The spectrum of practises of mathematical reconstruction is explored on the basis of a case study on a partly successful mathematical reconstruction of the Chinese Remainder Theorem. In the 19th century L. Matthiessen reconstructed two versions of this theorem on the basis of a corrupted secondary source concerning ancient Chinese mathematics. He identified the more restricted version of the theorem with a Gaussian approach, whereas the other more general one was described as something new surpassing contemporary mathematical European achievements. I identify and compare two different types of mathematical reconstructions in Matthiessen's contributions, and explore their historiographic functions. To capture the relation between mathematical reconstruction and anachronism, the time scheme in the case study is analyzed and linked to the concept of pluritemporality according to Landwehr. This more complex perspective on the category of time in historical research suggests that anachronism should be re-conceptualized. It allows for a discussion of some of the conditions under which mathematical reconstructions can be used in a historiographically sensitive way in a different setting. I argue that this kind of historiographically sensitive mathematical reconstruction can be regarded as a productive historiographical method