Cissoid

Definitions

• Webster's Revised Unabridged Dictionary
• n Cissoid (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.
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Century Dictionary and Cyclopedia
• n cissoid A curve of the third order and third class, having a cusp at the origin and a point of inflection at infinity.
• n cissoid 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.
• cissoid Included between the concave sides of two intersecting curves: as, a cissoid angle.
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Chambers's Twentieth Century Dictionary
• n Cissoid sis′soid a plane curve consisting of two infinite branches symmetrically placed with reference to the diameter of a circle, so that at one of its extremities they form a Cusp (q.v.), while the tangent to the circle at the other extremity is their common asymptote.
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Etymology

Webster's Revised Unabridged Dictionary
Gr. like ivy; ivy + e'i^dos form
Chambers's Twentieth Century Dictionary
Gr. kissoeidēs.

Usage

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