Daily Ohio statesman. [volume] (Columbus, Ohio) 1855-1870, 1867-12-21
THE pUzzLEw,s COLUMN.

We give below a Communication from Sammy
which should have reached Us two weeks since. But
there is no accounting for some of Uncle Samuel's
caprices. The letter is just as valuable this week
however. though received at al earlier date. and
we"take back" our let ture to Samivel of la wee
The convention is foregone conclusion. We
trust that not one of the class will be absent. We
will arrange the programme next week with brother
lnnis' assistance:
CoLLINsvILLE. O.. Nov. 25th. 1857
Mr.. EDIroR:-I am glad tnwelc2me our TWO new
will report often for duty. | am s.rry to see the
tide setting in in favor OF de;ayns the lated rla
ii tue % rest star are s suited don't woader az the ns
poetic eusipns of the boys in view of what is com
ing ght antcipa,ions M Hfsfen isi Of even heAVy
such sights as ou:hful poets tream,
OF feast and pomp and reyelry."
am Obliged to 'elta for q very inte estins letter
from his osn hand Brother Otose says he Is sur,
fdsdn1 miss Il according to the data of 'he ques-
tion IN my copy of the WEtkLY eTATEsMAN In
Perhaps that accounts for the ference in answers.
doa't agree zss. but | suppose the .'onus pro-
scrbed in circle twenty inches eter IA plus
incnes as gave. and drawing another circ around
IN Il viii be IT, same and this gives the
side of the cube. To find the side of the inscribed
multiply ths d~siss S sy so, u tbs qs o
the two sesments according TO the ru winch gave
last summer, this is area OF crescent lwl not n5n
No. a7o-I think brother lose refers to higher
mathematics than ever studied. for his idei OF
circle in orderto get his answer to this beautiful
problem. Ray defiues circle thus: "A D rtior of
plane bounded by q circumference every point Ct
to be plain figure bounded by a curved line. DO !.
and figure they define portion OF plane. &c. III
= the curved line then is ony the BOUNDARY of the
circle the circle must be the portion OF space on
closed by the curve. A fourth OF a rectans is
a q
Of the area contaiued within its boundi curve
Gle CON moi iastIy be cailei an epse but that an
ellIpse is imper ect CIRCLE. For authorlty refer
to Davies aud Robinson an Loomis. VINO say that
th circle may be called elipse whose excentrici-
. tyi zero. infinitely small. When A equals
the equation of the eo becomes the same as that
of the ,ircls, and since in the eliip'e and NAV
be any numbers. the circle becomesa mere case of
the ellipse think Otioss wl!l see that am right.
boy d ought to the das
With the data given propose to show a. the pig
and in reality Impossible. can make a THOUSAND
solutions for it on two false conditions These are
will ip say al ali right But now % for some answers S.
No. ess-sIsso.sl.
- Next two my own. ~ 1aE5 l-4
No. ssl-Can. hut it t kes too much time.,
No. 2s.-AD equals s.9s miles: BID equals % o.
: No 9ss-1. 2. and 8. -r.s-
p No. 294-Not time. ...-
No. as5-Tne roots not given may be any num-
bers; then the produc OF these connected to with
the opposite side will be the equation.
No. .296-Limestone 30 A; Delta 81. Is plus.
No. 9g7-One mile higher than your head
Method of solving 293--Let plus KY plus xy2
plus xy3 equals Is, and x2 plus x2y2 plus x2,4 plus
A2y5 equal IS from fiud the values of x2 ad
make tuem ial each other then reduce by dividing
by5 and multiplying by q plus y2) and then clear vi
fracti ms. AMI we have 45y4 plus 45 equal " Plus
34v plus 34y2 plus 34y3 17y4: en- transpOse 70
first member all the terms except 34y2 and divide
throug by y2 Then by factpring have
quadrst:c % n minus 33n equals "a In equals plus
ldivided by " equals So. a..-. b..
That will do, won't it, Otiose?
Solution to No. 292-This is hard to give in
column without tue diagram but will try to maze
it clear. -aa
From the headland A draw the line q equals
the sum of the two siie<, A. the Stremity make
the ang ACB equals half the givea ange. Fro
A as center with the distance A equals the ven
base describe cB cutting CB in sad b.
From dra BID. m king the angle CBD equa the
ange e. hen are t" find the sides of the trian-
gle ADD. Now BID and Cd eq ial and AID i.
double the angle o. Hence equtls 10 degrees and
% minutes. and AC equa so miles and ALB equals
II 0s miles. We have the proportion
E.0s sin g :: so sin ABC log so equals 1.69s97o
"a Sin 10 deg, % min. equals 9.523l3s
IL 222ius
r-r log .2324Ss
sss9s20
Sin sup-ABC equa's II deg. 81 min. % sec. plus
ABC equals IU2 deg. 2S min. 81 sec.
sub 10 deg 20 min. =