Sit 
scription of people, which I apprehend 
“to he certain fact, I. make so doubt 
but that, combined with other unknown 
causes, it is of no small consequence in 
producing alterations of the weather. 
dt appears therefore to be wisely ordered 
that in the moon the effects on the earth’s 
great attraction should be always ucarly 
the same at each particular place; and 
it may probably be a principal cause of 
the constant serenity which seems to 
take place in the lunar atmosphere. 
. Joun ANDREWS. 
Modbury, March 8, 1811. 
a 
For the Monthly Magazine. 
°REMARKS on the ELEMEN'S of the TRUE 
ARITHMETIC Of INFINITES, by THOMAS 
Tayton (the Platonst) ; in a LETTER 
to the auTHor, by w. saint, ad- 
dressed to THOMAS TaYLoR, ESQ. of 
WALWORTH. 
Norwich, March 4, 1811. 
sIR, 
%7 OUR “ Elements of the True Arith- 
‘metic of Ininites,” having acci- 
dentally fallen into my hands, I was 
anxious to see in what manner you had 
treated this subject, not only on account 
of your professed admiration of the sci- 
entific accuracy of the ancient mathema- 
ticians, but from the vaunting style in 
which you seemed to exult over the mo- 
derus, even in the very title page of 
your performance: I therefore eagerly 
applied to your book with the confident 
expectation that I should be made ac- 
-quainted with the true “ nature of infi- 
nitesimals,” and that I should find that 
‘you had treated this curious branch of 
mathematics in the most unexception- 
abie manner. Judge then, Sir, of my 
surprise when, instead of that divine ac- 
curacy, that logical precision, that lumi- 
‘nous arrangement, for which the wri- 
tings of the ancients are so pre-eminently 
dsstinguished, I met with. nothing but 
absurd premises, confused reasoning, and 
false conclusions! 
T can scarcely hope to convince you, 
‘Sir, that your peiformance abounds with 
errors and absurdities; but, as you have 
evinced an almost unexampled degree 
of boldness, not to say arromance, even 
“in the title page of your work, by decla- 
‘ring therein that you have * denzonstrated 
all the propositions in Dr. Wallis’s Arith- 
metic of Infinites, and also the principles 
of the Doctrine of #luxions, to be false,” 
LT think it but right to convince others, 
or at least to attempt to convince them, 
‘that, however juss your pretensions may 
Remarks on Taylor’s Elements 
“ay 
[May & 
be to an accurate knowledge of the an« 
cient philosophy, or to an intimate ac 
quaintance with Pagan theology, your 
claims to the higher honor of refoting 
Wallis or Newton have no foundation, 
except in the ebullitions of your own 
vanity. 
Now then, Sir, to the point: Fam 
ready to grant your three first postulates, 
though I cannot help rematking, that, in 
a work abounding with so many preten- 
sions to perfect accuracy, it would have 
accorded better with those pretensions, 
if these postulates had been preceded by 
definitions of the terms addition, sub- 
traction, division, &c, more particularly 
as you appear on sume eccasions to have 
used these terms in a sense differing from 
that in which they are commonly re- 
ceived. Your fourth postulate, however, 
I by no means so readily grant; it runs 
thus, ‘* Thatto multiply one number, or 
one series of numbers, by another, is 
the same thing as to add either of those 
numbers, or series of numbers, to itself, 
as alten as there are units in the other.” 
Now, to say nothing of the absurdity of 
cal,ing this a postulate, which is, in re= 
ality, a definilion, I do not believe that 
it conveys even your own meaning, for 
surely you will not say that 3 multiplied 
.by 2 is the same as 3 added twice to it- 
self{—for 3 added once to itself makes 6, 
and if added twice to itself it will make 
9; andI cannot think, Sir, that you meant 
to say that S multiplied by 2 is equal to 
9. Moreover, Sir, I beg to ask you what 
you can mean in this postulate by a 
*¢ series of numbers,” unless several or 
many numbers connected together by 
the sign plus or minus? And if so, I 
will further ask you how the units in 
either series are to be ascertained, (for 
the purpose of kuowing how many times 
the other series is to be “ added.to itse/f” 
to produce the product), unless by an 
actual summation of that series, that is 
by collecting its terms into one sum ac- 
cording to their signs? Now if you had 
to multiply the series i--i+1-+-1, Xe. 
ad infinitum by i—~1, since you have 
asserted in the corollaries to your first 
proposition that 1—1 is that “ which 18 
neither quantity nor nothing, but which 
is something belonging to number with 
outbeing number.’ You would thus have 
to add the infinite series 1+-1--1--4, 
&c. to itself, as many times as are de= 
noted by that which is neither quantity 
nor nothing, but which is something be- 
longing to number ,without being nam= 
ber.” In like manner, Sir, to. muluply 
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