Daily Ohio statesman. [volume] (Columbus, Ohio) 1855-1870, 1867-08-24
TIE PuzzLEx,s COLUMN.

2 We welcome a new correspondent this week
Amos" our hand is extended. Wegreetyou. Do
not forget to comply with our rule. Send the an
swers to your puzzles and your name. Not for pub
LEGATION, but for own tisfaction Delta, Guern
sey. Sammy. Billy Root and Robin fail to make their
appearance. They are marked "absent without
leave:" r -..- --.
! WASHINGTON, GUERNSEY Co.. o., Aug. 90 1867.
Mr.. EDITOR: l have for the last few weeks
thought that would send a few answers. and con-
sequenty have tried most OF them. and am eX-
tremely well pleased with the communl q TO- 9, es-
pecaly the demonstrations, They are quite treat,
and the whole column must great ins ructon to
the problems were TOO hard for my amount of geom
etry and trgonnmetry. getthe following ans ers:
Problem No: 16U-A gets l22. plus acres, Is III IA
Plus acres. This was very hard.
Problem No: ls1-lO bushels, which is a mean be-
Pro lem No 1920 cattle in each lot first cost 500
per head. second $50
Problem No. 1876 years old just II years older
Problem No ls9-Base and perp endicuar 54l
feet; the area is 81, 1855 Plus feet S X this is
very hard one; please overlook my answers if they
Probiem No. 1el-If he rolls the tape in a ball, or
rather q cylinder. he need not walk far. and
still have it tightly stretched all the time.
an CAD to see SO many taking part in this C l.
umn. AMOS.
WASHINGTON. GUERNSEY Co.. O., Aug. 90. '67.
Mr.. EDITOR: There is but very little mathemat-
les in me this week and has inOt intented to say
anything about IT. oay 1,s zee that GsO5sf Inns as
ways ready to vindicate what i see to be right
Come, G. ). lnns, and We will look over this prob
oorrect-24 feet and i squared=ls75 This is
correct. and the root is 43.3ol27ol plus. Now for
sake of p.OOf let call this 43 81 You this is
adding considerable to t-and 4s 81 plus 24=67 81.
SQUARE this and add the ,sqqsre Of to il and We
Now lnnis extract square root of this and you will
get 6767 plus small remainder. 0n the 5th Delta
made some mistake in your work. for after al
lowing the above amount. lack 3s hundreths of
are right and that am wrong show your work for
it, Herewith send few answers:
IN 2 acres nearly Those who are DESTROYS Of find
ing ru for this problem wi find it in R iy's AL
Eeh-a part 2t. page 222, and a problem Oh the pre-
ceding page similar.
No. lsl- 10 bushels of peas.
No Is. 90 cattle in first lot at $40 per head and
70 cattle in second lot at $50 per head.
No. 1853 1854 K cents per b.; 20 8 K bushels; horse
cost $l41. 81 K. That is right Come on. you cob
No. ls4-Dept6 sJl feet; length 74I s27 fest;
breadth 8 494-s27 feet, and will hold 800 bushels
) lid. This is answer by not reducing the lum-
be but considering that the bo4rds equal to a
continuous board 2ls feet long and 2IS inches thick
Vow, if the whole contents of the lumber is only
ei9 feet when thrown into board mea-ure, then
over forty and less than ftv bushels Winchester t
measure, The imperial b or 22ls 1872 inches in n.
No ls5-Base=92a feet; hypothenuse sls s55 x
feet; psrpe dicul r 222 feet.
No. Is6-Tne increase of globes is in proportion to
up to sec. is 200.
NJ. 1s7-Not yet comea able.
No. 169-Mv own.
No. l9O-NOt now.
This is near as can work it, There is an alb
.surdity IN this work; yes, two; but they are like
two negativessthey destroy each other. yorked
GREENvILLE. ONO. Aug. 81. 1867
Mr. EDITOR: Since Delta has requested me to
explain how some of the algebraic expressions were
obtained in the solution of Problem No. 13s. sub
Assume the triangle ABC, AB=6p AC=sO and
BC=l00; call the center of the circle touching the
base and perpendicular p and the center Of the cir
Gle to1ching the perpendicular and hypothenuseE
Fm let fall the e. and E
circ es from D draw DIX perpendicular to GE );
draw DE: Bisect the. angles A and B by the lines
pass through tbs points b and E. from o draw ON
Perpendicuar to ABB. The area of the triangle ABC
hence oM=a1oo divided BY 1aa@ao the ty tTanaIc
AMO has the angles A and equal, it is therefore
800 Now, let x2=D i. and ye=EG. then x2 plus
ys==REE and nd because GnKTEpn; n we have ys minus
K. we have (xa minus xa5a minus ty2 minus s xa,2@
sa"si: SsSs SSb .55 BsHsa Ss
we have the proportion ON NIB :EG: GB Or 20 :
4O:: W :e!9, hence 2ye=GB; but All plus HG plus
GB=AB, hence the equation x2 plus 2xy plus 2y2=
60 By course of reasoning analogous to that just
employed the other -equstions NAV be formed. 1
about No, l59. Now. :. X let US see whether you
are not mistaken. Suppose have two circles.
one 20 feet, and the other 8 feet in diameter and
suppose the less touches the greater internay now
the diameter OF the greatest circle that be
formed touch the less of these circles externally
and the greater internally is II feet Consider this
and let us know whether am correct.
will give following answers:
No. $50 A's share l22 acres BIS 177.2 acres.
No. 1910 bushels.
No ls4-5.576 plus feet, breadth, 1864 pus feet
length of box; it will hold sO7 6S plus bushels
4s o. square feet will make lid, that will project
lilo of foot.
No. 1s5-The sides are l94H, e59 and 3232< feet.
No. 1S6-3sI l8 plus cubic feet per second.
No. 1873. II square feet.
No. lS9-The area is 7U9.53S6 square feet.
E. B.