126 
‘pofition from which we set out is in- 
volved. in this improbability. If, there- 
fore, these several sets of readings be 
really found in the MS. 2, the probabi- 
lity of its being the de eee ae the 
MS. x, or, in other 
2, are only two diferent names of one 
and the same thing, 1s to the probability 
pmentrést &c. 
ay ee Eg 

‘of the contrary, as 
—itor QE.D, 
Corollary 1. “As the number of read- 
ings in any one set increases in arithmes 
tical | progression, the number of collated 
MSS. being given, the probability of 
again finding th 108e Teadings In any one 
manuscript decreases in geometrical pro- 
gression, of which the: common ratio is 
the first.term. For the probability of 
finding 4in the MS. 3, as appears from 
. ; 6 I 
the preceding demonstration, 1s — , that 
CA Tact ahacn a, 
I = 1° 5 
~,» &c.: again, the probability of finding 
P 
Pee is f 5 
a, is—, that of finding a and B, is 
2 
2 £ 3 . 2% : 
5? of finding A, B, andT, —,» and so 
on. 
Corollary 2. The probability, there- 
fore, that two supposed different manu- 
scripts are one and the same, imcreases 
in geometrical progression, as the num- 
ber « of the readings of each set, in which 
they coincide, increases in arithmetical 
progression. ‘This corollary immediately 
rollows from the preceding: for whatever 
ES expresses the probability: of not 
finding chese sets of readings in the MS. 
3, on the supposition that it is not the 
same with the MS. x, that same ratio 
will be transferred to the supposition it- 
ec as soon as exberience has determined 
hat the expe€tation founded on that sup- 
oo is false. 

Lo the Editor of the Monthly Magazine. 
Scns ie 
O*% reading over the letter of A. 
Search, on the principles, taken for 
granted, in the present mode of finding 
the roots in equations of the higher 
dimensions, the discovery, lately made in 
Germany, on some properties of zorhing, 
came into my mind, which a; ppeared to 
me a! be as useful in the coétrme of 
4 
Mathematical Correfpondence. 
words, that ® and - 
[March 
fluxions, as the other principles are in 
algebra. In asmall mathematical treatise, 
printed at Munster, in the year 1793, 
under the title of Tentamen circa princi- 
pia calculi, qui recepio nomine diferenti- 
alis audit; it is clearly proved, that no- 
thing may be equal to something else be- 
sides unity. T hus, in England, our ma- 
thematicians are content with making no~~ 
thing, divided by nothing, equal to unity : 
that 1s, 1--a divided by 1—w, is equal 
to unity, when # is equal to one; but 
our author says, it may be equal, not 
only tounity; but tow, and to #7, and 
to #3, and to 24, and 34%; and I am 
very much inchned to believe him, 
For if nothing ues by nothing, ‘can: 
produce unity, I do not see why, in other. 
circumstances, it may not generate any 
other quaatity. ‘The powers of nothing, 
believe me, Sir, are as great among the 
mathematicians, as those of zobody in 
every farm-house, in letting the pigs run 
Into the garden, the cattle out of the - 
5 
marsh, and in many other actions with 
which people, used to rural affairs, are 
very well acquainted. 
Besides, nothing divided by nothing, 
may clearly be equal to more than cne 
quantity ; for I have heard, I think, of 
some famous mathematician, a Fellows, too 
of the royal society, who has proved that 
one-halr may be equal either to nothing 
or infinity ; that is one half of a quantity 
_is equal ‘to one, either infinitely great 
or infinitely small. Who can doubt this, 
when it is set down upon paper, with ~ 
all the a of mathematical demon- 
stration >. So 1—a‘? divided by 1-4? = 
ity 1s 
—— KX — =H teatea*t2x34 &e. 
I= 
i+% 
mult iplied 1 into 1—24-+247—2473+2,7% 
&c. in which you may see, with half an 
eye, that there is one infinite series mul-. 
tiphed into another ; and the first infinite 
Series, is evidently an infinitely great 
quantity, when « 1s equal to unity, and 
the other infinite series Is equal to o, 
The produ&, therefore, of the two series, 
is 1-F2r, muitiplied into 03, bus an inti. 
nitely great quan tity multiplied into o, 
is equal to. 1; thereiore 2r%o=—=2, thati 
i—~+” 

= 2, ang T have not the lease 
a7 7 ; % 
doubt of making — =» when # isequal 
I 
is, 

——4 
to one, equal to two hundred or two- 
thousand. 
And now, Sir, if any of your readers. 
should be tempted to think, that the de- 
monstrations of the learned German, and 
eur 

