Book:Archimedes/On Spirals

Archimedes: On Spirals

Published $c. 250 BCE$.

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.