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The traditional§mathematics of the calendar and Chinese astronomy consist of temporary and§unstable collections of mathematical procedures, constantly under fire of§reforms and designed to predict and not to explain, astronomical phenomena and§those pertaining to related areas.§§Yet, beyond§appearances, the present modelling of the mathematical techniques hidden behind§the scenes of their voluminous corpus reveals instead that they depend on a§limited number of clear-cut mathematical structures.§§If a small§fraction of these techniques are not unheard of, on the contrary many of them§are essentially unexpected to the extant that they significantly broaden our§knowledge of the history of Chinese mathematics. But also, the issues addressed§in the corresponding Chinese historical sources focus not only on technical§questions but also on the problem of the applicability of mathematics to the§prediction of astronomical phenomena. Hence their interest for the comparative§history of mathematics ad astronomy.§§§