In the17and18century,information on mathematics of ancient China was exclusively drawn from the relevant writings of the catholic missionaries,who knew nothing but the Gou Gu theorem incorporated in Zhou Bi,which was erroneously dated in 1100 B.C.Misunderstandings could be found no less frequently in the western publications on China.This state continued in the first half of the 19century.Ignorant of the history of Chinese mathematics,J.F.Davis,authority on sinology at that time,assered that the Chinese know nothing about the place value of numbers and they have no algebra.Though more about Chinese mathematics was known to the westerners in the 19century than in the17and 18century,their knowledge of this subject was still limited.Some attainments in Chinese mathematics,such as those in The Nine Chapters on the Mathematical Art,one of the most important mathematical classic im China ,Liuhuis cyclotomic rule.Zu Chongzhis famous fractional value of π,Zugengs derivation of the volume of a sphere,etc.,were unknown to them.Completely ignorant of the work of the Chinese mathematician of the3century,some French mathematicians of the 19century made elementary study on π,but couldnt rediscover Lius remarkable acceleration method,which is equivalent to that of Richardsons linear extrapolation pubished in 1910.The original Chinese mathematical works and relevant research literatures being extremely scarce,the transmission of traditional Chinese mathematics in the West in the 19century was not smooth at all.In the first half of the 20century,despite of the publication of Y.Mikamis The Development of Mathematics in China and Japan,the transmission was impeded by suspicion,derogation and prejudice of such western historians as L.Van Hée,G.Loria.G.Vacca,etc.The history of the transmission of traditional Chinese mathematics tells us that it couldnt be properly appreciated and valued rhrough second-hand literatures alone and that both Chinese and western historians of science should do much more in studying,translating and promulgating it in order to makd it known to more Western scholars in the new century.