318. 
sion, namely, that the difference be- 
a A, Daneel 
and ———is 
. 1—1 i—1! 
be in direct violation of common sense, 
but I will only ask, how you make the 
tween 
, though, it 
fraction 
ai for though» I do not 
deny this equality, yet, if you admit it, 
¥ think you must likewise admit that the 
series 1—1+4-1~—1+-1—1, &c. ad infin. 
: ’ —1 . 
18 sal; for if = its equal 
ii 
ot 
will also=1; but 
1—1x 
(vide your 29th proposition) 
1 
— = 1+1-+1-+1 
a = 1414141, 
1 
&c. ad infin. therefore 11X77 = 
1—1 (14-141+4-1, &c. ad infin.) that is 
= 1—141—1+1—1, &c. ad infin. as 
thus appears: 
1+-1+41-+41, &c. ad infin. 
1—1 
1+41+-1+41, &c. ad infin. 
=—1—1—1—1, &c. ad infin. 
4—1-+-1—14-1—1+4 1—1, &c. ad infin. 
therefore this series is also =1, but in 
your first prop. you obtained this series 
— 
“vi+1 
strous absurdities you are led by your 
own accurate reasoning in the “ Ele- 
ments of your True Arithmetic.” 
What I have:said will, I think, be am- 
ply sufficient to shew the fallacy of your 
reasoning, in this your work of boasted 
accuracy. J cannot, however, refrain 
from adding a few remarks on your ninth 
proposition, which is thus enunciated. 
“© Numbers connected together by an 
affirmative or negative sign, are dif- 
ferent from the same numbers when ac- 
tually added together, or subtracted, ond 
expressed by one number!” Had this 
proposition been promulgated by any 
ordinary person, I should doubtless have 
considered it as the effect of folly or 
madness; but, as proceeding from one 
who holds a respectable rank in the re- 
public of letters, I would willingly at- 
tribute it to some other cause. Sin- 
gularly strange and ridiculous as this 
Proposition must appear, its demon- 
stration, however, is, if possible, still 
more absurd; it begins by stating that, 
© 441 is not the same as 2; for 141 
subtracted from 2 leaves the infini- 
tesimal 1—1,” Now, sir,. allow me to 
x 
3; see therefore to what mon- 
Remarks on Taylor's Elements 
[May 1, 
ask you, in taking 1-1 from 2, did you 
obtain the remainder 1—1? You have 
carefully concealed the. modus operandi, 
for, if you had not, the absurdity of your 
attempt at demonstration would have 
been most glaring; since you could only 
obtain the remainder 1—1 by actually 
subtracting the first term of 14-1 from 
2, and by only denoting the subtraction 
of the last term, by putting it down with 
the minus sign or — prefixed: now, upon 
what principle could you, in subtracting 
a number which consists of two parts, or 
members, from another number, actually 
subtract the first part, or member, and 
only denote the subtraction of the other: 
part, or member, by connecting it with 
the sign —or minus, with the result of 
the actual subtraction of the first mem= 
ber; when, in the very words of your 
proposition, you assert, that numbers. 
connected together by a negative sign, 
are different from the same numbers when 
actually subtracted and expressed by one 
number? What a “ splendid instance,” 
have you here exhibited of the accuracy 
of your reasoning ! What, sir, in future 
will be thought of Thomas -Taylor, the 
Platonist 2 Of Thomas Taylor, the trans= 
lator of Proclus on Euclid ? Of Thomas 
Taylor, the admirer of Grecian geometry ? 
OF Thomas Taylor, who boasts himself 
the vindicator of the very scientific aca 
curacy of the ancients? Of Thomas 
Taylor, who, in the Elements of his True 
Arithmetic, reasons thus: “1-4-1 is not 
thesame as 2; but sir Isaac Newton, in 
all his researches, both mathematical 
and philosophical, reasoned on the sup- 
position that 1-4+1 was the same as 23 
therefore, the results of sir Isaac New= 
ton’s researches are a mass of errors and 
JSulsehoods; and Newton himself, was 
not only a man of a “ rambling and pre= 
cipitate genius, but a perpetual blun= 
derer?” I am fully aware, that, in an- 
swer to these questions, you will say, 
that you are perfectly indifferent to, the 
Opinions of others, both with respect to 
yourself and your works; for that you 
“ have long since Jearnt, from the school 
of Pythagoras, that the praise or re= 
prehension of -the stupid, is alike ridi- 
culous.” Highly as I applaud this truly 
philosophical indifference, yet I must 
say, that, howevep regardless you may be 
of your own .reputation, you ought at 
least to possess some little respect for the 
reputation of those ancients, whom you 
so frequently and so ardently profess to 
venerate and admire, I entreat you, 
Tee EUR) 
