This man, whose value was unknown at the time, is counted among the greatest scholars of Ancient Greek mathematics, along with Archimedes and Euclid.
(3rd-2nd century BC) Ancient Greek mathematician. His work on conics greatly influenced the development of analytical geometry. He was born in Perge in Pamphylia, one of the great settlement centers of the Ancient Age, in Anatolia. This city, which is located within the borders of Antalya province today, was under the rule of the Egyptian king Ptolemy III at that time. The only documentary sources on the life of Apollonios are the collections of the Alexandrian mathematician Pappos. From what Pappos tells, it is understood that Apollonios was educated and lectured in Euclid's school in Alexandria, and it is most likely thought that he died in this city. It is known that Apollonios worked for a while in Bergama, where the largest library and university of the Hellenistic period after Alexandria were located, and wrote his famous work, Konikler, here. He dedicated various parts of his work to the ancient Greek thinker Eudemos, whom he knew here, and to Attalos I, king of Pergamum. A part of Apollonios' works other than Conics has survived to the present day thanks to some quotations from Pappos's work called The Collection.
Apollonius of Perga (c. 240 BC – c. 190 BC) was an Ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the contributions of Euclid and Archimedes on the topic, he brought them to the state prior to the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today. Gottfried Wilhelm Leibniz stated, “He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times.”
Apollonios had the opportunity to examine Euclid's famous work Stoichea ("Elements") and another work on conics in Alexandria, and he made extensive use of these studies while preparing Conics. The first four volumes of Konikler, which consist of eight booklets, are in their original language, three of which are written by the Arab mathematician Sabit b. It has survived with the translation of Kurra, and the last volume has been lost. In 1710, Halley published all seven volumes translated into Latin. In the preface to the first volume, Apollonios explains that he determined the main lines of the work in Alexandria and completed the details in Bergama, and states that he handled the first four volumes, which are devoted to the basic features of the curves, at the simplest level. Indeed, these chapters are a systematic compilation of the work of Euclid and other great mathematicians, apart from the new theorems and original results in Volume 3. According to Apollonios, who introduced new and original definitions of cones starting from Volume V, which is still valid today, cones are planar curves that emerge as a result of the intersection of a cone and a plane. It is Apollonios who first named the cones, which Euclid described as "right-angled cone", "wide-angle cone", and "narrow-angle cone", as an ellipse, hyperbola, and parabola. It is believed that while making these namings, he started out from the "geometric algebra" of Pythagoras. Although Apollonios brought the concept of conics to a very advanced point, he did not define the directing of conics anywhere, and he used the concept of focus indirectly only for ellipses and hyperbolas. Although Pappos mentioned these two concepts later, it was necessary to wait for Kepler the development of the focus theory and for Newton the use straightening in geometric applications.
Apollonios, in his work called Proportional Cut, which has reached our day with its Arabic translation, also examines the drawing of the distances of a third line passing through a fixed point and intersecting any two lines, between the predetermined points on these two lines and the intersection points, in such a way as to form certain proportions. He deals with a similar problem of proportion in Pappos' work on Determination of the Field, which has survived with quotations from his collections. In Bounded Sections, on the other hand, it examines the ratios that an N point will create with other points on a line on which A, B, C, and D points are determined. It investigates the condition that there is a constant ratio between the product of the lengths AN and CN and the product of the lengths of BN and DN. His treatise Tangents is about drawing a circle in very different conditions. This circle will either be tangent to the three given lines or circles or pass through the three given points. Moreover, when these circles, points, and lines are combined in various ways, ten different arrangements emerge, such as the drawing of a circle passing through a point and tangent to two lines. Two of them are in the Elements of Euclid, six are in the first volume of the Tangents, and the remaining two are in the II. dissolved in the skin. Drawing a circle that satisfies the condition of being tangent to three circles is one of the most challenging geometry problems and is known as the "Apollonios problem".
In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane. Apollonius of Perga (c. 262 BC – c. 190 BC) posed and solved this famous problem in his work Ἐπαφαί (Epaphaí, "Tangencies"); this work has been lost, but a 4th-century AD report of his results by Pappus of Alexandria has survived.
Starting from the end of the 16th century, with the work of the French mathematician Viete, the interest in Tangents gradually increased, and the general solution to the problem was later realized by Gauss and many other mathematicians. It is known that Apollonios, who provided a rich source for geometers after him with his work Plane Focals, also had a work called Comparison of Twelve and Twenty-Faced, a book titled Cylinder Shaped Helix mentioned by the Ancient Greek sage Proklos, and a study on the basic subjects of geometry. Apollonios, who is thought to have calculated the "Pi" number, which Archimedes determined as a value between 3.1/7 and 3.10/71, more accurately than he and to have introduced the "tetrates system" to multiply or specify large numbers, was first mentioned by Eudoxos of Knidos and Euclid He also developed the theory of irrational numbers, which was examined by.
Apollonios, who also deals with optics, showed that parallel rays coming to a spherical mirror do not focus in the center of the sphere as it was thought, and also examined the focal properties of the parabolic mirror. Some sources also state that he made a sundial that shows the time quite accurately by using conical planes. Although it is known that Apollonios was also interested in astronomy, like almost all the mathematicians of that age, his contributions to this field are not clear. However, from the Almagest of the great astronomer Ptolemy, it is understood that Apollonios developed the theories of "loop" (epicycle) and "eccentric motion" and argued that the apparent irregularities in the motions of the Sun, Moon, and planets could be explained in this way.
In the Hellenistic period, when natural sciences made great progress, Apollonios was not given the necessary attention, and the problems he thought about were accepted as a mathematical game for centuries. However, in the 1600s, when Kepler felt the need to apply the concepts of parabola and ellipse to determine the locations of planets and other celestial bodies, Apollonios and its conics came to the fore again. Later, Newton also benefited from Kepler's work while thinking about the laws of gravity. Thus, these concepts, which found application in the 17th century, gave Apollonios a well-deserved but belated reputation as indispensable elements of mathematical astronomy and analytical geometry that began to develop in the 19th century. Today, together with Apollonios, Archimedes, and Euclid, he is considered among the greatest scholars of Ancient Greek mathematics, which lived its heyday between 300-200 BC.