Archimedes, Apollonius, & Ptolemy

Archimedes of Syracuse

• c. 287-212 BCE

• Wrote “research monographs” on various subjects rather than exhaustively on them. Examples:– On the Measurement of the Circle– The Method– Quadrature of the Parabola– On Spirals– On the Sphere and Cylinder I & II, etc.

• “Eureka”

On the Measurement of the Circle

r

r

c

c

Proposition 1:

The two areas are equal.

The Method

Oldest copy is a palimpsest from the 10th century

• recently (1998) sold for $2 million• Being preserved by Walters Art Gallery in

Baltimore• In poor condition• Facsimiles may be available in the future• Parabola segment = 4/3 inscribed triangle

– see Fig. 3.2 p. 71 (Katz, brief ed.)

Apollonius of Perge

• c. 250 - 175 BCE

• Known chiefly for his work on conic sections

• Angle trisection via conic sections – Fig. 3.14 p.83 (Katz, brief ed.)

Ptolemy’s cosmology as realized by Andreas Cellarius in 1660 in his work Atlas Coelestis … From the collection of The British Library.