430 Frratum in My. Frend’s Letter correéted. [ Feb, 
ahs 2grn 
yi a r-5 stem? rb : 
ga, the ordinate FL; and 1,14/t—y?: i 2: cmag/1—j LC, hence ¢—.—a4/1—y? th® 
abfeiffa AL. , 
Shooter’s Hill, Dec. 9, 1796. _ & Draconis. 
eee Se 

ting x ‘as found above =a, and 

ry We get Tipiieemes yes 
To the Eaitor of the Monthly Magazine. 
SIR, 
1 TROUBLE you with this, to requeft you to infert the following correction, requifite to make 
page 39 of your laft Number, as far as it relates to the equation fent by me, mtelligible. Your 
fompofitor has leit out fome part of what I wrote, and difterted the other ; juft as if, m writing a 
euvtation from the Hebrew, he had contrived, like a learned bifhop, to print it without any re. 
gard to the neceHary tran{pofitions, in printing a language read fo differently from ourown. There 
cannot be a greater miftake, among the printers of mathematics, than that which is too frequent, 
the printing of a folutidn, as if it were common profe, and a man had nothing to do but to read 
on. To fave a little paper, the whole is thus frequently made confufed and unintelligible. Thus, 
im my equation, the thing propofed to be done, was to find the value of y: but no _y appears at 
the conclafion ; and-«, which was only a fubfidiary, is turned intoa principal. A perfon, expert 
im the mathematics, will readily fee where the error lies, and how it may be corretted: for the 
fake of others, you wiil be kind enough to reprint the laft line in the following manner : 
From + = ,266666 
5 
take (== .0012 26 

a y = ,265420 
this value of y is true to fix places. 
By my method of dividers, other numbers might have been affumed for the value of ys and, 
1 
= 8 4. os . : 
inftead of making ——-x=>y, if it had not been to give an eafy inftance of my mode, I fhould 
; ; 
i 8 oar ce ae ep . x G « . 
have made y equal to —- —»x. The reafon for taking that term, in preference to many others, 
301 a 
may afford a little employment to perfens whofe curiofity.is gratified by thefe purtuits. 
; l remain, your’s, &c, ' 
inner Temple. ' W. Frenn, 
Question MXIT (No, X1).—Apfwered by Mr. T. Hickman. 
Ow the indefinite line AB, take AC and CB=the given quantities ; then Ep 
a 
on AB, asa diameter, defcribe the femicircle AEDB, and perpendicular to 
AB draw the radius FE, and the ordinate-CD. Then it is well known that 
CD is the geometrical, and FE the arthmetical mean, between the cwo 
quantities AC and CB; fom whence it is evident, that the arithmetical al- <A! C B 
ways exceeds the geometrical me:n; except when the two quantities are 
equal, when the means themfelves are likewife equal. . 
CS memmeed 
The fame anfwered algebraically by the fropofer, Mr. B. W’. 
Let M be the arithmetical, and m the geometrical mean, between the two quantities @ and 65 
a being the greater, and é the lefs. : 
Then a+4=2M, 
Binds abs n2 
Square the former, and multiply the latter by 4, fo fhall 
a2t2abtt—=sMi2, sat 
and 4ab—=4m?. Hence, by fubtra@ion, 
a—2ab+-b?=4M*—4n, 
a—p. 2 = 
or M2—1?=( ora. » which is a pofitive value > 
Confequently, M? is greater than »?, and M greater than m. That is, the arithmetic mean bee 
tween two numbers is greater than the geometric mean. 

The fame otherwife anfwered Ly Philomathes, of Thornbury. 
Let a be the greater number, and & the lefs, Then the arithmetical mean is pas and the 
3 
&eometrical 
