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d. Duplicate proportion or ratio (Math.), the proportion or ratio of squares. Thus, in geometrical proportion, the first term to the third is said to be in a duplicate ratio of the first to the second, or as its square is to the square of the second. Thus, in 2, 4, 8, 16, the ratio of 2 to 8 is a duplicate of that of 2…

A geometrical projection of a building, or other object, on a plane perpendicular to the horizon; orthographic projection on a vertical plane; -- called by the ancients the orthography. Angle of elevation (Geodesy), the angle which an ascending line makes with a horizontal plane. -- Elevation of the host (R. C. Ch.),…

A genus of spiders, including the common garden spider (E. diadema). They spin geometrical webs. See Garden spider.

drawn through the apex of the umbo bisects the valve, or divides it into two equal and symmetrical parts. -- Mutually equilateral, applied to two figures, when every side of the one has its equal among the sides of the other.

to be 1390 foot pounds upon the Centigrade, or 772 foot pounds upon the Fahrenheit, thermometric scale, whence it is often called Joule's equivalent, and represented by the symbol J. This is equal to 424 kilogram meters (Centigrade scale). A more recent determination by Professor Rowland gives the value 426.9 kilogram…

An unsymmetrical, divalent, hydrocarbon radical, C2H4 metameric with ethylene but written thus, CH3.CH to distinguish it from the symmetrical ethylene, CH2.CH2. Its compounds are derived from aldehyde. Formerly called also ethidene.

An instrument for the volumetric measurement of gases; -- so named because frequently used to determine the purity of the air.

The fundamental forms of organic life, that are composed of two equal and symmetrical halves. Syd. Soc. Lex.

An ancient geometrical method in which an exhaustive process was employed. It was nearly equivalent to the modern method of limits.

One of the metrical tales of the Trouvères, or early poets of the north of France.

iel Fahrenheit in the graduation of his thermometer; of or relating to Fahrenheit's thermometric scale. -- n.

umbers in the resulting series being such that points representing them are capable of symmetrical arrangement in different geometrical figures, as triangles, squares, pentagons, etc.

Contention; strife; scolding; specif., a kind of metrical contest between two persons, popular in Scotland in the 16th century. [Obs. or Scot.]

used with numerals, chiefly in composition, to denote multiplication or increase in a geometrical ratio, the doubling, tripling, etc., of anything; as, fourfold, four times, increased in a quadruple ratio, multiplied by four.

A combination of syllables consisting a metrical element of a verse, the syllables being formerly distinguished by their quantity or length, but in modern poetry by the accent.

rmometer, reckoned from its zero of expansion. -- Circular functions. See Inverse trigonometrical functions (below). -- Continuous function, a quantity that has no interruption in the continuity of its real values, as the variable changes between any specified limits. -- Discontinuous function. See under Discontinuo…

eties differing in color and in their constituents, but with the same crystallization (isometric), and conforming to the same general chemical formula. The commonest color is red, the luster is vitreous, and the hardness greater than that of quartz. The dodecahedron and trapezohedron are the common forms.…

The formation or production of any geometrical magnitude, as a line, a surface, a solid, by the motion, in accordance with a mathematical law, of a point or a magnitude; as, the generation of a line or curve by the motion of a point, of a surface by a line, a sphere by a semicircle, etc.

One skilled in geometry; a geometrician; a mathematician. I. Watts.

To investigate or apprehend geometrical quantities or laws; to make geometrical constructions; to proceed in accordance with the principles of geometry. Nature geometrizeth, and observeth order in all things. Sir T. Browne.