# Book:Archimedes/On Spirals

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## Archimedes:

## Contents

## Archimedes: *On Spirals*

Published $c. 250 BCE$.

### Subject Matter

### 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.

## Sources

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.5$: Archimedes (ca. $287$ – $212$ B.C.)