On the existing fragments of Yang Hui's `Hsiang Chieh Suan Fa' (Q2537093)

The existing fragments of one of Yang Hui's earliest works, the ``Hsiang Chieh Suan Fa'' (1261) are grouped, translated and commented on in this paper. Two important factors of the collection are pointed out. Firstly, the ``Hsiang Chieh Suan Fa'' has the earliest extant representation of the ``Pascal Triangle'' and secondly, there is a problem on the extraction of the fourth root whose solution illustrates clearly Horner's Method (1819) of solving numerical equations of higher degree.