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of the Pythagorean philosophy is the idea of number, the recognition of the numerical and mathematical relations of things. Encyc. Brit. Pythagorean proposition (Geom.), the theorem that the square described upon the hypothenuse of a plane right-angled triangle is equal to the sum of the squares described upon the othe…

at which can be increased, diminished, or measured; especially (Math.), anything to which mathematical processes are applicable.

a hollow cylinder. This singular phenomenon was first discovered by Sir W. R. Hamilton by mathematical reasoning alone, unaided by experiment. -- Differential refraction (Astron.), the change of the apparent place of one object relative to a second object near it, due to refraction; also, the correction required to be…

To serve as a sign or symbol of; as, mathematical symbols represent quantities or relations; words represent ideas or things.

r operation; consequence or effect; as, the result of a course of action; the result of a mathematical operation. If our proposals once again were heard, We should compel them to a quick result. Milton.

A mathematical instrument, consisting of a slip of wood, ivory, or metal, with one or more sets of spaces graduated and numbered on its surface, for measuring or laying off distances, etc., as in drawing, plotting, and the like. See Gunter's scale.

Any lineal or mathematical diagram; an outline. To draw an exact scheme of Constantinople, or a map of France. South.

A mathematical instrument, consisting of two rulers connected at one end by a joint, each arm marked with several scales, as of equal parts, chords, sines, tangents, etc., one scale of each kind on each arm, and all on lines radiating from the common center of motion. The sector is used for plotting, etc., to any scale…

usually go together; an assortment; a suit; as, a set of chairs, of china, of surgical or mathematical instruments, of books, etc. [In this sense, sometimes incorrectly written sett.]

e on ways or guides by screws or otherwise, and having compound motion. -- Slide rule, a mathematical instrument consisting of two parts, one of which slides upon the other, for the mechanical performance of addition and subtraction, and, by means of logarithmic scales, of multiplication and division. -- Slide valve.…

described by a point, called the generatrix, moving along a straight line according to a mathematical law, while the line is revolving about a fixed point called the pole. Cf. Helix.

Right, in a mathematical sense; passing from one point to another by the nearest course; direct; not deviating or crooked; as, a straight line or course; a straight piece of timber. And the crooked shall be made straight. Isa. xl. 4. There are many several sorts of crooked lines, but there is only one which is straight…

To adjust, as the mathematical scale to the actual scale, or to that in actual use.

s yet closely suggestive of its origin in nature, and this system of tuning, although not mathematically true, yet satisfies the ear, while it has the convenience that the same twelve fixed tones answer for every key or scale, C# becoming identical with D, and so on.

the final university examination for classical honors, optional to all who have taken the mathematical honors. C. A. Bristed. -- Tripos paper, a printed list of the successful candidates for mathematical honors, accompanied by a piece in Latin verse. There are two of these, designed to commemorate the two tripos days.…

To alter or change in succession; to alternate; as, one mathematical quantity varies inversely as another. While fear and anger, with alternate grace, Pant in her breast, and vary in her face. Addison.

f elementary matter in continuous vortical motion. It is conveniently regarded in certain mathematical speculations as the typical form and structure of the chemical atom. -- Vortex wheel, a kind of turbine.

ncompressible, frictionless fluid. Various properties of such atoms (vortex atoms) can be mathematically deduced.

eous and equal displacement of the particles composing a wave of vibration. (b) (Geom.) A mathematical surface of the fourth order which, upon certain hypotheses, is the locus of a wave surface of light in the interior of crystals. It is used in explaining the phenomena of double refraction. See under Refraction. -- W…

rtaining to a zone; having the form of a zone or zones. Zonal equation (Crystallog.), the mathematical relation which belongs to all the planes of a zone, and expresses their common position with reference to the axes. -- Zonal structure (Crystallog.), a structure characterized by the arrangements of color, inclusions…