1797.] New Queftions....Original Anecdotes.—Colanel Frederick. 132 
al Sia 

geometrical mean 4/ ab; the {quares of which are Now, if it be poflible, 
4 
let thefe two be equal, or a?-L-2ab+-?==4ab : fubtract 4ah from each, fo fhall a?—24b-1-b?=0 ¢ 
confequently, its root a—b—=0, and a==5; that is a lefs number equal to a greater, which is 
abfurd. In like manner, if it be faid the arithmetical mean is the lefs of the two; then 
a*t2ab-s? is lefs than 4ab, and a*—22b-|-5? lefs than 0, or nothing, or the fquare a—bi? nega- 
tive, which is abfurd. Confequently, a*-24b-+-b? is greater than 4a, or the arithmetical mean 
greater than the geometrical, 


New MatTHEMATICAL QUESTIONS, 

Question XAVI.—By Hermes, of Bath. 
Required, an eafy method of finding two numbers fuch, that each of them, as well “as theit 
{um and difference, being increafed by unity, fhall, in all the four cafes, be fquare numbers ¢ 


QuEsTION XXVIL——By Mr. T. Hickman. 
Given x?y-lLxy?=7y 
ae 8 I 
-and —|—==) ; 
x 
to find x and y by fimple equations ? 
* 
% 

~ Query (to Mechanics) fy 4Z YX, of Oundle, Northamptonflire. 
There are certain inftruments ufed by clock-makers, and others, for the purpofe of opening of 
enlarging holes in metal plates, &&c. called roaches ; they ae made of a pyramidical form, with 
four or five fides.—How comes it, that the four-fided broach makes a five-fided hole, and that the 
five-fided broach makes a round hole ? 

ORIGINAL ANECDOTES AND REMARKS 
OF 
EMINENT PERSONS. 

Memoirs OF THE LATE COLONEL 
FREDERICK. Communicated by a Gen- 
ileman who knew bim many Years, and 
accompanied with a Charatter of himfelf, 
drawn up by bis own band. 
OME men feem defined from their 
Y early infancy to become the {port of 
fortune, and every thing about them ap- 
peers involved in paradox. This is pre- 
cifely the cafe with the fubje& of thefe 
Memoirs ; and thofe who have known 
him during forty years, find themfelves 
at this moment utterly incapable of a 
fatisfa€lory folution of the enigma. In 
fhort, the birth, life, and even fome cir- 
cumftances attending the death of Colonel 
Frederick, are myfterious; and in treat- 
ing of thefe particulars, a candid and 
liberal man muft confefs, that he is only 
prefented with a choice of difficulties. 
The ‘writer of this fhort narrative, 
who became acquainted with him at an 
early period of his life, formerly heard 
from a perfon of title, who had refided 
long abroad, that he was originally a 
 Polith Jew; but he has many reafons 
MONTHLY Mac, No. XIV. 
Me 
to difhelieve this, and fufpeéts, that it 
was fabricated in malice, the-refult of a 
petty altercation. A refpeétable general 
officer, who lived long in England, and 
who fome years fince retired to Swiffer. 
land, his native country, folemnly af- 
ferted. that he had converfed with an 
acknowledged daughcer of Baron Neuhoff, 
commonly known by the name and title 
of Theodore, king of Corfica, while re- 
fiding in one of the Spanith convents for 
noble ladies ; and he was affured by her, 
that her father had no legitimate child 
but herfelf; fhe added, that the Colonel 
muft, therefore, either be an impoftor, 
or a baftard. Some obfervations were 
made, at the fame time, refpecting the 
age of the parties, whence it was infer- 
red, that the: fuppofed faét was ime 
poffible. 
Since his death, a rumour has alfo 
been propagated, that he was an Ex-ca- 
puchin, who, efcaping from a convent in 
Italy, repaired to England; and finding 
the fenfibility of the people affeéted by 
the melancholy end of Theodore, he, by 
§ ~ Means 

