In the preface of Volume 1, Apollonius tells Odmos about the writing process: "The geometer Nauklatus came to Alexandria and encouraged me to write this book. I finished it before he left by boat, without careful consideration. Now I have time to revise it roll by roll and send it to you in batches. "

The writing of The Theory of Conic Curves is the same as that of Euclid and Archimedes. First establish several definitions, and then prove the proposition in turn. The reasoning is very strict, and some properties have been proved in Euclid's Elements of Geometry, so it is used as known, but the original text does not indicate that it comes from Elements. For easy reference, add the source. (Compare [6] the original Greek text with the English translation on pages 280-335. Later generations are quite critical of this. Archimedes' biographer even said that Apollonius took Archimedes' unpublished work on conic curves as his own. This is Otto Keos' record. But he also said that this view is incorrect. Pappus accused Apollonius of adopting the work of many predecessors (including Euclid) in this field, but never attributed it to these pioneers. Of course, he has made great progress on the basis of his predecessors, and his outstanding contribution should also be affirmed.

Conic curve theory is a classic, which can be said to represent the highest level of Greek geometry. Since then, there has been no substantial progress in Greek geometry. It was not until17th century that B. Pascal and R. Descartes made a new breakthrough. The Theory of Conic Curves consists of eight volumes, the Greek of the first four volumes and the Arabic of the last three volumes are preserved, and the last volume is lost. This book brings together the achievements of predecessors and puts forward many new properties. He popularized the method of Menek Muse (the earliest Greek mathematician who systematically studied conic curves in the 4th century BC), proved that all three kinds of conic curves can be cut from the same cone, and gave names such as parabola, ellipse, hyperbola and positive focal chord. The concept of coordinate system has been written in the book. He took the diameter of the cone bottom as the abscissa and the vertical line passing through the vertex as the ordinate, which greatly inspired the establishment of coordinate geometry in later generations. The eight-volume book On Conic Curve has exhausted the essence of conic curve, leaving little room for future generations to intervene. It was not until17th century that B Pascal and R Descartes made substantial progress.