Linné on line Mathematics in Linnaeus’ time Mathematics past and present Euclid Euclid's *Elements*

## Euclid's *Elements*

No other book on mathematics has been so influential as Euclid's *Elements*.

*Elements* is very logical in structure, with **definitions, axioms, theorems, and proofs.**

**Definitions, axioms:** The cornerstones of a theory are definitions and axioms. New concepts are introduced in a theory by definitions. The first three in *Elements* are definitions of point, line, and plane. Axioms provide concepts with properties that cannot be proven, but since we regard them as true, they support the theory. One of the axioms in the first book says: ”It is possible to draw a straight line between any two points whatsoever.” Another says: ”A whole is greater than any of its parts.” Self-evident? An axiom should be self-evident.

**Theorems and proofs:** By proving relations and new properties for concepts, the theory is developed. For instance, Pythagoras' proposition is proven in theorem 47 in Book 1.