7796.) 
put 7s=AB=1600, 7==BC==1k00,) s== ad 
==AC==2500, w=tang. angle AOD or 75° 
é=tang. BOD or 72°, c==tang COD or ae 
and xo=the common perp. OD. Then 
trigonometry, as Liai:x:ax==AD; in like 
manner is BD==)x, and CD==cx. Again, as 
AC (G) : AD-LCD (ax-er) :: AD—CD 
(ux—cx) —— 2 SAP CEs andein like 
Bo : BD4-CD :: BD—CD : 
=BF—CF ; the difference of thefe 
Qa Fn (2-2), 
two gives AF-—BF=AB=7== 
b2x2@ 02.42 
— from which 

manner as 
b2 x2 2.472 

7 

wooce poe 
$ 
eq uation we 

have 

==887°53 yards, the per- 
eee 

pendicular height of the balloon as required. 
Scholium. The theorem above given, may 
be of confiderable ufe to determine the height 
and diftance of a cloud, a meteor, or other ob- 
jects in motion. 
IN. B. Shlutions to Queftion AIL, by Mr Fe 
F. rrand Mr. 7. H, are deferred ull our 
next for want of rooms 

ee 
New MATHEMATICAL QUESTIONS, 
To be anfwered in No. Vill, the Mag. for 
September. 
QUESTION AVIL—By Mr. 0. G. Gregory, of 
Yaxley. 
THE dimenfions of a cylindrical tube are fuch, 
that, having a plate of tin at one end, with an 
aperture in its centre, the other end hehe open 
and turned towards the heavens, the field of 
wiew it takes in, is one twentieth of the hemi- 
{phere :-——The young perufers of the mathemati- 
cal part of the Monthly Magazine are requefted 
to find the internal diameter of this tube, the 
jength being one foot eight inches ? 
Question XVIII.—~By Mr. E. Warren. 
Given the difference of the times of fun-rifing 
at the top and bottom of a mountain, fituated 
in a given Jatitude, and on a given cay 5 ; to de- 
rermine the height of the mountain ? 

New Mathematical Queftions. 
SEER PIS Pon 
477 
Question XIX: By: Philalethes. 
Of feven numbers, in a continued geometrical 
- progreffion, having given the fum of the twa 
leaft ==yo, and the fum of the two gregteft = 
281250: to find the feven numbers ? 
%% The folutions F the abowe gueflions mul be 
fent, at the dateft, in the firff werk of Sept-mber; 
but the fooner the better. nd all Commiutvic.tions 
mult be foft paid, and direSed, For.the Mont’ ly 
Magazine, at Mr. Johnfon’s, Boosfeller, St. 
Paul’s Church Yard, Rondon. 

pF mee 2 
ERRATA: P. 394, col. a, Lory for read 
Hid 72 mann /}2 
72 mene jy? , oe 
-—... Ib, line r3- from the bottom, for 371—= 
r2t.72 a 
€d yead, 374==C 7... Pa. 396, cols 1,(1 7, for 
ABFx, read ABE 
Pa. 213, col. i, bh 24) from the: pour for 
atx and a—b read x aie and x-—4 
[Pn 2.13. col. His 1. 25 for proper ee propofed. 
[b. col. it, 1. 3, for guadratures read quadrazics. 
Pa. 304, cul. i, 1. 1r and 12, read, that is 


nad 2 
N—iNx ue Ne,” cc. "Pi 205..col. 1, 1. 25 
ae? 
FI 2a 
read «13 $587 X 4-=4'32674,the value,” é&c- 
3078 
2n BA Ga Dia Dea ees 
Ib, colo, 25, for —— 
a | aa Te 
30(1——1:) — (2 j m2 x 
P. 393, col i, 136, for “ fee do you,” read 
65 fem ta? Tb, coleai. 1. 44. for “ fummonea* ? 
read ( (ummed”? Ib. col. ii, 1. 47. for “parts?” 
1 read ‘© points.’? 



2 FeLi 2 
P, 394, coli, 1. 28 1 Lip) 
te) 2 Den tsyie 
A “ph ae 
: yo 
P, 395, col. i, 1. go, for 34/— ~ read 3 Ve 
a 
Tb coliyng. i 38 for han read. then. 
NB. For want of room, we have this month 
het. Se AW aa At i flat ORR GALT : : o 
been compelled fo ag er (Re COMMUN Cation relative 
to Mr, Frend’s P: runciples of algebra. We are 
oblized, a9) the quriter >and Als favour shall certainly 
ae Im our Text. 

ANECDOTES AND REM At NSA ‘ 
EMIN ENT 
[This article is devoted to the ee of Bio 
et 
PE Kn S 
ONS 
ograpbical Anecdotes, Pc apers, Letters, Se. and. 
awe requeft ibe Communications of fuch of our Readers as can affift us in thefe objects. | 
ANECDOTES oF PERSONS CONNECTED 
WITH THE FRENCH REVOLUTION. 
| Continued from cur lafi.| 
MoncGE, 
RIGINALLY a fone-cutter at 
Mezieres, in Champagne, became 
a mathematician of fome celebrity, in 
confequence of the liberality ef the Abbé 
‘Boffuct, and minitter of the marine, on 
the recommendation of Condorcet*. He 
was an honeft and virtuous, but dull and 
plodding, 

* “ On ne favoit qui mettre a la marine; Con- 
dovcet parla de fl idonges farce quill Pavoit us 
refimdre des froblémes de géondtrie a V dcadémie 
7 
aes 
