This chapter proves a number of propositions which demonstrate elementary algebraic statements that are more familiar to us in the form of equations. Algebra as we know it had not been developed when Euclid wrote "The Elements". Hence, the results are more of historical importance than practical use except when they appear in subsequent proofs.
The following table lists results from this book which are also known in modern mathematics, but which were proven by Euclid purely geometrically about 2500 years ago:
Euclid's Elements | Corresponding Contemporary Results |
---|---|
Prop 2.01 | distributivity law for real numbers. |
Prop 2.04, Prop 2.05, and Prop 2.07 | binomial theorem and other binomial formulae |
Prop 2.12 and Prop 2.13 | law of cosines |
Moreover, this book contains the following compass and ruler constructions: