cissoid

Definitions

• n. Any of a family of curves defined as the locus of a point, P, on a line from a given fixed point and intersecting two given curves, C1 and C2, where the distance along the line from C1 to P remains constant and equat to the distance from P to C2.

from the GNU version of the Collaborative International Dictionary of English

• n. A curve invented by Diocles, for the purpose of solving two celebrated problems of the higher geometry; viz., to trisect a plane angle, and to construct two geometrical means between two given straight lines.

from The Century Dictionary and Cyclopedia

• n. A curve of the third order and third class, having a cusp at the origin and a point of inflection at infinity.
• n. It was invented by one Diocles, a geometer of the second century b. c., with a view to the solution of the famous problem of the duplication of the cube, or the insertion of two mean proportionals between two given straight lines. Its equation is x=y (a—x). In the cissoid of Diocles the generating curve is a circle; a point A is assumed on this circle, and a tangent M M' through the opposite extremity of the diameter drawn from A; then the property of the curve is that if from A any oblique line be drawn to M M', the segment of this line between the circle and its tangent is equal to the segment between A and the cissoid. But the name has sometimes been given in later times to all curves described in a similar manner, where the generating curve is not a circle.
• Included between the concave sides of two intersecting curves: as, a cissoid angle.

Etymologies

Ancient Greek, meaning "ivy-like". (Wiktionary)

Examples

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• How cissoidish! as opposed to the conchoid of Nicomedes

As my father used to say when I asked him what he did during his workday:
"I went around in square circles."

July 13, 2012

• "A curve invented by Diocles, for the purpose of solving two celebrated problems of the higher geometry; viz., to trisect a plane angle, and to construct two geometrical means between two given straight lines."

--Websters (1913)

Gotta love a dictionary that uses viz.

July 13, 2012