Book:Archimedes/On Spirals
Jump to navigation
Jump to search
Archimedes: On Spirals
Published $\text {c. 250 BCE}$
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. $\text {287}$ – $\text {212}$ B.C.)
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Archimedes of Syracuse (c. 287-212 bc)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Archimedes of Syracuse (c.287-212 bc)