Second letter, to George Khatzykes, who served under Andronikos II, usually called "Letter to Khatzykes", is on the value of the Greek alphabetical numbers, on finger-reckoning ("how to represent integers from 1 to 9,999 on the fingers of the hands"), on the four arithmetical procedures, and on the order of numbers in a base-ten system. The second letter is more advanced then the first one, "explaining the operations with fractions with a sequence of unit fractions (of the type 3 + 1/3 + 1/14 + 1/42 ···) and the extraction of the square root of a non-square number. This is followed by a procedure for calculating the date of Easter and a series of practical problems involving the money, weights, and measures used at that time."
