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Apollonius and the Conics

Apollonius was born around 262 BC in the town of Perga, in what is now Turkey. He is sometimes called Apollonius of Perga because of the place where he was born.

Apollonius wrote several books including a work called Conics. This book was about the conic sections, curves that are created by slicing through a double cone with a plane. Here is one example:

Conic sections include the parabola, the hyperbola, and the ellipse.

Apollonius was not the first person to write about conic sections, but he discovered many new things about them. He gave the curves the names we use today, and studied the second branch of the hyperbola. His book was very famous, and people went on studying it for hundreds of years. For example, Hypatia wrote a commentary on the Conics around 400 AD.

Apollonius often used reference lines to help study conic sections. For example, he studied ellipses by measuring distances along a diameter and along a tangent to the ellipse perpendicular to the diameter:

Apollonius's system of measurements worked a lot like the coordinate plane. But there were several important differences.

First, Apollonius's reference lines were not always at right angles. Sometimes they slanted or tilted:

Second, Apollonius did not use negative numbers. He could only travel one way along each of his reference lines.

But the most important difference between Apollonius' system and the coordinate plane is that Apollonius always drew the curve he was trying to study first, and then added lines. Today we might set down the axes of our coordinate plane and then graph a parabola or a hyperbola. But to do this, we need to know an equation for the parabola or hyperbola. Apollonius did not use algebra, so he had to study geometry without graphing.


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