Power of a point

Power Pow"er, n. [OE. pouer, poer, OF. poeir, pooir, F. pouvoir, n. & v., fr. LL. potere, for L. posse, potesse, to be able, to have power. See {Possible}, {Potent}, and cf. {Posse comitatus}.] 1. Ability to act, regarded as latent or inherent; the faculty of doing or performing something; capacity for action or performance; capability of producing an effect, whether physical or moral: potency; might; as, a man of great power; the power of capillary attraction; money gives power. ``One next himself in power, and next in crime.'' --Milton. [1913 Webster]

2. Ability, regarded as put forth or exerted; strength, force, or energy in action; as, the power of steam in moving an engine; the power of truth, or of argument, in producing conviction; the power of enthusiasm. ``The power of fancy.'' --Shak. [1913 Webster]

3. Capacity of undergoing or suffering; fitness to be acted upon; susceptibility; -- called also {passive power}; as, great power of endurance. [1913 Webster]

Power, then, is active and passive; faculty is active power or capacity; capacity is passive power. --Sir W. Hamilton. [1913 Webster]

4. The exercise of a faculty; the employment of strength; the exercise of any kind of control; influence; dominion; sway; command; government. [1913 Webster]

Power is no blessing in itself but when it is employed to protect the innocent. --Swift. [1913 Webster]

5. The agent exercising an ability to act; an individual invested with authority; an institution, or government, which exercises control; as, the great powers of Europe; hence, often, a superhuman agent; a spirit; a divinity. ``The powers of darkness.'' --Milton. [1913 Webster]

And the powers of the heavens shall be shaken. --Matt. xxiv. 29. [1913 Webster]

6. A military or naval force; an army or navy; a great host. --Spenser. [1913 Webster]

Never such a power . . . Was levied in the body of a land. --Shak. [1913 Webster]

7. A large quantity; a great number; as, a power o? good things. [Colloq.] --Richardson. [1913 Webster]

8. (Mech.) (a) The rate at which mechanical energy is exerted or mechanical work performed, as by an engine or other machine, or an animal, working continuously; as, an engine of twenty horse power. [1913 Webster]

Note: The English unit of power used most commonly is the horse power. See {Horse power}. [1913 Webster] (b) A mechanical agent; that from which useful mechanical energy is derived; as, water power; steam power; hand power, etc. (c) Applied force; force producing motion or pressure; as, the power applied at one and of a lever to lift a weight at the other end. [1913 Webster]

Note: This use in mechanics, of power as a synonym for force, is improper and is becoming obsolete. [1913 Webster] (d) A machine acted upon by an animal, and serving as a motor to drive other machinery; as, a dog power. [1913 Webster]

Note: Power is used adjectively, denoting, driven, or adapted to be driven, by machinery, and not actuated directly by the hand or foot; as, a power lathe; a power loom; a power press. [1913 Webster]

9. (Math.) The product arising from the multiplication of a number into itself; as, a square is the second power, and a cube is third power, of a number. [1913 Webster]

10. (Metaph.) Mental or moral ability to act; one of the faculties which are possessed by the mind or soul; as, the power of thinking, reasoning, judging, willing, fearing, hoping, etc. --I. Watts. [1913 Webster]

The guiltiness of my mind, the sudden surprise of my powers, drove the grossness . . . into a received belief. --Shak. [1913 Webster]

11. (Optics) The degree to which a lens, mirror, or any optical instrument, magnifies; in the telescope, and usually in the microscope, the number of times it multiplies, or augments, the apparent diameter of an object; sometimes, in microscopes, the number of times it multiplies the apparent surface. [1913 Webster]

12. (Law) An authority enabling a person to dispose of an interest vested either in himself or in another person; ownership by appointment. --Wharton. [1913 Webster]

13. Hence, vested authority to act in a given case; as, the business was referred to a committee with power. [1913 Webster]

Note: Power may be predicated of inanimate agents, like the winds and waves, electricity and magnetism, gravitation, etc., or of animal and intelligent beings; and when predicated of these beings, it may indicate physical, mental, or moral ability or capacity. [1913 Webster]

{Mechanical powers}. See under {Mechanical}.

{Power loom}, or {Power press}. See Def. 8 (d), note.

{Power of attorney}. See under {Attorney}.

{Power of a point} (relative to a given curve) (Geom.), the result of substituting the co["o]rdinates of any point in that expression which being put equal to zero forms the equation of the curve; as, x^{2} + y^{2} - 100 is the power of the point x, y, relative to the circle x^{2} + y^{2} - 100 = 0. [1913 Webster]