DEFERENT
, or Deferens, in the ancient astronomy, an imaginary circle, which, as it were, carries about the body of a planet, and is the same with the eccentric; being invented to account for the eccentricity, perigee, and apogee of the planets.
DEFICIENT Hyperbola, is a curve having only one asymptote, though two hyperbolic legs running out infinitely by the side of the asymptote, but contrary ways. See Curve.
This name was given to the curves by Newton, in his Enumeratio Linearum tertii Ordinis. There are 6 different species of them, which have no diameters, expressed by the equation , the term ax3 being negative. When the equation | has all its roots real and unequal, the curve has an oval joined to it. When the two middle roots are equal, the oval joins to the legs, which then cut one another in shape of a noose. When three roots are equal, the nodus is changed into a very acute cusp or point. When, of three roots with the same sign, the two greatest are equal, the oval vanishes into a point. When any two roots are imaginary, there is only a pure serpentine hyperbola, without any oval, decussation, cusp, or conjugate point; and when the terms b and d are wanting, it is of the 6th species.
There are also 7 different species of these curves, having each one diameter, expressed by the above equation when the term ey is wanting: according to the various conditions of the roots of the equation , as to their reality, equality, their having the same signs, or two of them being imaginary.
Deficient Numbers, are those whose aliquot parts added together, make a sum less than the whole number: as 8, whose parts 1, 2, 4, make only 7; or the number 16, whose parts 1, 2, 4, 8 make only 15.
