Serenus of Antinouplis
Encyclopedia
Serenus of Antinouplis was an ancient Hellenistic mathematician
.
founded by Hadrian
. Two sources confirm that he was born in Antinouplis. It was once believed that he was born in Antissa
, but this has been shown to have been based on an error.
Serenus wrote a commentary on the Conics of Apollonius
, which is now lost. We hear from Theon of Smyrna
that the main result of the commentary was that of a number of angles that are subtended at a point on a diameter of a circle that is not the center, then with equal arcs of that circle, the angle nearer to the center is always less than the angle farther away from the center. But he was also a prime mathematician in his own right, having written two works entitled On the Section of a Cylinder and On the Section of a Cone, works that came to be connected to Apollonius' Conics. This connection helped them to survive through the ages.
In the preface of On the Section of a Cylinder, Serenus states that his motivation for writing this work, as summarized by Heath, was that "many persons who were students of geometry were under the erroneous that the oblique section of a cylinder was different from the oblique section of a cone known as an ellipse, whereas it is of course the same curve." The work consists of thirty-three propositions.
In propositions one though fifty-seven of On the Section of a Cone, Serenus deals largely with the areas of triangular sections of right and scalene cones that are created by planes passing through the vertex. He shows when the area of a triangle of a certain class of triangles is at its maximum. Propositions fifty-eight through sixty-nine form a separate section of the book and deal with the volumes of right right cones in relation to their heights, their bases and the areas of triangular sections through the axis.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
Life and work
Serenus came either from Antinoeia or from Antinouplis, a city in EgyptEgypt
Egypt , officially the Arab Republic of Egypt, Arabic: , is a country mainly in North Africa, with the Sinai Peninsula forming a land bridge in Southwest Asia. Egypt is thus a transcontinental country, and a major power in Africa, the Mediterranean Basin, the Middle East and the Muslim world...
founded by Hadrian
Hadrian
Hadrian , was Roman Emperor from 117 to 138. He is best known for building Hadrian's Wall, which marked the northern limit of Roman Britain. In Rome, he re-built the Pantheon and constructed the Temple of Venus and Roma. In addition to being emperor, Hadrian was a humanist and was philhellene in...
. Two sources confirm that he was born in Antinouplis. It was once believed that he was born in Antissa
Antissa
Antissa was a city of the island Lesbos , near to Cape Sigrium, the western point of Lesbos. The place had a harbour. The ruins found by Richard Pococke at Calas Limneonas, a little NE. of cape Sigri, may be those of Antissa. This place was the birth-place of Terpander, who is said to be the...
, but this has been shown to have been based on an error.
Serenus wrote a commentary on the Conics of Apollonius
Apollonius of Perga
Apollonius of Perga [Pergaeus] was a Greek geometer and astronomer noted for his writings on conic sections. His innovative methodology and terminology, especially in the field of conics, influenced many later scholars including Ptolemy, Francesco Maurolico, Isaac Newton, and René Descartes...
, which is now lost. We hear from Theon of Smyrna
Theon of Smyrna
Theon of Smyrna was a Greek philosopher and mathematician, whose works were strongly influenced by the Pythagorean school of thought. His surviving On Mathematics Useful for the Understanding of Plato is an introductory survey of Greek mathematics.-Life:Little is known about the life of Theon of...
that the main result of the commentary was that of a number of angles that are subtended at a point on a diameter of a circle that is not the center, then with equal arcs of that circle, the angle nearer to the center is always less than the angle farther away from the center. But he was also a prime mathematician in his own right, having written two works entitled On the Section of a Cylinder and On the Section of a Cone, works that came to be connected to Apollonius' Conics. This connection helped them to survive through the ages.
In the preface of On the Section of a Cylinder, Serenus states that his motivation for writing this work, as summarized by Heath, was that "many persons who were students of geometry were under the erroneous that the oblique section of a cylinder was different from the oblique section of a cone known as an ellipse, whereas it is of course the same curve." The work consists of thirty-three propositions.
- Proposition six proves the existence an oblique cylinder of the parallel circular sections subcontrary to the series of which the bases are two.
- Proposition nine proves that the section by any plane not parallel to that of the bases or of one of the subcontrary sections but cutting all the generators is not a circle.
- Propositions fourteen and sixteen, the main results, are follow ups of the previous propositions where the said section is proved to have the property of the ellipse.
- Proposition seventeen puts the property that was found in propositions fourteen and sixteen into the Apollonian form using the latus rectum.
- Propositions twenty-nine to thirty-three deal with an optical problem. He gives a definition of parallelsParallelsParallels may refer to:* Circle of latitude , imaginary east-west circles connecting all locations that share a given latitude* "Parallels", the third track from the 1977 Yes album Going for the One...
that was generally ridiculed.
In propositions one though fifty-seven of On the Section of a Cone, Serenus deals largely with the areas of triangular sections of right and scalene cones that are created by planes passing through the vertex. He shows when the area of a triangle of a certain class of triangles is at its maximum. Propositions fifty-eight through sixty-nine form a separate section of the book and deal with the volumes of right right cones in relation to their heights, their bases and the areas of triangular sections through the axis.