ety or order similar to, and possibly influenced by, the earlier Orphic cult.
..... Click the link for more information. , PlatoPlato
, 427?–347 B.C., Greek philosopher. Plato's teachings have been among the most influential in the history of Western civilization. Life
After pursuing the liberal studies of his day, he became in 407 B.C. a pupil and friend of Socrates. From about 388 B.
..... Click the link for more information. , and AristotleAristotle
, 384–322 B.C., Greek philosopher, b. Stagira. He is sometimes called the Stagirite. Life
Aristotle's father, Nicomachus, was a noted physician. Aristotle studied (367–347 B.C.
..... Click the link for more information. , and by the schools associated with them. The Pythagorean theorem, known earlier in Mesopotamia, was discovered by the Greeks during this period.
During the Golden Age (5th cent. B.C.), Hippocrates of Chios made the beginnings of an axiomatic approach to geometry and Zeno of EleaZeno of Elea
, c.490–c.430 B.C., Greek philosopher of the Eleatic school. He undertook to support in his only known work, fragments of which are extant, the doctrine of Parmenides by demonstrating that motion and multiplicity are logically impossible.
..... Click the link for more information. proposed his famous paradoxes concerning the infinite and the infinitesimal, raising questions about the nature of and relationships among points, lines, and numbers. The discovery through geometry of irrational numbers, such as √2, also dates from this period. Eudoxus of CnidusEudoxus of Cnidus
, 408?–355? B.C., Greek astronomer, mathematician, and physician. From the accounts of various ancient writers, he appears to have studied with Plato in Athens, spent some time in Heliopolis, Egypt, founded a school in Cyzicus, and spent his later years
..... Click the link for more information. (4th cent. B.C.) resolved certain of the problems by proposing alternative methods to those involving infinitesimals; he is known for his work on geometric proportions and for his exhaustion theory for 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 Alex