1. 1 3000 1
1
3000
3000
(Writing Numbers)
(place value system)
365
5 5 6 60 3 300
3000
1 10
365
3 602 21 60 43 12103
Three hundred
and sixty-five 365
3 100 6 10 5
3 100 6 10 5
0 9
10
10 11

2. 2 3000 2
2
3000
3000
(Fractions)
5 8 5/8 0.625
2/3 1 p.10
(aliquot fraction) 1/2 1/3 1/4
2/5 1/5 1/5 1/5 1/5
1/6 1/30 2/5 2/5 1/5 1/6 1/30
1650
60
(minute parts) 60
(second minute parts)
60
60
60
1/2 1/3 1/4 1/9 4
(1/2 1/4 1/5 1/8) 4 (1/3 1/6 1/7 1/9)
1/3 0.3333 3 1/7
12 13

3. 3 2000 3
3
3000
3000
(Quadratic Equations)
quadratus quadratic
0.75 x2 + x = 0.75
1 x 1
1 0.5 1 0.5
2
ax bx c 0 0.5 0.5 0.25 2
(0.5) = 0.25
0.25 0.75 1 0.25 + 0.75 = 1
a b c 1 1 =1
X 0.5 1- 0.5 = 0.5
0.5 x = 0.5
ax2 + bx = c
a=1
0.75
14 15

4. 4 1850 4
4
(The Greatest Pyramid)
3000
3000
(frustum of a pyramid)
h r
R
(1/3) h ( R2+ Rr+ r 2 )
r
2
1850
6 6 h
4 2
4 16
4 2 8
2 4 4
R
16 8 4 28
6 3 2
2 28 56
(1/3) x 6 (42+2x4+22) = 56
16 17

5. 5 5
5
3000
腦。） 70 2037
p
4x(8/9) 2 3.16 3.14 23
3
96 ENIAC p.190 pp.101-102
223/71 22/7
(429-501) 355/113
(Madhava)
/4 = 1- 1/3+ 1/5 - 1/7+
11
1949 ENIAC（譯註：電子數值積分電腦(Electronic
Numerical Integrator and Computer)，是世界上第一部可變程式的電
18 19

6. 6 7
6 7
(The Pythagoreans) (Pythagoras s Theorem)
600
150
a b c
c 4 b
a+b a
c
4
c c2 a
c
b
(reality)
a b a2 + b2
c2 = a2 + b2
20 21