DIOCLES CONTRIBUTION TO MATHEMATICS
Although little is known about
the life of Diocles, it is known that he was a contemporary of Apollonius and that he flourished sometime
around the end of the 3rd century BC and the beginning of the 2nd century BC.
Diocles is thought to be the first
person to prove the focal property of the parabola.
His name is associated with the geometric curve called
the Cissoid of Diocles, which was used by Diocles
to solve the problem of doubling the
cube. The curve was alluded to by Proclus in
his commentary on Euclid and attributed to Diocles by Geminus as
early as the beginning of the 1st century.
Fragments of a work by Diocles
entitled On burning mirrors were preserved by Eutocius in
his commentary of Archimedes' On the Sphere and the Cylinder.
Historically, On burning mirrors had a large influence on
Arabic mathematicians, particularly on al-Haytham,
the 11th-century polymath of Cairo whom Europeans knew as "Alhazen".
The treatise contains sixteen propositions that are proved by conic sections.
One of the fragments contains propositions seven and eight, which is a solution
to the problem of dividing a sphere by a plane so that the resulting two
volumes are in a given ratio. Proposition ten gives a solution to the problem
of doubling the cube. This is equivalent to solving a certain cubic equation.
Another fragment contains propositions eleven and twelve, which use the cissoid
to solve the problem of finding two mean proportionals in between two
magnitudes. Since this treatise covers more topics than just burning mirrors,
it may be the case that On burning mirrors is the aggregate of
three shorter works by Diocles. In the same work, Diocles, just after
demonstrating that the parabolic mirror could focus the rays in a single point,
he mentioned that It is possible to obtain a lens with the same property.
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