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principle, or end; a complete exhibition of essential principles or facts, arranged in a rational dependence or connection; a regular union of principles or parts forming one entire thing; as, a system of philosophy; a system of government; a system of divinity; a system of botany or chemistry; a military system; the…

is held of another by service; property which one holds of a lord or proprietor in consideration of some military or pecuniary service; fief; fee.

The ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another. See Versor.

faith is to be based solely upon what is delivered from competent authority, exclusive of rational processes.

riple measure (Mus.), a measure of tree beats of which first only is accented. -- Triple ratio (Math.), a ratio which is equal to 3. -- Triple salt (Chem.), a salt containing three distinct basic atoms as radicals; thus, microcosmic salt is a triple salt. -- Triple star (Astron.), a system of three stars in close pr…

Made thrice as much; threefold; tripled. Triplicate ratio (Math.), the ratio of the cubes of two quantities; thus, the triplicate ratio of a to b is a3: b3.

Designating, or pert. to, a gear for reducing or increasing a velocity ratio two to one.

Most remote; furthest; final; last. Ultima ratio Etym: [L.], the last reason or argument; the last resort. -- Ultima Thule. [L.] See Thule.

result; final. Those ultimate truths and those universal laws of thought which we can not rationally contradict. Coleridge.

The power to understand; the intellectual faculty; the intelligence; the rational powers collectively conceived an designated; the higher capacities of the intellect; the power to distinguish truth from falsehood, and to adapt means to ends. There is a spirit in man; and the inspiration of the Almighty them understandi…

se; -- said of a curve when the coördinates of the point on the curve can be expressed as rational algebraic functions of a single parameter th.

In a uniform manner; without variation or diversity; by a regular, constant, or common ratio of change; with even tenor; as, a temper uniformly mild. To vary uniformly (Math.), to vary with the ratio of the corresponding increments constant; -- said of two dependent quantities with regard to each other.…

A salt of orthosilicic acid, H4SiO4; -- so called because the ratio of the oxygen atoms united to the basic metals and silicon respectively is 1:1; for example, Mg2SiO4 or 2MgO.SiO2.

Especially, that which is seen otherwise than by the ordinary sight, or the rational eye; a supernatural, prophetic, or imaginary sight; an apparition; a phantom; a specter; as, the visions of Isaiah. The baseless fabric of this vision. Shak. No dreams, but visions strange. Sir P. Sidney.

ness, quantity, or caliber of voice or tone. Atomic volume, Molecular volume (Chem.), the ratio of the atomic and molecular weights divided respectively by the specific gravity of the substance in question. -- Specific volume (Physics & Chem.), the quotient obtained by dividing unity by the specific gravity; the recip…

Flexible rods the period of vibration of which in two planes at right angles are in some exact ratio to one another. When one end of such a rod is fixed, the free end describes in vibrating the corresponding Lissajous figure. So called because devised by Sir Charles Wheatstone.