Two arrangements of the trigrams and hexagrams circulate in the Yijing tradition. The received or after-heaven order is the one carried by the transmitted text. The before-heaven order, associated with Shao Yong and attributed by him to Fuxi, arranges the sixty-four hexagrams in a sequence generated by successive division, and displays them in a square and a surrounding circle.
Zhu Xi reproduced these diagrams at the front of his own work on the Yijing, and in doing so made them standard furniture of the tradition, which is the main reason Shao Yong's influence outran the number of people who read him. The diagrams travelled further than that. In 1701 the Jesuit Joachim Bouvet, working in Beijing, sent the before-heaven arrangement to Leibniz, who had been developing binary arithmetic and who recognised the sequence as a binary count. He took it as evidence that the ancient Chinese had possessed a knowledge since lost.
Modern historians treat that reading with care. The order does correspond to a binary enumeration, because both are generated by the same operation of repeated division, but nothing in the Chinese tradition treats the broken and solid lines as digits or performs arithmetic with them. The correspondence is real and the inference from it was Leibniz's. That episode, in which a Song cosmologist's diagram becomes an exhibit in a European argument about the antiquity of mathematics, is one of the odder passages in the history of the Yijing.