Apollonius named the ellipse, parabola and hyperbola after a bookkeeping idea
Slice a cone at different angles and you get three curves whose names we owe to Apollonius of Perga. They come from a Greek geometric test of whether an area fits a square exactly: parabola meant application, ellipse meant falling short, and hyperbola meant overshooting.
Apollonius lived roughly from 240 to 190 BC and, with Euclid and Archimedes, ranks among antiquity's greatest mathematicians. Almost nothing personal survives. The sixth-century commentator Eutocius places him in the reign of Ptolemy III of Egypt, which suggests a birth after 246 BC. Perga, in Pamphylia in Anatolia, changed hands between the Seleucids and the Attalids of Pergamon during that era, but Apollonius seems to have studied and written in Alexandria, reportedly among the later followers of Euclid.
The best clues come from the covering letters he wrote with each book of his Conics. He explains that a geometer called Naucrates, staying as a guest in Alexandria, asked for the work, and received a rough draft of all eight books. The first two prefaces go to Eudemus of Pergamon, who wanted each revised book before release; the second was carried by Apollonius's son, also named Apollonius. By Book IV Eudemus had died, and the later prefaces address a mysterious Attalus, possibly the book-loving Pergamene ruler Attalus II. Book VIII was promised but may never have been sent.
Conics set out 387 propositions across its first seven books, arranged in Euclid's style of givens and things to prove. Book I lays down the basic definitions. A plane through the apex cuts a triangle; one parallel to the base gives a circle; tilted, it gives an ellipse until the tilt matches the cone's side, when it becomes a parabola; and a plane cutting both halves of a double cone yields the two-branched hyperbola. His names for these curves are still used today.
Survival was precarious. Only Books I to IV exist in Apollonius's Greek. Books V to VII reached us only because the Banū Mūsā brothers paid Thābit ibn Qurra to put them into Arabic, and Book VIII is lost, though Edmond Halley attempted a Latin reconstruction. Most of his other writings, including astronomy, are known only from summaries by Pappus of Alexandria. His eccentric-orbit explanation of wandering planets held sway until the Renaissance, and a lunar crater carries his name.
Source: Apollonius of Perga
