The History of Mathematical Proof in Ancient Traditions

570 tian miao

valuable suggestions. I am especially in debt to Karine Chemla and

Catherine Jami. As we were discussing and working together frequently

during the year, it is not easy to identify all the inspirations I have gained

from them. Th erefore, here, I would like to take this chance to express my

gratitude to them.

Appendix

Th e content of the Detailed Outline of Mathematical Procedures for the

Right-Angled Triangle

Problem a G i v e n F i n d O t h e r

• 1 a , b c


• 2 a , c b


• 3 b , c a
   4 a , b + a b , c Problem 1^ b^
   5 a , b − a b , c Problem 1
   6 a , c + a b , c Problem 2
   7 a , c − a b , c Problem 2


• 8 a , c + b b , c


• 9 a , c − b b , c
   10 b , b + a a , c Problem 1
   11 b , b − a a , c Problem 1
  •12 b , c + a a , c
  •13 b , c − a a , c
   14 b , c + b a , c Problem 3
   15 b , c − b a , c Problem 3
  •16 c , a + b a , b
  •17 c , b − a a , b
   18 c , c + a a , b Problem 2
   19 c , c − a a , b Problem 2
   20 c , b + c a , b Problem 3
   21 c , c − b a , b Problem 3
   22 a + b , b − a a , b , c Problem 1
  •23 a + b , a + c a , b , c
  •24 a + b , c − a a , b , c
   25 a + b , c + b a , b , c Problem 24
   26 a + b , c − b a , b , c Problem 23
  •27 b − a , a + c a , b , c
  •28 b − a , c − a a , b , c
   29 b − a , b + c a , b , c Problem 27
   30 b − a , c − b a , b , c Problem 28
  Continued