XIV[14arg] What the number is which is called hemiolios and what epitritos; and that our countrymen have not rashly ventured to translate those words into Latin.
CERTAIN numerical figures which the Greeks call by definite terms have no corresponding names in Latin. But those who have written in Latin about numbers have used the Greek expressions and have hesitated to make up Latin equivalents, since that would be absurd. For what name could one give to a number which is said to be hemiolios or epitritos? But hemiolios is a number which contains in itself some other whole number and its half, as three compared with two, fifteen with ten, thirty with twenty; epitritos is a number which contains another whole number and its third part, as four compared with three, twelve with nine, forty with thirty. It does not seem out of place to note and to remember these numerical terms; for unless they are understood, some of the most subtle calculations recorded in the writings of the philosophers cannot be comprehended. [p. 345]