob- 
ject for envy or finance in a great and. power- 
ful nation, pridipg itself on generosity and hu- 
mianity.” 
, The history of algebra is extremely 
well given, and due respect is paid to the 
memory of Vieta; yet with all the wish 
to detract from the merits of Harriot, 
«nd to shew the errors in the account 
given by Wallis, the author does not 
seem to have been conscious himself of 
allthe worth of hjs countryman. Vieta 
discovered the fundamental property of 
equations, or the nature of the co-effi- 
cients: he did not carry it to tne whole 
extent of the. proposition; but, on the 
other hand, he did not divert into any 
error. ‘The property discovered by Vieta, 
and demonstrated by him in the case of 
certain equations, was’ said to. be made 
veneral by Harriot; but in thisgenerali- 
zation a strict regard was not paid to 
truth, nor to the rigour of mathematical 
demonstration. Vieta could. not have 
‘made the discovery of Harriot, because 
he could not have allowed of the expres- 
sion of negative, or false, or impossible 
roots; nor could he possibly have seen 
or allowed that such a root could enter 
into an equation. Where an equation 
really does admit of more roots than one, 
‘he shews the order of the co-eflicients as 
far'as he has considered the equations ; 
and if his successors had followed him in 
ihe same track, they would, like him, 
fave delivered only trath, and’ not have 
MATHEMATICS AND NATURAL PHILOSOPHY. 
led their disciples into inextricable laby~ 
rinths. We are willing therefore to allow 
to Vieta much more than his countryman 
has done, for science is of no. country ; 
and of all men in the world scientific men 
have little reason to boast of country, as 
their history is a proof of the little value 
set upon their labours when living, what- 
ever boasts they may afford to those who 
scarcely will or can read their works 
when dead ; and we allow also to Vieta 
the praise of leading the way by his py- 
ramidal numbers to the famous bino- 
mial theorem, generally though impro- 
perly, and even by Montucla ascribed to 
pit toe Newton. 
e may observe that in the history of 
algebra, as well asevery part of the work, 
this edition is much improved by the in- 
creased number of writers quoted on 
every subject, and we might add, that 
this is a very considerable part of the 
merit of the work ; and we should have 
been under greater obligations to the 
successor of Montucla, it by a copious 
index he had rendered the access to every 
fact, discovery, and writer easier than it 
is at present. ‘The book will be possessed 
by every mathematician of eminence, and 
must be considered by him chiefly as a 
book of reference; every thing therefore 
should have been calculated to increase 
the utility of the publication. 
The interesting history of fluxions, 
from their disputed origin to the great 
improvements made in that part/of sci- 
ence, is detailed with great accuracy and 
perspicuity; butweregretted thattheworks 
of La Grange, La Croix, and Arbogaste, 
could not have been sufficiently examin- 
ed by this industrious writer. The pres 
sent is an interesting period for the doc- 
trine of fuxions: the French writers are 
taking bold steps; but, im general, in 
adopting new methods, and aiming at 
generalising their ideas, they rum into a 
degree of obscurity which is not easily 
penetrated by those who are fond of the 
ancient mathematical precision. The im- 
portant question on assurances, in which 
so much has been done in this country, is 
not noticed with the attention it) me+ 
rits. ‘Phe works of Priceyand: Morgan, 
and Maseres, are indeed mentioned, but 
the extent of their discoveries is no? pro- 
perly laid before the reader, ir) fy tind 
In optics the former work is much im- 
proved ; but it is evident thavthe com- 
pletion of this part lay with the editor of 
the two last volumes. Newton and Here 
sche! here meet with: deserved praise; 
