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A calculating frame used for arithmetical calculations in ancient Greece, ancient Rome and later, up to the 18th century, in Western Europe. The frame was su

...ium B.C. describe some first practical applications of magnetic phenomena. Ancient Hindus used the magnet for extracting iron ferrules of arrows from the bodi

The conic sections were known already to the mathematicians of Ancient Greece. The most complete work concerned with these curves at that time was the bo ...cal properties of a conic section given by this equation were known to the ancient geometers, and served for Apollonius of Perga as the reason for giving the

...he remaining axioms. Attempts at proofs occurred as long ago as in Ancient Greece. These attempts continued in the East in the Middle Ages and then in Wester

...added. Operations on fractions (cf. [[Fraction|Fraction]]) were reduced in Ancient Egypt to operations on aliquot fractions, i.e. on fractions of the type $ ...in executing arithmetic operations. There are numerous tables employed by ancient Babylonians to effect multiplication and division.

...f which apparently preceded the introduction of written language. The most ancient systems of numbering (see [[Numbers, representations of|Numbers, representa ===Ancient Greece===

...he creation of the theory of rational numbers by the scientists of Ancient Greece led to the study of rational solutions of indefinite equations. This point ...a10]</TD> <TD valign="top"> B.L. van der Waerden, "Geometry and algebra in ancient civilisations" , Springer (1983)</TD></TR><TR><TD valign="top">[a11]</TD> <

...ogether with the simplest geometrical figures, were the first and the most ancient mathematical concepts. Number theory arose from problems in [[Arithmetic|ar In Ancient Greece (6th century B.C.) divisibility of integers was studied, and particular sub

...d been successfully employed in various forms by the scientists of Ancient Greece and of Europe in the Middle Ages to solve problems in geometry and in natur 1) The simplest problems, solved by the mathematicians of Ancient Greece by the method of exhaustion (cf. [[Exhaustion, method of|Exhaustion, method

...on of a fairly large store of factual material, and arose first in Ancient Greece in the 6th–5th centuries B.C.. The development of mathematics up to that ...In this way material was accumulated which gradually added up to that most ancient mathematical science: [[Arithmetic|arithmetic]]. The measurement of area an

...ted to the method of exhaustion developed by the mathematicians of Ancient Greece (cf. [[Exhaustion, method of|Exhaustion, method of]]). This method arose in

...century B.C. and the 1st century A.D. geometry mainly developed in Ancient Greece. The result was an accumulation of knowledge on metric relationships govern ...gn="top">[a19]</TD> <TD valign="top"> M. Kline, "Mathematical thought from ancient to modern times" , Oxford Univ. Press (1972) {{MR|0472307}} {{ZBL|0277.0100

...t of the classic definition of area and volume, which goes back to ancient Greece. Thus, a set $ E \subset \mathbf R^{k} $