# crunodal Sentence Examples

• The name lemniscate is sometimes given to any crunodal quartic curve having only one real finite branch which is symmetric about the axis.

• For a crunodal cubic the six inflections which disappear are two of them real, the other four imaginary, and there remain two imaginary inflections and one real inflection.

• The oval may unite itself with the infinite branch, or it may dwindle into a point, and we have the crunodal and the acnodal forms respectively; or if simultaneously the oval dwindles into a point and unites itself to the infinite branch, we have the cuspidal form.

• crunodal or acnodal), or cuspidal; and we see further that there are two kinds of non-singular curves, the complex and the simplex.

• There is thus a complete division into the five kinds, the complex, simplex, crunodal, acnodal and cuspidal.

• Each singular kind presents itself as a limit separating two kinds of inferior singularity; the cuspidal separates the crunodal and the acnodal, and these last separate from each other the complex and the simplex.

• And it then appears that there are two kinds of non-singular cubic cones, viz, the simplex, consisting of a single sheet, and the complex, consisting of a single sheet and a twin-pair sheet; and we thence obtain (as for cubic curves) the crunodal, the acnodal and the cuspidal kinds of cubic cones.

• The singular kinds arise as before; in the crunodal and the cuspidal kinds the whole curve is an odd circuit, but in an acnodal kind the acnode must be regarded as an even circuit.

• The name lemniscate is sometimes given to any crunodal quartic curve having only one real finite branch which is symmetric about the axis.

• For a crunodal cubic the six inflections which disappear are two of them real, the other four imaginary, and there remain two imaginary inflections and one real inflection.

• The oval may unite itself with the infinite branch, or it may dwindle into a point, and we have the crunodal and the acnodal forms respectively; or if simultaneously the oval dwindles into a point and unites itself to the infinite branch, we have the cuspidal form.

• crunodal or acnodal), or cuspidal; and we see further that there are two kinds of non-singular curves, the complex and the simplex.

• There is thus a complete division into the five kinds, the complex, simplex, crunodal, acnodal and cuspidal.

• Each singular kind presents itself as a limit separating two kinds of inferior singularity; the cuspidal separates the crunodal and the acnodal, and these last separate from each other the complex and the simplex.

• And it then appears that there are two kinds of non-singular cubic cones, viz, the simplex, consisting of a single sheet, and the complex, consisting of a single sheet and a twin-pair sheet; and we thence obtain (as for cubic curves) the crunodal, the acnodal and the cuspidal kinds of cubic cones.

• The singular kinds arise as before; in the crunodal and the cuspidal kinds the whole curve is an odd circuit, but in an acnodal kind the acnode must be regarded as an even circuit.