# Book:Archimedes/On Spirals

## Archimedes: On Spirals

Published $\text {c. 250 BCE}$.

### Archimedes' Definition

If a straight line of which one extremity remains fixed be made to revolve at a uniform rate in a plane until it returns to the position from which it started, and if, at the same time as the straight line revolves, a point moves at a uniform rate along the straight line, starting from the fixed extremity, the point will describe a spiral in the plane.

### Contents

$28$ propositions, including:
Proposition $20$: Tangent to Archimedean Spiral at Point
Proposition $24$: Area Enclosed by First Turn of Archimedean Spiral

## Critical View

Some sources suggest that his discovery of the Tangent to Archimedean Spiral at Point was discovered by techniques which are nothing short of differential calculus.