See also:

• CONCHOID (Gr. «oyXn, shell, and ethos, form)

CONCHOID (Gr. «oyXn, See also:

• SHELL
• SHELL (O. Eng. scell, scyll, cf. Du. sceel, shell, Goth. skalja, tile; the word means originally a thin flake,. cf. Swed. skalja, to peel off; it is allied to " scale " and " skill," from a root meaning to cleave, divide, separate)

shell, and ethos, See also:

• FORM (Lat. forma)

form)  , a See also:

• PLANE

plane See also:

• CURVE (Lat. curvus, bent)

curve invented by the See also:

• GREEK
• GREEK, ETRUSCAN AND

Greek mathematician Nicomedes, who devised a See also:

• MECHANICAL

mechanical construction for it and applied it to the problem of the duplication of the See also:

• CUBE (Gr. K46os, a cube)

cube, the construction of two mean proportionals between two given quantities, and possibly to the trisection of an See also:

• ANGLE (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Gr. ayKOS, a bend; both connected with the Aryan root ank-, to

angle as in the 8th lemma of See also:

• ARCHIMEDES (c. 287–212 B.C.)
• ARCHIMEDES, SCREW OF

Archimedes . See also:

• PROCLUS, or PROCULUS (A.D. 410-485)

Proclus grants Nicomedes the See also:

• CREDIT (Lat. credere, to believe)

credit of this last application, but it is disputed by Pappus, who claims that his own See also:

• DISCOVERY

discovery was ' See also:

• DOUBLE
• DOUBLE (from the Mid. Eng. duble, the form which gives the present pronunciation, through the Old Er. duble, from Lat. duplus, twice as much)

Double and triple concertos are concertos with two or three See also:

• SOLO, OR SOLO WHIST

solo players . A See also:

• CONCERTO (Lat. concertus, from certare, to strive, also con-fused with concentus)

concerto for several solo players is called a concertante . See also:

• ORIGINAL

original . The See also:

• CONCHOID (Gr. «oyXn, shell, and ethos, form)

conchoid has been employed by later mathematicians, notably See also:

• SIR

Sir See also:

• ISAAC (Hebrew for " he laughs," on explanatory references to the name, see ABRAHAM)

Isaac See also:

• NEWTON
• NEWTON, ALFRED (1829–1907)
• NEWTON, JOHN (1725-1807)
• NEWTON, JOHN (1823-1895)
• NEWTON, SIR CHARLES THOMAS (1816-1894)
• NEWTON, SIR ISAAC (1642-1727)

Newton, in the construction of various cubic curves . The conchoid is generated as follows: Let 0 be a fixed point and BC a fixed straight See also:

• LINE

line; draw any line through 0 intersecting BC in P and take on the line PO two points X, X', such that PX = PX' = a See also:

• CONSTANT, BENJAMIN (1845-1902)

constant quantity . Then the See also:

• LOCUS (Lat. for " place "; in Gr. rinros)

locus of X and X' is the conchoid . The conchoid is also the locus of any point on a See also:

• ROD (O.E. rodd, probably related to Norw. rudda, stick, rodda, stake)
• ROD, EDOUARD (1857-1910)

rod which i A, is constrained to move so that it & C always passes through a fixed point, while a fixed point on the rod travels along a straight line . To obtain the See also:

• EQUATION (from Lat. aequatio, aequare, to equalize)

equation to the curve, draw AO perpendicular to BC, and let A0=a; let the constant quantity PX = PX' = b . Then taking 0 as See also:

• POLE (FAMILY)
• POLE, REGINALD (1500-1558)
• POLE, RICHARD DE LA (d. 1525)
• POLE, WILLIAM (1814—1900)

pole and a line through 0 parallel to BC as the initial line, the polar equation is r =a cosec B ±b, the upper sign referring to the See also:

• BRANCH (from the Fr. branche, late Lat. branca, an animal's paw)

branch more distant from O . The cartesian equation with A as origin and BC as See also:

• AXIS (Lat. for " axle ")

axis of x is x2y2=(a+y)2 (b2–y2) . Both branches belong to the same curve and are included in this equation .

Three forms of the curve have to be distinguished according to the ratio of a to b . If a be less than b, there will be a See also:

• NODE (Lat. nodus, a loop)

node at 0 and a See also:

• LOOP

loop below the initial point (curve i in the figure); if a equals b there will be a See also:

• CUSP (Lat. cuspis, a spear, point)

cusp at 0 (curve 2); if a be greater than b the curve will not pass through 0, but from the cartesian equation it is obvious that 0 is a conjugate point (curve 3) . The curve is symmetrical about the axis of y and has the axis of x for its asymptote .