2-----

200030,,(2-1).56,,,,,.

,.,.,.8,,,,.,.6,

,,.63,36.,.

2.1 6----3,,,.

2.1.1 ,.(Thales,636----546)----. ,,,,..

,: 12345

14002-3

.

2.1.2 Pythagoras,572497Samos,40Crotone),

111010

28=1+2+4+7+14,12(1+2+5)2202842201+2+4+5+10+11+20+22+44+55+110=2841+2+4+71+142=220

2-511+21+2+31+2+3+4n1+2+3++n= n(n+1)/2 ; 1,4,9,16n 2n+1 +(2n+1)=

2n+1= , 21

n+1= +2m+1 (2.2) (2.2)21

m=1,2,3,4345512137242594041

1010=1+2+3+412348

ABMGH: , , MG=GHAH=MB

Hippasus,470

213 (Zeno,490430)45

12

3

(Hippias,5)

2-6ABAADBCADBE`G

AB=a

, , y //AD LAL

(Hippocrates,5)2-7

ACOAEBAB = AEB=AOBAEB=AEB-ADB=AOB-ADB=

20001831(Vantzal,1814-1848)(Lindemann,1852-1939)gf 1882

214 (Plato,472347)4072012387

(Democritous460370)4

Eudoxus4567

(Menaechmus,4) Aristotle384-322

2.2 336-323334323

(Euclid330-275)Apollonius,262-190(Archimeds,287-212)

2.2.1

300

(Theon,)13465 6 12355 (1) (2)

(3)(4)(5). 54442000

195 1 2 3 4 5

48

2-13ABCABEDBCGFACJICABCTDEHAFCE ,

23456 789

[ a,bkp=abk,p+1a,.b,kp+1a,b,kp+1qqa,b,,kq|p,qp+1p+1

10 a,b25 31112133605

3001482

910The Data952(OnDivisions of figures)36

2.2.2

430 212Marcellus

(Heath,1860-1941)

1

234/34 2a1/3

51423/23/23456

0.011000100(Heiberg)1906

r2r2rr2-5Nx x(2r-x) TTN=NS=2rN[ x(2r-x) + ]2r=

Nx

(1) (2) 11/14 (3)223/7122/7 1AKA

()KK AEONONKK

(2)KEHATG>GA=GH TEAHAH KKKK

K101

2-17ACBLABLCCMNBCCAMENDED

,

1/4n

AA4/3 A>S>4/3 ,Sm

S+ = S<

A< -A2m-1 -A>

2.4 =

> - > A A=

2-18FTPOT

2.2.3 (perga) 848771

2 3

44 57 6 7

2.3

131~6 , ,KV , ,KKV K , 1~4

a=2b=3(x+3)-(x+2)=1,41/4

x=97/64. b-a= b-a=(z+y)(z-y)=uv uv u=z+y , v=z-y

1901251 , 1/21801/2

14647

:1234

5678910