Definitions
from The Century Dictionary.
 noun A curve of the third order and third class, having a cusp at the origin and a point of inflection at infinity.
 noun 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.
from the GNU version of the Collaborative International Dictionary of English.
 noun (Geom.) 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 Wiktionary, Creative Commons Attribution/ShareAlike License.
 noun geometry 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.
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Ancient Greek, meaning "ivylike".
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Examples

Diocles (about the end of the second century B. C.) is known as the discoverer of the _cissoid_ which was used for duplicating the cube.

I was so fascinated by the shape and mathematical description of a simple curve (cardioid or cissoid per  haps) that I had stumbled across in my reading that again I could not rest until I had explored in depth as many curves as I could
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ruzuzu commented on the word cissoid
"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
fbharjo commented on the word cissoid
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