THE PEOGRESS OF SCIENCE IN CHINA. 
377 
forming the Imperial Calendar. Later, again, in the Chow-pi, 
a work on trigonometry (b.c. 1100), we trace a great advance 
in the knowledge of mathematical principles, as may be seen 
from the following translation of the first section, which may 
be said to contain an epitome of the whole work, taken from 
“The Chinese and Japanese Eepository” of April 1864: — “I, 
formerly Chow-kung, addressing Shang-kaon, said, ‘I have 
heard it said, my lord, that you are famous at numbers ; may 
I venture to ask how the ancient Fo-hi established the degrees 
of the celestial sphere ? There are no steps by which one may 
ascend the heavens, and it is impracticable to take a rule and 
measure the extent of the earth ; I wish to ask, then, how he 
ascertained these numbers ? ’ Shang-kaon replied, ^ The art of 
numbering originates in the circle and quadrangle. The circle 
is derived from the quadrangle. The quadrangle originates in 
the right angle. The right angle originates in the multiplica- 
tion of the nine digits. Hence separating a right angle into 
its component parts, if the base be equal to 3, and the altitude 
to 4, a line connecting the farther extremities will be 5. Square 
the external dimension, and half the amount will give the area 
of the triangle. Add together all the sides, and the result will 
equal the sum of 3, 4, and 5. The square of the hypothenuse 
being 25, is equal to the squares of the two short sides of the 
triangle. Thus, the means by which Yu restored order 
throughout the empire, was by following out the principles of 
these numbers.’ Chow-kung exclaimed, ‘ How truly great is 
the theory of numbers ! May I ask what is the principle of 
the use of the rectangle ? ’ Shang-kaon replied, ‘ The plane 
rectangle is formed by uninclined straight lines. The direct 
rectangle is used for observing heights. The reversed rectangle 
is used for fathoming depths. The fiat rectangle is used for 
ascertaining distance. By the revolution of the rectangle, the 
circle is formed. By the junction of rectangles, the square is 
formed. . . . The numbers of the square being the standard, 
the dimensions of the circle are deduced from the square. . . . 
This knowledge begins with the straight line, the straight line 
is a component part of the rectangle, and the numbers of the 
rectangle are applicable to the construction of all things.’ 
Chow-kung exclaimed, ‘ Excellent indeed ! ’ ” 
And we may well echo the exclamation. But unfortunately 
this promise of great scientific results was doomed, during many 
succeeding ages, to be obscured. Evil days overtook the lovers 
of literature and science. Their books were burnt, many of 
their number were put to death, and the remainder, 
“Neglected and oppress’d, 
Wished to be with them and at rest.” 
