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Apollonius of Perga

Apollonius of Perga (Greek: Ἀπολλώνιος ὁ Περγαῖος Apollṓnios ho Pergaîos; c. 240 BC – c. 190 BC) was an ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the earlier contributions of Euclid and Archimedes on the topic, he brought them to the state prior to the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today. With his predecessors Euclid and Archimedes, Apollonius is generally considered among the greatest mathematicians of antiquity.[1]

Apollonius

c. 240 BC

c. 190 BC

Geometry

Aside from geometry, Apollonius worked on numerous other topics, including astronomy. Most of this work has not survived, where exceptions are typically fragments referenced by other authors like Pappus of Alexandria. His hypothesis of eccentric orbits to explain the apparently aberrant motion of the planets, commonly believed until the Middle Ages, was superseded during the Renaissance. The Apollonius crater on the Moon is named in his honor.[2]

Proposition I.3: “If a cone is cut by a plane through the vertex, the section is a triangle.” In the case of a double cone, the section is two triangles such that the angles at the vertex are .

vertical angles

Proposition I.4 asserts that sections of a cone parallel to the base are circles with centers on the axis.

[b]

Proposition I.13 defines the ellipse, which is conceived as the cutting of a single cone by a plane inclined to the plane of the base and intersecting the latter in a line perpendicular to the diameter extended of the base outside the cone (not shown). The angle of the inclined plane must be greater than zero, or the section would be a circle. It must be less than the corresponding base angle of the axial triangle, at which the figure becomes a parabola.

Proposition I.11 defines a parabola. Its plane is parallel to a side in the conic surface of the axial triangle.

Proposition I.12 defines a hyperbola. Its plane is parallel to the axis. It cut both cones of the pair, thus acquiring two distinct branches (only one is shown).

Λόγου ἀποτομή, De Rationis Sectione ("Cutting of a Ratio")

Χωρίου ἀποτομή, De Spatii Sectione ("Cutting of an Area")

Διωρισμένη τομή, De Sectione Determinata ("Determinate Section")

Ἐπαφαί, De Tactionibus ("Tangencies")

[19]

Νεύσεις, De Inclinationibus ("Inclinations")

Τόποι ἐπίπεδοι, De Locis Planis ("Plane Loci").

The Editors of Encyclopædia Britannica (2006). . Encyclopaedia Britannica.

"Apollonius of Perga"

O'Connor, John J.; , "Apollonius of Perga", MacTutor History of Mathematics Archive, University of St Andrews

Robertson, Edmund F.

David Dennis; Susan Addington (2009). (PDF). Mathematical Intentions. quadrivium.info.

"Apollonius and Conic Sections"

at wilbourhall.org

Scans of old editions of some of Apollonius' works in several languages