IM 67118, also known as Db2-146, is an Old Babylonian clay tablet in the collection of the Iraq Museum that contains the solution to a problem in plane geometry concerning a rectangle with given area and diagonal.

The steps of the solution are believed to represent cut-and-paste geometry operations involving a diagram from which, it has been suggested, ancient Mesopotamians might, at an earlier time, have derived the Pythagorean theorem.

The tablet was excavated in 1962 at Tell edh-Dhiba'i, an Old Babylonian settlement near modern Baghdad that was once part of the kingdom of Eshnunna, and was published by Taha Baqir in the same year.

[5] In modern mathematical language, the problem posed on the tablet is the following: a rectangle has area A = 0.75 and diagonal c = 1.25.

In stage 2, the well-attested Old Babylonian method of completing the square is used to solve what is effectively the system of equations b − a = 0.25, ab = 0.75.

It must be emphasized, however, that the modern notation for equations and the practice of representing parameters and unknowns by letters were unheard of in ancient times.

It is now widely accepted as a result of Jens Høyrup's extensive analysis of the vocabulary of Old Babylonian mathematics, that underlying the procedures in texts such as IM 67118 was a set of standard cut-and-paste geometric operations, not a symbolic algebra.

Høyrup argues that the cut-and-paste geometry would have been performed in some medium other than clay, perhaps in sand or on a "dust abacus", at least in the early stages of a scribe's training before mental facility with geometric calculation had been developed.

Note that there was no "sexagesimal point" in the Babylonian system, so the overall power of 60 multiplying a number had to be inferred from context.

The translation is "conformal", which, as described by Eleanor Robson, "involves consistently translating Babylonian technical terms with existing English words or neologisms which match the original meanings as closely as possible"; it also preserves Akkadian word order.

[9] Old Babylonian mathematics used different words for multiplication depending on the underlying geometric context and similarly for the other arithmetic operations.

Vaiman notes that the cuneiform sign for šàr resembles a chain of four right triangles arranged in a square, as in the proposed figure.

[24] Høyrup writes that the problem of IM 67118 "turns up, solved in precisely the same way, in a Hebrew manual from 1116 ce".

[25] Although the problem on IM 67118 is concerned with a specific rectangle, whose sides and diagonal form a scaled version of the 3-4-5 right triangle, the language of the solution is general, usually specifying the functional role of each number as it is used.

[26] The manner of discovery of the Pythagorean rule is unknown, but some scholars see a possible path in the method of solution used on IM 67118.

The observation that subtracting 2A from c2 yields (b − a)2 need only be augmented by a geometric rearrangement of areas corresponding to a2, b2, and −2A = −2ab to obtain rearrangement proof of the rule, one which is well known in modern times and which is also suggested in the third century CE in Zhao Shuang's commentary on the ancient Chinese Zhoubi Suanjing (Gnomon of the Zhou).

Høyrup believes that this surveyor culture survived the demise of Old Babylonian scribal culture that resulted from the Hittite conquest of Mesopotamia in the early 16th century BCE and that it influenced the mathematics of ancient Greece, of Babylon during the Seleucid period, of the Islamic empire, and of medieval Europe.

[32] On the basis that no third-millennium BCE references to the Pythagorean rule are known, and that the formulation of IM 67118 is already adapted to the scribal culture, Høyrup writes, "To judge from this evidence alone it is therefore likely that the Pythagorean rule was discovered within the lay surveyors' environment, possibly as a spin-off from the problem treated in Db2-146, somewhere between 2300 and 1825 BC.