 determining areas and volumes.
The later (Hellenistic) period of Greek science is associated with the school of Alexandria. The greatest work of Greek mathematics, EuclidEuclid
, fl. 300 B.C., Greek mathematician. Little is known of his life other than the fact that he taught at Alexandria, being associated with the school that grew up there in the late 4th cent. B.C.
..... Click the link for more information. 's Elements (c.300 B.C.), appeared at the beginning of this period. Elementary geometry as taught in high school is still largely based on Euclid's presentation, which has served as a model for deductive systems in other parts of mathematics and in other sciences. In this method primitive terms, such as point and line, are first defined, then certain axioms and postulates relating to them and seeming to follow directly from them are stated without proof; a number of statements are then derived by deduction from the definitions, axioms, and postulates. Euclid also contributed to the development of arithmetic and presented a geometric theory of quadratic equations.
In the 3d cent. B.C., ArchimedesArchimedes
, 287–212 B.C., Greek mathematician, physicist, and inventor. He is famous for his work in geometry (on the circle, sphere, cylinder, and parabola), physics, mechanics, and hydrostatics.
..... Click the link for more information. , in addition to his work in mechanics, made an estimate of π and used the exhaustion theory of Eudoxus to obtain results that foreshadowed those much later of the integral calculus, and Apollonius of PergaApollonius of Perga,
fl. 247–205 B.C., Greek mathematician of the Alexandrian school. He produced a treatise on conic sections that included, as well as his own work, much of the work of his predecessors, among whom was Euclid.
..... Click the link for more information. named the conic sections and gave the first theory for them. A second Alexandrian school of the Roman period included contributions by Menelaus (c.A.D. 100, spherical triangles), Heron of AlexandriaHeron of Alexandria
mathematician and inventor. The dates of his birth and death are unknown; conjecture places them between the 2d cent. B.C. and the 3d cent. A.D. He is believed to have lived in Alexandria; although he wrote in Greek, his origin is uncertain.
..... Click the link for more information. (geometry), PtolemyPtolemy
(Claudius Ptolemaeus), fl. 2d cent. A.D., celebrated Greco-Egyptian mathematician, astronomer, and geographer. He made his observations in Alexandria and was the last great astronomer of ancient times.
..... Click the link for more information. (A.D. 150, astronomy, geometry, cartography), PappusPappus
, fl. c.300, Greek mathematician of Alexandria. He recorded and enlarged on the results of his predecessors, including Euclid and Apollonius of Perga, in his Mathematical Collection (8 books; date conjectural).
..... Click the link for more information. (3d cent., geometry), and DiophantusDiophantus
, fl. A.D. 250, Greek algebraist. He pioneered in solving a type of indeterminate algebraic equation where one seeks integer values for the unknowns; work in this field is known as Diophantine analysis. Only 6 of the 13 books with which he is credited are extant.
..... Click the link for more information. (3d cent., arithmetic).
Chinese and Middle Eastern Advances
Following the decline of learning in the West after the 3d cent., the development of mathematics continued in the East. In China, Tsu Ch'ung-Chih estimated π by inscribed and circumscribed polygons, as Archimedes had done, and in India the numerals now used throughout the civilized world were invented and contributions to geometry were made by AryabhataAryabhata
, c.476–550, Hindu mathematician and astronomer. He is one of the first known to have used algebra; his writings include rules of arithmetic and of plane and spherical trigonometry, and solutions of quadratic equations.
..... Click the link for more information. and BrahmaguptaBrahmagupta
, c.598–c.660, Indian mathematician and astronomer. He was among the first to meaningfully discuss the