Apollonius of Perga lived from approximately 262 B.C.E.-190 B.C.E. Born in Perga, which is known today as Murtina in Turkey, Apollonius was known as “The Great Geometer.” He introduced the idea of the parabola, ellipse, and hyperbola in his famous book titled, Conics. Though Apollonius was born in Perga, as a young scholar he traveled to Alexandria and studied under followers of Euclid. He also traveled to Pergamum. Pergamum had a university and library similar to those of Alexandria. While in Pergamum, Apollonius worked with Eudemus of Pergamum and Eudemus gained an interest in Apollonius’ work with conics. Apollonius actually had his son (also named Apollonius) take the second edition of book two of Conics from Alexandria to Pergamum to give to Eudemus which gives insight into the complicated way authors had to go about publishing at this time.
Various versions of Apollonius’ book, Conics, may be found today. The story behind this is an interesting one. Apollonius explained in the preface of book one, in a letter to Eudemus, that earlier drafts of his work circulated before he was ready. His good friend Naucrates the geometer came to stay with him in Alexandria, and encouraged him to investigate the topics he then addressed in Conics. Naucrates was about to set sail, so Apollonius sent with him the eight books he had put together, even though they were not edited to his liking. He had intentions to come back to them later, but book one and book two circulated before they were corrected.
Conics was written in eight books. Books one through four are devoted to an elementary introduction. Books one through three do not necessarily present new ideas, but they develop and improve upon those of Apolonius’ predecessors. Apollonius defines conic sections as “curves formed when a plan intersects the surface of a cone.” Book one discusses how to form the three sections (parabola, ellipse, and hyperbola) and discusses the characteristics of these sections with more detail than previous authors. Book two describes how hyperbolas are related to their asymptotes and he describes how to draw tangents to given conics. Book three introduces new discoveries and theorems which Apollonius described as “pretty.” He acknowledges that Euclid did not work out the synthesis of a locus in relation to three or four lines, but instead only observed a small portion of it. Apollonius believed Euclid needed the theorems he presented in book three in order to complete many of his proofs. Along with introducing new theorems, book four shows in how many points the sections of a cone can coincide with one another or with the circumference of a circle.
Books five to seven are unique and considered more advanced. In these books, Apollonius discusses normals to conics and demonstrates how many can be drawn from a point. He contributed to the development of the Cartesian equation of the evolute (the locus of the centers of the curvature) with his propositions determining the center of curvature. Book five focuses predominantly on minima and maxima. Book six addresses equal and similar conics. Book seven explains determinative theorems, and book eight provides some theorems determined in this way.
Apollonius had many other works, though none quite as popular as Conics. Apollonius was the author of Cutting of a Ration, Cutting an Area, On Determinant Section, Tangencies, Plane Loci, On the Burning Mirror, and On Verging Constructions. In On the Burning Mirror, Apollonius showed that parallel rays of light are not brought to a focus by a spherical mirror (as had been formerly thought) and he examined the focal properties of a parabolic mirror. In another book by Apollonius entitled Quick Delivery, he came up with a better approximation for pi than the previous method used by Archimedes.
Conics was written in eight books. Books one through four are devoted to an elementary introduction. Books one through three do not necessarily present new ideas, but they develop and improve upon those of Apolonius’ predecessors. Apollonius defines conic sections as “curves formed when a plan intersects the surface of a cone.” Book one discusses how to form the three sections (parabola, ellipse, and hyperbola) and discusses the characteristics of these sections with more detail than previous authors. Book two describes how hyperbolas are related to their asymptotes and he describes how to draw tangents to given conics. Book three introduces new discoveries and theorems which Apollonius described as “pretty.” He acknowledges that Euclid did not work out the synthesis of a locus in relation to three or four lines, but instead only observed a small portion of it. Apollonius believed Euclid needed the theorems he presented in book three in order to complete many of his proofs. Along with introducing new theorems, book four shows in how many points the sections of a cone can coincide with one another or with the circumference of a circle.
Books five to seven are unique and considered more advanced. In these books, Apollonius discusses normals to conics and demonstrates how many can be drawn from a point. He contributed to the development of the Cartesian equation of the evolute (the locus of the centers of the curvature) with his propositions determining the center of curvature. Book five focuses predominantly on minima and maxima. Book six addresses equal and similar conics. Book seven explains determinative theorems, and book eight provides some theorems determined in this way.
Apollonius had many other works, though none quite as popular as Conics. Apollonius was the author of Cutting of a Ration, Cutting an Area, On Determinant Section, Tangencies, Plane Loci, On the Burning Mirror, and On Verging Constructions. In On the Burning Mirror, Apollonius showed that parallel rays of light are not brought to a focus by a spherical mirror (as had been formerly thought) and he examined the focal properties of a parabolic mirror. In another book by Apollonius entitled Quick Delivery, he came up with a better approximation for pi than the previous method used by Archimedes.