18t1.] 
’ 
number of terms, the product will be 
double the sum of all the series.” 
‘* In the series of squares 0-+-1-+-4-+-9 
4-16, &c. infinitely continued, the last 
term being multiplied into the number 
of terms, will be triple, to the sum of all 
the series.” 
“«Tn the series of cubes 04-1-+-8-++27 
+644-125, &c. infinitely continued, the 
last term being multiplied into the num- 
ber of terms will be quadruple the sum 
of all the series.” 
What other reason, Mr. Saint, can be 
assigned for your omitting to notice this 
discovery of mine, than a conviction of 
the truth of it? 
You will find your next objection 
answered in the 29th propositicn of my 
treatise, if you read it with attention ; 
and I shall therefore proceed to your last 
remark, You ask me “ how in taking 
1+1 from 2, I obtained the remainder 
4—1.”. It was as follows, Mr. Saint, 
From 2 
Subtract. 141 
Remainder is i—1 
' Memoirs of the late Paul Sandby, esq. 
457 
Ts not the subtraction lawfully made ace 
cording to the algebraic rule for sub- 
traction? AndTI also add, is it not ac 
tually made? For there is no other 
way of actually subtraeting +41 from 0, 
than by changing the sign, At least this 
is acknowledged to be the case by all 
modern writers on algebra. Now, Sir, 
if the expression {—1 while it remains 
in this form, and no actual subtraction 
is made of 1 from 1, is an infinitesimal, 
which I have abundantly proved it is, 
it most clearly foliows that 1—1 while 
it remains in this form, and one unity is 
not-actually added to the other, differs 
from the aggregate 2 by 1—1. 
And now, Sir, I shall conclude with 
thanking you for the opportunity you 
have afforded me of vindicating my Ariths 
metic of Infinites, and also for the com- 
pliment you bave paid to my heart; but 
it would have been better, if, in doing 
it, you had not run. your head against 
mine, as I am afraid it has injured 
yours. Tuomas TayLor. 
Manor Place, Walworth, 
May 7th, 1811. 
yA A SR ES ARES eS arte oan an —| 
MEMOIRS AND REMAINS OF EMINENT PERSONS, 
. MEMOIRS OF THE LATE 
PAUL SANDBY, Esa. R.A. &c. &c, 
HOUGH the subject of this Me- 
— moir has left behind him that, 
which will, in time to come, distinguish 
him from the common dead; a_ few 
facts, relating to an individual, whose 
long career and exertions of eminent 
talents, have been a public good, will, I 
presume, be acceptable to the numerous 
yeaders of the Monthly Magazine. 
Mr. Paul Sandby was born in Not- 
tingham, in the year 1726, and came 
to Loudon at the early age of six- 
teen; was, svon after placed in the 
drawing-room in the Tower, (instituted 
for the purpose of instructing persons 
in drawing military plans, &c.) and 
from thence he was selected to attend 
the survey of the Highlands of Scotland, 
(as draughtsman) then carrying on under 
Colonel: David Watson, and which 
took place soon after the rebellion in 
1745. 
As circumstances are the great go- 
vernors of men, and may in most in- 
stances be said to be the makers of 
. them; perhaps, the destination of Mr, 
Sandby to the Highlands was the source 
of his eminence as a landscape painter, 
at least in the formation of his pecu- 
liar style, as, though he there saw na- 
ture in her wildest form, the necessity 
under which he lay of attending to 
particular accuracy in filling up the 
plans, may be supposed to have formed 
in him that curreet and faithful habit, 
with which he after viewed and deli» 
neated her. 
It is now too late, (except perhaps 
from his intimate connexions,) to learn 
how he passed his early days, or under 
whose superintendence he received his 
education; but from the respectable 
and ancient family from whom he 
sprung, and his personal and mental 
acquirements, it was evident that he had 
been carefully attended to. The cire 
cumstances that led to his professional 
excellence are more our immediate en- 
quiry, and more interesting to others, — 
and to those especially who are to fole 
low his pursuits in art. 
In the life of a painter little variety . 
is to be looked for; the next day being 
but a repetition of the last, and the 
succeeding one varying only as he creeps 
on towards perfection, Mr. Sandby, 
however, 
