New-York tribune., 1908-09-27

CONE interesting -aLaCleS may be found II
y r95-ae-na-.15. One Of the Oldest Is the
--llC1--g. .- IS equal 70 Z square. Therefore,
7--A- EQUALS r. Therefore . lG-u5 equals
i1r .--t- Therefore Q equals g > O.
Therefore ec-4-- --. Therefore, 7 equals >.
Another s5-l--- o. Z may be written 6F
--uals T. S1ua-a both sides, and f-t equals
Therefore 81 equals C. Therefore. 4 equals
C Therefore. - equals e.. But G equals u
nd d equals =. Therefore Il equals l.
Tie following problem appeared n Paris II
----. L -re product u Two mum De-S Is equal
e. -W1 Cthe- number the mum beTs VIII be II
c-rua--.1r. and Z -- a --gpo-uOn the 1lrSt term
IS greater than the second term the third term
Is greater than the fourth Thus. Il al Is equal
e. -- We may obtain --e --0purtlCl q: e =: &C. Z,
nd then L 2 -- greater than p Is also greater
nan l. The e--a--"- -- sa-ls-ed L We take
ra.ues as follows. . a.---- Z equals 7; equals
equals This Shows that the value q Is
greater than --e -. --e .- - since = IS greater
than. Bur ~.-.e . Is greater than Z, = must
1e greater than
The following -a----- Has printed N one OF
LIZ magazine about ----a- wears ago sup
pose three coins a-e thrown -1-l and We wish TO
determine the ~. ability IS al -hree coming
uCwn alike. Since each must come with either
head o. tai ---e--l.=-. either head or tai has
Exactly one chance IN -v. .- being upper
most. From this - follows thar --e chance OF
al three appearing che same IS equal 10 the
-ube OF = a- This IS true Tor either
heads - -a-ls. Hence -re probability OF
al appea--E either head C- tail IS :.
But a. least -wr must come up alike. since
mere a-e only Two sides. and ri the third com
ne probability IS 2 ? that Z comes UP head
= t1a- II comes 10 Tai ---s the probability
nat 2 comes Gown So as Q. show the same SIDE
IS ne other ~. .. a-l therefore the prob
-.-1tE ---- u VIII come DOWN the same IS the
--a- al --.-ee W.- come down alike IS ,.
f,lcl1 E'-eparel q long Gst OF geometIc 1al-
---ier. "---1 has been lost. There are, how
t'r- many lroV-- ge---ec-lC -aIlaCles that test
-e ingenuity y che worker. Among these
IA. ye -Ie1-lyn-- such la--acies as 70 prove
--a- z rlg1t angle IS greater than & right angle;
= tl1.t ----- part .- q ---= IS equal 10 the
e-l-1 LIE, Z. prove every triangle lsOsCeleS,
----' i t"o opposite sides .- q 1uaG-llateral are
- l-e --1e- "a. sides mast be parallel 70
- -sJ = equal 70 8 or , 3
&c e-e-E11e knows --l- Il Is equal ap-
E.Ai--@te-y . 7--r-. .- about -
= ---l2ts Ee-a-.- "-= r-opounded by Zen0
-1--s ~s',uI-es ago. DE sand Il is evident that
= $40" NAY not move where L IS not, and
--e II Is --s- ~ impossible for Il 70 move
--e1t = -s- Q. p. "a space that Il CO-uDle1eiv
---' ~ = -9---"s t-- ~ arrow cannot move at
@-- -l-Tei.-e III motion is impossible.
10 tle same man is due the famous problem
- .'ll- Ac-i--=s and --- tortoise. He claimed
-' Il ------t. -.- -e- times as last as the
- .--se' - q --e tortoise had 1900 yards
-. II ----- never l.. gver-aien. Tor when
---i-ies 1@- gene 600 yards the tortoise
t-15 -7 SUI -e acc Ea-ls ahead, and when
~ rc--eS Ha- re -re Ioo yards the tortoise
80 s..-r De &c yards ahead, and 50 on forever.
..---.--e1 "gu-- ---s get nearer and nearer 70
-. '--1-ise a-- would never be able 10 over
I'M Le1g made the divisions OF time