In this chapter we provide translations of key texts bearing on Leibniz’s mature justifications of the use of infinitesimals and of the differential algorithm itself, including previously little known texts such as Towards a Science of the Infinite, the Quaestio de jure and the Regula de Transitu, as well as fresh translations of well-known texts such as his letters to Pinsson and Varignon, and a complete new translation of Cum prodiisset.