Diocles (Διοκλῆς in
Ancient GreekAncient Greek is the historical stage in the development of the Greek language spanning across the Archaic , Classical , and Hellenistic periods of ancient Greece and the ancient world. It is predated in the 2nd millennium BC by Mycenaean Greek...
, ca. 240 BCE - ca. 180 BCE) was a
GreekIn the context of Ancient Greek art, architecture, and culture, Hellenistic Greece corresponds to the period between the death of Alexander the Great in 323 BC and the annexation of the classical Greek heartlands by Rome in 146 BC...
mathematicianA mathematician is a person whose primary area of study and/or research is the field of mathematics. Mathematicians are concerned with particular problems related to logic, space, transformations, numbers and more general ideas which encompass these concepts...
and geometer.
Although little is known about the life of Diocles, it is known that he was a contemporary of
ApolloniusApollonius of Perga [Pergaeus] was a Greek geometer and astronomer noted for his writings on conic sections. His innovative methodology and terminology, especially in the field of conics, influenced many later scholars including Ptolemy, Francesco Maurolico, Isaac Newton, and René Descartes...
and that he flourished sometime around the end of the
third centuryThe 3rd century BC started the first day of 300 BC and ended the last day of 201 BC. It is considered part of the Classical era, epoch, or historical period.-Overview:...
and the beginning of the
second century BCThe 2nd century BC started the first day of 200 BC and ended the last day of 101 BC. It is considered part of the Classical era, although depending on the region being studied, other terms may be more proper .-Overview:Fresh from its victories in the Second Punic War, the...
.
Diocles is thought to be the first person to prove the focal property of the
parabolaIn mathematics, the parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface...
. His name is associated with the geometric
curveIn mathematics, a curve consists of the points through which a continuously moving point passes. This notion captures the intuitive idea of a geometrical one-dimensional object, which furthermore is connected in the sense of having no discontinuities or gaps. Simple examples include the sine wave...
called the
Cissoid of DioclesThe cissoid of Diocles is an unbounded plane curve with a single cusp, which is symmetric about the line of tangency of the cusp, and whose pair of symmetrical branches both approach the same asymptote as a point moving along the cissoid moves farther away from the cusp...
, which was used by Diocles to solve the problem of
doubling the cubeDoubling the cube is one of the three most famous geometric problems unsolvable by compass and straightedge construction...
.
Diocles (Διοκλῆς in
Ancient GreekAncient Greek is the historical stage in the development of the Greek language spanning across the Archaic , Classical , and Hellenistic periods of ancient Greece and the ancient world. It is predated in the 2nd millennium BC by Mycenaean Greek...
, ca. 240 BCE - ca. 180 BCE) was a
GreekIn the context of Ancient Greek art, architecture, and culture, Hellenistic Greece corresponds to the period between the death of Alexander the Great in 323 BC and the annexation of the classical Greek heartlands by Rome in 146 BC...
mathematicianA mathematician is a person whose primary area of study and/or research is the field of mathematics. Mathematicians are concerned with particular problems related to logic, space, transformations, numbers and more general ideas which encompass these concepts...
and geometer.
Life and work
Although little is known about the life of Diocles, it is known that he was a contemporary of
ApolloniusApollonius of Perga [Pergaeus] was a Greek geometer and astronomer noted for his writings on conic sections. His innovative methodology and terminology, especially in the field of conics, influenced many later scholars including Ptolemy, Francesco Maurolico, Isaac Newton, and René Descartes...
and that he flourished sometime around the end of the
third centuryThe 3rd century BC started the first day of 300 BC and ended the last day of 201 BC. It is considered part of the Classical era, epoch, or historical period.-Overview:...
and the beginning of the
second century BCThe 2nd century BC started the first day of 200 BC and ended the last day of 101 BC. It is considered part of the Classical era, although depending on the region being studied, other terms may be more proper .-Overview:Fresh from its victories in the Second Punic War, the...
.
Diocles is thought to be the first person to prove the focal property of the
parabolaIn mathematics, the parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface...
. His name is associated with the geometric
curveIn mathematics, a curve consists of the points through which a continuously moving point passes. This notion captures the intuitive idea of a geometrical one-dimensional object, which furthermore is connected in the sense of having no discontinuities or gaps. Simple examples include the sine wave...
called the
Cissoid of DioclesThe cissoid of Diocles is an unbounded plane curve with a single cusp, which is symmetric about the line of tangency of the cusp, and whose pair of symmetrical branches both approach the same asymptote as a point moving along the cissoid moves farther away from the cusp...
, which was used by Diocles to solve the problem of
doubling the cubeDoubling the cube is one of the three most famous geometric problems unsolvable by compass and straightedge construction...
. The curve was alluded to by
ProclusProclus Lycaeus , called "The Successor" or "Diadochos" , was a Greek Neoplatonist philosopher, one of the last major Classical philosophers . He set forth one of the most elaborate and fully developed systems of Neoplatonism...
in his commentary on
EuclidEuclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician and is often referred to as the "Father of Geometry." He was active in Hellenistic Alexandria during the reign of Ptolemy I...
and attributed to Diocles by
GeminusGeminus of Rhodes, was a Greek astronomer and mathematician, who flourished in the 1st century BC. An astronomy work of his, the Introduction to the Phenomena, still survives; it was intended as an introductory astronomy book for students...
as early as the beginning of the first century.
Fragments of a work by Diocles entitled
On burning mirrors were preserved by Eutocius in his commentary of
ArchimedesArchimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity...
'
On the Sphere and the Cylinder. Historically,
On burning mirrors had a large influence on Arabic mathematicians, particularly on al-Haytham. 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.