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A mathematical instrument for laying down and measuring angles on paper, used in drawing or in plotting. It is of various forms, semicircular, rectangular, or circular.

.) See Methylene blue, under Methylene. -- Pure chemistry. See under Chemistry. -- Pure mathematics, that portion of mathematics which treats of the principles of the science, or contradistinction to applied mathematics, which treats of the application of the principles to the investigation of other branches of knowl…

Same as Tetragonal. Pyramidal numbers (Math.), certain series of figurate numbers expressing the number of balls or points that may be arranged in the form of pyramids. Thus 1, 4, 10, 20, 35, etc., are trangular pyramidal numbers; and 1, 5, 14, 30, 55, etc., are square pyramidal numbers.

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…

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

y the justices of peace in counties and by the recorders in boroughs. -- Quarter square (Math.), the fourth part of the square of a number. Tables of quarter squares have been devised to save labor in multiplying numbers. -- Quarter turn, Quarter turn belt (Mach.), an arrangement in which a belt transmits motion betw…

ot a perfect power of the degree indicated by the radical sign; a surd. -- Radical sign (Math.), the sign sq. root (originally the letter r, the initial of radix, root), placed before any quantity, denoting that its root is to be extracted; thus, sq. roota, or sq. root(a + b). To indicate any other than the square roo…

The movable limb of a sextant or other angular instrument. Knight. Radius bar (Math.), a bar pivoted at one end, about which it swings, and having its other end attached to a piece which it causes to move in a circular arc. -- Radius of curvature. See under Curvature.

ysical; mental. Moral philosophy was his chiefest end; for the rational, the natural, and mathematics . . . were but simple pastimes in comparison of the other. Sir T. North.

titution of reciprocals for given quantities. See the Phrases below. Reciprocal equation (Math.), one which remains unchanged in form when the reciprocal of the unknown quantity is substituted for that quantity. -- Reciprocal figures (Geom.), two figures of the same kind (as triangles, parallelograms, prisms, etc.), s…

l, a dial whose plane is inclined to the vertical line through its center. Davies & Peck (Math. Dict.).

ry little help us to a more positive idea of infinite duration. Locke. Recurring decimal (Math.), a circulating decimal. See under Decimal. -- Recurring series (Math.), an algebraic series in which the coefficients of the several terms can be expressed by means of certain preceding coefficients and constants in one un…

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.

opposite directions. -- Reverse fire (Mil.), a fire in the rear. -- Reverse operation (Math.), an operation the steps of which are taken in a contrary order to that in which the same or similar steps are taken in another operation considered as direct; an operation in which that is sought which in another operation…

t; a comet that has been seen at two of its approaches to the sun. -- Periodic function (Math.), a function whose values recur at fixed intervals as the variable uniformly increases. The trigonomertic functions, as sin x, tan x, etc., are periodic functions. Exponential functions are also periodic, having an imaginary…

The second growth of grass in a season; aftermath. [Prov. Eng. & Local, U.S.]

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.