Apollonius of Perga

Apollonius of Perga (Ancient Greek: Ἀπολλώνιος ὁ Περγαῖος Apollṓnios ho Pergaîos; c. 240 BC – c. 190 BC) was an ancient Greek geometer and astronomer known for his important work on conic sections. He built on the ideas of earlier thinkers like Euclid and Archimedes, defining the shapes we now call ellipse, parabola, and hyperbola. These definitions are still used today and were crucial before the development of analytic geometry.

Apollonius was not only a great mathematician but also studied astronomy. Although much of his astronomical work did not survive, later writers like Pappus of Alexandria mentioned his ideas. One of his important theories was about how the planets move in eccentric orbits, a belief that lasted until the Middle Ages. Today, a feature on the Moon called the Apollonius crater honors his lasting contributions to science. Together with Euclid and Archimedes, Apollonius is regarded as one of the greatest mathematicians of antiquity.

Life

We know very little about the life of Apollonius, but he was an important ancient Greek mathematician who lived around 240–190 BC. He was born in Perga, a city in a place called Pamphylia, but he likely spent most of his life working and studying in Alexandria, in Egypt.

Apollonius wrote special letters to his friends to ask them to review his books on a subject called conic sections, which include shapes like ellipses, parabolas, and hyperbolas. One of his friends, Eudemus, helped him check his work. Apollonius sent his books to another important person named Attalus, who loved collecting books and supported artists and scholars.

Writings

Apollonius wrote many works on geometry, but only one, called Conics, survives today. This book has eight parts, but we only have the first four in the original Greek. Parts five through seven exist in an Arabic translation, and we do not know much about the eighth part.

Conics talks about shapes called conic sections, which include ellipses, parabolas, and hyperbolas. These shapes are made by cutting a cone with a flat surface. For example, if you cut the cone at an angle, you get an ellipse. If you cut it parallel to a side, you get a parabola. And if you cut it parallel to the cone’s axis, you get a hyperbola. Apollonius was the first to define these shapes in the way we still use today.

Attributed ideas

Apollonius made many contributions to geometry and astronomy. He is known for describing how two different ways of tracking planet movements are related. One way uses a circle called an "eccentric," and the other uses circles called a "deferent and epicycles." This idea was later explained by the astronomer Ptolemy in his work called the Almagest.

Apollonius also helped connect geometry with algebra, even before algebra was fully developed. Ancient Greek mathematicians used pictures to solve problems that we might now solve with numbers and equations. For example, instead of saying a square’s area is its side length times itself, they would draw the square and measure its sides with lines. Apollonius used similar geometric methods to study special curves called conic sections, like ellipses, parabolas, and hyperbolas. His work laid important groundwork for later advances in mathematics.

Legacy

The work of Apollonius, called the Conics, influenced geometry from ancient times through the middle ages and into modern times. In the 4th century, Serenus of Antinoöpolis wrote about parts of the Conics, and in the 6th century, Eutocius of Ascalon also wrote a commentary on it.

Later, in the 9th century, the Banū Mūsā had the Conics translated into Arabic. The first printed version in Latin appeared in 1566. In 1626, Jacobus Golius found an Arabic copy of more books of the Conics, which helped scholars understand the full work better. Over time, new ways of studying geometry developed, but Apollonius' ideas remained important. Translations of his work into English began in the late 19th century, with notable versions by Thomas Heath in 1896, Ivor Thomas in 1941, and R. Catesby Taliaferro in 1952, as part of the Encyclopædia Britannica's Great Books of the Western World series. Ancient Greek mathematics and analytic geometry have continued to build on his foundations.