History of Conic Sections

Menaechmus is credited with the discovery of conic sections.

360 BCE

In Ancient Greece, King Minos wanted to build a tomb and said that the current dimensions were not good enough, and he wanted the cube to be doubled in size but not in length. Although many mathematicians tried to solve this impossible problem, it was not until the idea came to Plato's Academy that Menaechmus discovered the parabola and hyperbola while attempting to find a solution.

Menaechmus discovers parabolas, hyperbolas, and ellipses

355 BCE

He found these by examining the intersection of a right circular cone of varying vertex angles and a plane perpendicular to an element of the cone. However, he did not call these by their names we know today, but instead, he referred to a parabola as a "section of a right-angled cone", a hyperbola as a "section of an obtuse-angled cone", and an ellipse as a "section of an acute-angled cone".

Aristaeus and Euclid investigated the different curves

350 BCE

Although there is little to no evidence of their studies of conic sections, many believed they helped inspire future published works such as Archimedes and Apollonius.

Archimedes

250 BCE

The next major contribution to conic sections is from Archimedes. Although he never published an entire work for conic sections, he did publish several books that mentioned them such as "Quadrature of the Parabola", "Conoids and Spheroids", "Floating Bodies", and "Plane Equilibrium". It is believed Euclid is the probable source of his basic principles of cones that he assumes without proof in his works. An example of these assumptions is that all parabola are similar.

Apollonius of Perga, the "Great Geometer"

230 BCE

He made the biggest contributions to the conic sections through his eight books dedicated to the subject that contained 487 propositions. The first four books were discovered in a Greek translation, books five to seven were found in an Arabic translation, while the eighth book has never been recovered. He never claimed the material covered in the first four books as his own besides a few theorems in Book III, so it is believed those are a summary of everything already known about conics.

Apollonious of Perga Continued

229 BCE

In his works, he showed that it is not required for an intersecting plane to be perpendicular to the cone, that is he showed the cone could be right, oblique, or scalene. He also disproved that each conic section comes from a different cone, and he proved that they can be determined from the same cone. He also was the first to use double-napped cones instead of single-napped cones because it had a better use at defining the conic sections.

Apollonius renames the conic sections

228 BCE

Apollonius gives the conic sections the names we know today which are parabola, hyperbola, and ellipse derived from the Greek origin, paraboli, hyperboli, and ellipsis.

Pappus and Proclus

400

Although they were both great mathematicians themselves, their major contribution on conic sections was providing commentaries on previous works of conics such as from Apollonius, Aristaeus, and Euclid's works. In fact, Pappus had written that "the four books of Euclid's conics were completed by Apollonius". They are the reason why previous mathematicians are credited for their work because they had access to old works that are no longer available.

Renaissance Era and Johannes Kepler

1605

It was not until the Renaissance era for conic sections to arise again due to the revival in the interest of greek culture and knowledge. With this came the works of Johannes Kepler that showed the elliptic path of Mars revolving around the sun. This new discovery fueled a new motivation to study conic sections, however, there was more of a focus on mechanics and astronomy. Kepler also discovered that there were five types of conic sections that added circles and lines to the previous three.

Other Contributers

Period: 1650 to 1900

After those pioneers, there were many other mathematicians that contributed to conic sections, especially in the development of projective geometry where conics are fundamental objects as circles in Greek geometry, such as Newton, Poncelet, Steiner, Dandelin, Dupin, Gergonne, Brainchon, and Chasles.