cissoid definition

  • noun:
    • some of a family of curves thought as the locus of a place, P, on a line from certain fixed point and intersecting two offered curves, C1 and C2, where the distance along the range from C1 to P continues to be constant and equat on distance from P to C2.
    • A curve invented by Diocles, for the true purpose of resolving two celebrated issues of the higher geometry; viz., to trisect a plane perspective, and build two geometrical means between two provided straight outlines.
    • A curve of this third-order and third class, having a cusp during the origin and a point of inflection at infinity.
    • it absolutely was created by one Diocles, a geometer of this second century b. c., with a view into answer regarding the famous dilemma of the duplication regarding the cube, or perhaps the insertion of two mean proportionals between two offered right lines. Its equation is x=y (a—x). In cissoid of Diocles the generating curve is a circle; a spot A is believed on this circle, and a tangent M M' through the contrary extremity associated with diameter attracted from A; then the residential property regarding the curve is that if from A any oblique line be attracted to M M', the segment with this range involving the group and its own tangent is equivalent to the portion between A and the cissoid. But the name has sometimes been offered in subsequent times to any or all curves described in a similar manner, where the generating bend is not a circle.
    • Any of a family group of curves understood to be the locus of a place, P, on a line from a given fixed-point and intersecting two provided curves, C1 and C2, in which the distance over the line from C1 to P remains constant and equat on distance from P to C2.
    • A curve conceived by Diocles, for the purpose of resolving two famous problems of the higher geometry; viz., to trisect an airplane perspective, also to build two geometrical means between two given right lines.
    • A curve regarding the third order and third class, having a cusp during the beginning and a point of inflection at infinity.
    • It was designed by one Diocles, a geometer associated with 2nd century b. c., with a view towards option associated with the popular problem of the duplication of cube, or the insertion of two mean proportionals between two provided straight outlines. Its equation is x=y (a—x). Within the cissoid of Diocles the generating curve is a circle; a place A is assumed about this circle, and a tangent M M' through the opposite extremity of this diameter attracted from A; then the property associated with bend is if from A any oblique line be drawn to M M', the part for this line involving the group and its tangent is equal to the portion between A and the cissoid. But the name has actually sometimes already been given in later times to all or any curves explained in a similar way, where in actuality the generating curve is not a circle.
  • others:
    • Included between your concave edges of two intersecting curves: since, a cissoid perspective.
    • Included amongst the concave sides of two intersecting curves: since, a cissoid direction.

Related Sources

  • Sentence for "cissoid"
138 votes

How would you define cissoid?

All the definitions on AZdictionary were written by people just like you. Now's your chance to add your own!