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.
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   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.
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   3. Capacity of undergoing or suffering; fitness to be acted
      upon; susceptibility; -- called also {passive power}; as,
      great power of endurance.
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            Power, then, is active and passive; faculty is
            active power or capacity; capacity is passive power.
                                                  --Sir W.
                                                  Hamilton.
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   4. The exercise of a faculty; the employment of strength; the
      exercise of any kind of control; influence; dominion;
      sway; command; government.
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            Power is no blessing in itself but when it is
            employed to protect the innocent.     --Swift.
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   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.
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            And the powers of the heavens shall be shaken.
                                                  --Matt. xxiv.
                                                  29.
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   6. A military or naval force; an army or navy; a great host.
      --Spenser.
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            Never such a power . . .
            Was levied in the body of a land.     --Shak.
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   7. A large quantity; a great number; as, a power o? good
      things. [Colloq.] --Richardson.
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   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.
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   Note: The English unit of power used most commonly is the
         horse power. See {Horse power}.
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      (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.
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   Note: This use in mechanics, of power as a synonym for force,
         is improper and is becoming obsolete.
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      (d) A machine acted upon by an animal, and serving as a
          motor to drive other machinery; as, a dog power.
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   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.
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   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.
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   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.
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             The guiltiness of my mind, the sudden surprise of
             my powers, drove the grossness . . . into a
             received belief.                     --Shak.
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   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.
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   12. (Law) An authority enabling a person to dispose of an
       interest vested either in himself or in another person;
       ownership by appointment. --Wharton.
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   13. Hence, vested authority to act in a given case; as, the
       business was referred to a committee with power.
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   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.
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   {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 coordinates 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.
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