At the turn of the 19th century, arithmetic underwent a reform. Lagrange and Delambre developed diverse reflections on this discipline and contributed to the revival of the study of the ancient Greeks' mathematics. Through analyzing Lagrange's lectures on arithmetic and the popular arithmetic treatises, I reestablish how Lagrange's innovative ideas were adopted in the later books. Moreover, this paper clarifies the role that “complex numbers” played in these treatises and investigates Delambre's memoir on the ancient Greek arithmetic, so as to reveal the way in which Delambre read the ancients' texts and reconstructed their arithmetic using “complex numbers”.

在 19 世纪之交，算术经历了一次改革。Lagrange 和 Delambre 对这门学科进行了不同的思考，并为古希腊数学研究的复兴做出了贡献。通过分析拉格朗日的算术讲座和流行的算术论文，我重新确定了拉格朗日的创新思想是如何在后来的书中采用的。此外，本文还阐明了“复数”在这些论文中所起的作用，并考察了德兰布尔关于古希腊算术的回忆录，以揭示德兰布尔阅读古人文本并使用“复数”重构他们的算术的方式。