Apollonius of Perga (ca B.C. – ca B.C.) was one of the greatest mal, and differential geometries in Apollonius’ Conics being special cases of gen-. The books of Conics (Geometer’s Sketchpad documents). These models in Apollonius of Perga lived in the third and second centuries BC. Apollonius of Perga greatly contributed to geometry, specifically in the area of conics. Through the study of the “Golden Age” of Greek mathematics from about.
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Apollonius of Perga is famous for his work in geometry, particularly on ov. Unfortunately, most of these books are lost, although, a few did survive. There is not a lot of information that has survived regarding the life of Apollonius of Perga. Most of the information comes from his own work where he mentions details about his life in the prefaces of the books of his only surviving major work, Conics.
Apollonius was born in Perga, Pamphylia modern day Antalya in Turkey.
He was born between the years and B. He did his most famous work during the reign of Egyptian king Ptolemy Philopater during the years to B.
Apollonius lived in Alexandria and there is some dispute as to whether he studied with students of Euclid. Pappus, another mathematician who lived in Alexandria around the 4 th century A. Apollonius also wrote about visiting Pergamum and Ephesus. Pergamum is now known as Bergama and is in Izmir, Turkey. While in Pergamum, Apollonius met a man by the name of Eudemus.
Apollonius writes to Eudemus in the prefaces of his first three books. In the preface of his second book, Apollonius states that he is giving the book to his son also named Apollonius to send to Eudemus. This is the basis for the assumption that Apollonius was a mature man when he wrote his book Conics.
Conics | work by Apollonius of Perga |
In the preface of the second book, Apollonius mentions introducing Eudemus to a man named Philonideswhen they were all at the city of Ephesus. This helps set the time period when Apollonius wrote Conics. He was a philosopher as well as a mathematician and knew the Seleucid kings Antiochus IV Epiphanes reigned — b. Antiochus reigned between and B. This means that the introduction occurred sometime in the mids B. Further dating of the work can be done on the basis of Apollonius having a full-grown son.
Since his son conjcs old enough to deliver the second book to Eudemus, Apollonius must apolloniua been working around the second and third centuries. There is some internal evidence in the Conics to support this timeline.
Apollonius writes about Archimedes, apoplonius died around to B.
Apollonius writes in the preface to the fourth book that Eudemus has died and the rest of the books in Conics are addressed to a man named Attalus. Apollonius wrote a number of books but only two of them still exist today. The reason we know about the books is that in the 4 th century A.
Apollonius of Perga | Greek mathematician |
Apollonius is best known for his work Conics. Conics consists of eight different books but only seven still survive. The first four have survived in the original Greek but there is an Arabic translation of seven of the eight books. Apollonius wrote the book at the request of Naucrates, another mathematician who had visited him in Alexandria.
Apollonius had to finish the book quickly because Naucrates was leaving Alexandria. After writing the book and giving it to Naucrates, Apollonius spent more time on the book and revised some of the material. The revised edition is what make up the book. The definition of a conic states that it is the curve one gets at the intersection of a cone and a plane. By changing the place and angle of the intersection, different conic sections are created.
This basically just means that you can cut a cone in a specific angle to get different curves. To some extent, the first four books utilize the work of other mathematicians although Apollonius claims that he was expanded on the work and developed the work more than previous writers.
Most of the material would be well known to them. Book one looks at conics and their properties. He develops ways to create the three conics or sections, which he identifies as parabola, ellipse, and hyperbola. He then describes the three sections. Apollonius also looks at the basic properties of these three sections. Apollonius states that he has developed the concepts to a higher degree than previous writers.
Book two looks at diameters and axes of the conic sections as well as asymptotes. An axis is simply a straight line the cuts an object into two. An asymptote is a straight line that comes close to a curve but does not meet it.
Book three contains some original material and does not simply restate the work of other mathematicians. Apollonius states that he discovered new ideas on how to create solid loci a locus is another conic section.
He writes that after he came up with some of these ideas, he realized that Euclid had not figured out how to create locus using three and four lines. Apollonius stated that this was impossible to do without using the theorems that he had discovered. Apollonius also dealt with focal properties and with rectangles found in conic segments. Book four looks at the different ways that conic sections or the circumference of a circle can meet each other.
Apollonius states that a lot of the material in book four has not been addressed by other mathematicians. The first four books are a result of Apollonius organizing the work of other mathematicians into a more organized whole.
Previously, this work was a set of various theorems that were not connected in any way. Apollonius was a good enough mathematician to see how the various theorems could be connected according to his general method.
Conics of Apollonius
Book five is the most famous of the books that make up the Conic and the one that has received the most praise. In books five to seven, Apollonius looks at normals to conics.
Normals ae the mathematical name for lines that are perpendicular to an object, in this case, perpendicular to a conic. From these points, it is only possible to draw apoollonius normal to the other side of the conic. An evolute is a curve in geometry that describes a set of points at the centre of curvature for another curve.
Treatise on conic sections
Apollonius also looks at propositions dealing with the inequalities between functions of conjugate diameters. Conjugate diameters are two diameters of ellipses or hyperbolas that cut across lines chords that are parallel to one another. Book eight has been lost but there has been an attempt to restore it using the work of Pappus. A lemma is a helping theorem. It is a proposition that is used to help prove a larger proposition or theorem. The main reason for this is that the work is very difficult to read, particularly given the lack of mathematical symbols that modern mathematicians use.
Even though the text is difficult to read, it has been studied and praised by some of the greatest mathematicians, including Newton, Fermat, and Halley.
Apollonius wrote other books but these have all been lost. Pappus summarized six other books written by Apolloniusas well as summarizing Conics. In these six missing works, Apollonius took an in depth look at specific or general problems. Each book was divided into two books and according to Pappus, the works were important works that were studied by ancient mathematicians.
One book titled Cutting of a Ratio De Rationis Sectione is the only other book written by Apollonius that still exists, although the Arabic version is the only one that exists.
In this book, Apollonius looked athow to draw a straight line through a point and two other straight lines in such a way that the cut off sections have a specific ratio. Apollonius looked at specific cases as well as more general cases. Another book, Cutting of an Area De Spatii Sectionelooked at the same problem as in Cutting of a Ratio but in this book, Apollonius used rectangles.
The rectangle created by two intercepts needs to be equal to a specific rectangle.
According to Pappus, the book Tangencies De Tactionibus looked at the problem of how to describe a circle when you have three things circles, straight lines, or points in such a way so that the circle passes through the given points and touches the given circles or straight lines. In the lost book Inclinations De InclinationibusApollonjus wanted to demonstrate how a specific, straight line moving towards a point can be placed between two straight or circular lines.
The last missing work is called Plane Loci De Locis Planis and apollonis at a number of propositions about loci that are straight lines or circles. Other writers besides Pappus have mentioned the work done by Apollonius. According to these writers, Apollonius came up with the concept of eccentric orbits to explain the motion of the planets and the different speeds of the moon. His work on conics was the main work on the subject and a number of later mathematicians wrote commentaries or annotations on his work.
Apollonius of Perga – Famous Mathematicians.