Techniques of Fractions in Ancient Egypt and Greece

Abstract

In this and several other such passages Greek writers acknowledged their debt to the ancient Egyptian arithmetical methods². The reference here to “parts” (moria) is noteworthy, in that by using the standard term for proper measuring parts, or submultiples of the unit, the writer appears to allude to the manipulation of unit-fractions. A technique of precisely this sort dominates the computations with fractions found in the ancient Egyptian papyri—most notably, the Rhind Mathematical Papyrus—and despite the passage of over two millennia is still to be found in late Greek papyri from the Graeco-Roman and Byzantine periods. This is perhaps the most striking of several | evidences of the continuity of the Egyptian and Greek technical traditions, all the more impressive in view of the fact that the availability of the Mesopotamian sexagesimal mode, from at least the second century B.C. on, failed to displace the cumbersome and limited Egyptian mode, save in the context of astronomical computation³. Thus, despite the undeniable influence of Mesopotamian techniques, especially in the fields of elementary and metrical geometry and astronomy, our sources must be taken seriously when they affirm their debt to the Egyptian tradition⁴.

The subject-matter of [logistic] is all things which can be numbered; its branches are the methods called Greek and Egyptian for multiplication and division and the summation and separation of parts (moria).¹