The second book of the work "On the Cutting Edge", where the remaining 63 cases of the same problem are solved, the examination of which began with the first book. The work is one of the few examples of the method of mathematical analysis that have survived from antiquity, while it serves as a model due to its complete and strictly geometric handling of the problem it attempts to solve. With this edition, the work is presented for the first time to the Greek-speaking readership along with the Arabic text and the modern Greek translation.