APOLONIO DE PERGA: BIOGRAPHY, CONTRIBUTIONS AND WRITINGS - ARTE - 2025

Apollonius of Perga (Perga, c. 262 BC - Alexandria, c. 190 BC) was a mathematician, geometrist and astronomer of the School of Alexandria recognized for his work on the conics, an important work that represented significant advances for astronomy and aerodynamics, among other fields and sciences where it is applied. Its creation inspired other academics such as Isaac Newton and René Descartes for their later technological advances at different times.

The ellipse, parabola and hyperbola were born from his work Secciones Cónicas, terms and definitions of geometric figures that are still important today in solving mathematical problems.

Apollonius of Perga is the author of Conical Sections.

He is also the author of the hypothesis of eccentric orbits, in which he solves and details the tentative movement of the planets and the variable speed of the Moon. In his Theorem of Apollonius he determines how two models can be equivalent if they both start from the correct parameters.

Biography

Known as "the great geometer", he was born in approximately 262 BC. C. in Perga, located in the dissolved Pamphylia, during the governments of Ptolemy III and Ptolemy IV.

He was educated in Alexandria as one of the disciples of Euclid. It belonged to the golden age of mathematicians of Ancient Greece, made up of Apollonius along with the great philosophers Euclid and Archimedes.

Subjects such as astrology, the conic and schemes to express large numbers characterized his studies and main contributions.

Apollonius was a prominent figure in pure mathematics. His theories and results were so far ahead of their time that many of them were not verified until a long time later.

And his wisdom was so focused and humble that he himself affirmed in his writings that theories should be studied "for their own good," as he declared in the preface to his fifth book of Conics.

Contributions

The geometric language used by Apollonius was considered modern. Hence his theories and teachings have largely shaped what we know today as analytical geometry.

Conical sections

His most important work is Conical Sections, which is defined as the shapes obtained from a cone intersected by different planes. These sections were classified into seven: a point, a line, a pair of lines, the parabola, the ellipse, the circle and the hyperbola.

It was in this same book that he coined the terms and definitions of three essential elements in geometry: hyperbola, parabola, and ellipse.

He interpreted each of the curves that make up the parabola, ellipse, and hyperbola as a fundamental conic property equivalent to an equation. This in turn was applied to oblique axes, such as those formed by a diameter and a tangent at its end, which are obtained by sectioning an oblique circular cone.

He showed that oblique axes are just a specific matter, explaining that the way the cone is cut is irrelevant and of no importance. He proved with this theory that the elementary conic property could be expressed in the form itself, as long as it was based on a new diameter and the tangent located at its end.

Classification of problems

Apolonio also classified the geometric problems in linear, plane and solid depending on their solution with curves, straight lines, conics and circumferences according to each case. This distinction did not exist at the time and signified a remarkable progress that laid the foundations to identify, organize and spread their education.

Solution of equations

Using innovative geometric techniques, he proposed the solution to second degree equations that are still applied today in studies in this area and in mathematics.

Epicycle theory

This theory was implemented in principle by Apollonius of Perga to explain how the alleged retrograde movement of the planets in the solar system worked, a concept known as retrogradation, in which all the planets except the Moon and the Sun entered.

It was used to determine the circular orbit around which a planet rotated considering the location of its center of rotation in another additional circular orbit, in which said center of rotation was displaced and where the Earth was.

The theory became obsolete with the later advances of Nicolás Copernicus (heliocentric theory) and Johannes Kepler (elliptical orbits), among other scientific facts.

Writings

Only two works by Apollonius have survived today: Conical Sections and On the Section of Reason. His works were developed essentially in three fields, such as geometry, physics and astronomy.

The 8 books of conic sections

Book I: Methods of obtaining and fundamental properties of conics.

Book II: Diameters, axes and asymptotes.

Book III: Remarkable and New Theorems. Properties of the lights.

Book IV: Number of points of intersection of conics.

Book V: Segments of maximum and minimum distance to the conics. Normal, evolving, center of curvature.

Book VI: Equality and similarity of conic sections. Inverse problem: given the conic, find the cone.

Book VII: Metric Relationships on Diameters.

Book VIII: Its content is unknown, as it is one of his lost books. There are different hypotheses about what could have been written on it.

About the reason section

If there are two lines and each one has a point above them, the problem is to draw another line through another point, so that when cutting the other lines, segments that are within a given proportion are required. The segments are the lengths located between the points on each of the lines.

This is the problem that Apollonius raises and solves in his book On the Reason Section.

Other works

On the section of the area, determined section, flat places, inclinations and tangencies or "the problem of Apollonius" are other of his many works and contributions that have been lost in time.

The great mathematician Papo of Alexandria was the one who was mainly in charge of spreading the great contributions and advances of Apollonius of Perga, commenting on his writings and dispersing his important work in a large number of books.

This is how from generation to generation the work of Apollonius transcended Ancient Greece until it reached the West today, being one of the most representative figures in history for establishing, characterizing, classifying and defining the nature of mathematics and geometry in the world.

References

1. Boyer, Carl P. A History of Mathematics. John Wiley & Sons. New York, 1968.
2. Fried, Michael N., and Sabetai Unguru. Apollonius of Perga's Conica: Text, Context, Subtext. Brill, 2001.
3. Burton, DM The history of mathematics: An introduction. (fourth edition), 1999.
4. Gisch, D. “Apollonius' problem: A study of solutions and their connections”, 2004.
5. Greenberg, MJ Euclidean and non-euclidean geometries development and history. (third edition). WH Freeman and Company, 1993.