See also:

• CISSOID (from the Gr. rcunr6s, ivy, and ethos, form)

CISSOID (from the Gr. rcunr6s, See also:

• IVY (A.S. ifig, Ger. Epheu, perhaps connected with apium, anent)

ivy, and ethos, See also:

• FORM (Lat. forma)

form)  , a See also:

• CURVE (Lat. curvus, bent)

curve invented by the See also:

• GREEK
• GREEK, ETRUSCAN AND

Greek mathematician Diocles about 18o B.C., for the purpose of constructing two mean proportionals between two given lines; and in See also:

• ORDER
• ORDER (through Fr. ordre, for earlier ordene, from Lat. ordo, ordinis, rank, service, arrangement; the ultimate source is generally taken to be the root seen in Lat. oriri, rise, arise, begin; cf. " origin ")
• ORDER, HOLY

order to solve the problem of duplicating the See also:

• CUBE (Gr. K46os, a cube)

cube . It was further investigated by See also:

• JOHN
• JOHN (1167–1216)
• JOHN (1290-c. 1320)
• JOHN (1296-1346)
• JOHN (1371–1419)
• JOHN (1468-1532)
• JOHN (1801-1873)
• JOHN (Heb. llni')
• JOHN (ZAPOLYA) (1487-1540)
• JOHN, 4TH MARQUESS OF TWEEDDALE (c. 1695-1762)
• JOHN, DON (1545-1578)
• JOHN, DON (1629–1679)
• JOHN, GOSPEL OF ST
• JOHN, or HAYS (1513–1571)
• JOHN, THE APOSTLE
• JOHN, THE EPISTLES OF

John See also:

• WALLIS, JOHN (1616-1703)

Wallis, Christiaan See also:

• HUYGENS, CHRISTIAAN (1629-1695)
• HUYGENS, SIR CONSTANTIJN (1596-1687)

Huygens (who determined the length of any arc in 1657), and See also:

• PIERRE

Pierre de See also:

• FERMAT, PIERRE DE (1601-1665)

Fermat (who evaluated the See also:

• AREA

area between the curve and its asymptote in 1661) . It is constructed in the following manner . Let APB be a semicircle, BT the tangent at B, and See also:

• APT

APT a See also:

• LINE

line cutting the circle in P and BT at T; take a point Q on AT so that AQ always equals PT; then the See also:

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

locus of Q is the See also:

• CISSOID (from the Gr. rcunr6s, ivy, and ethos, form)

cissoid . 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 devised the following See also:

• MECHANICAL

mechanical construction . Take a See also:

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

rod LMN See also:

• BENT
• BENT (E1. BENI)
• BENT, JAMES THEODORE (1852–1897)

bent at right angles at M, such that MN=AB; let the See also:

• LEG
• LEG (a word of Scandinavian origin, from the Old Norwegian leggr, cf. Swed. lagg, Dan. laeg; the O. Eng. word was sceanca, shank)

leg LM always pass through a fixed point 0 on AB produced such that OA = CA, where C is the See also:

• MIDDLE

middle point of AB, and cause N to travel along the line perpendicular to AB at C; then the midpoint of MN traces the cissoid . The curve is symmetrical about the See also:

• AXIS (Lat. for " axle ")

axis of x, and consists of two See also:

• INFINITE (from Lat. in, not, finis, end or limit; cf. findere, to deave)

infinite branches asymptotic to the line BT and forming a See also:

• CUSP (Lat. cuspis, a spear, point)

cusp' at the origin . The cartesian See also:

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

equation, when A is the origin and AB = 2a, is y2(2a—x)=x3; the polar equation is r=2a See also:

• SIN
• SIN (O. Eng. syn: a common Teutonic word, cf. Dutch zonde, Ger. Siinde)

sin B tan B . The cissoid is the first See also:

• POSITIVE (or PORTABLE) ORGAN

positive pedal of the See also:

• PARABOLA

parabola y2+8ax=o for the vertex, and the inverse of the parabola y2=8ax, the vertex being the centre of See also:

• INVERSION (Lat. invertere, to turn about)

inversion, and the semi-latus rectum the See also:

• CONSTANT, BENJAMIN (1845-1902)

constant of inversion . The area between the curve and its asymptote is 3aa2, i.e. three times the area of the generating circle . The See also:

• TERM

term cissoid has been given in See also:

• MODERN

modern times to curves generated in similar manner from other figures than the circle, and the See also:

• FORM (Lat. forma)

form described above is distinguished as the cissoid of Diocles . A cissoid 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 is the angle included between the See also:

• CONCAVE

concave sides of two intersecting curves; the See also:

• CONVEX

convex sides include the sistroid angle .

See John Wallis, Collected See also:

• WORKS

Works, vol. i . ; T . H . Eagles, See also:

• PLANE

Plane Curves (1885) . CIS-See also:

• SUTLEJ

SUTLEJ STATES, the See also:

• SOUTHERN

southern portion of the See also:

• PUNJAB

Punjab, See also:

• INDIA
• INDIA, FRENCH

India . The name, now obsolete, came into use in 1809, when the See also:

• SIKH

Sikh chiefs See also:

• SOUTH
• SOUTH, ROBERT (1634–1716)

south of the Sutlej passed under See also:

• BRITISH

British See also:

• PROTECTION

protection, and was generally applied to the See also:

• COUNTRY (from the Mid. Eng. contre or contrie, and O. Fr. cuntree; Late Lat. contrata, showing the derivation from contra, opposite, over against, thus the tract of land which fronts the sight, cf. Ger. Gegend, neighbourhood)

country south of the Sutlej and See also:

• NORTH
• NORTH, BARONS
• NORTH, MARIANNE (1830—1890)
• NORTH, ROGER (1653-1734)
• NORTH, SIR THOMAS (1535?-16o1?)

north of the See also:

• DELHI, DEHLI

Delhi territory, bounded on the E. by the Himalayas, and on the W. by See also:

• SIRSA

Sirsa See also:

• DISTRICT

district . Before 1846 the greater See also:

• PART

part of this territory as See also:

• INDEPENDENT

independent, the chiefs being subject merely to See also:

• CONTROL (Fr. contrdle, older form contre rolle, from Med. Lat. contra-rotulus, a counter roll or copy of a document used to check the original; there is no instance in English of the use of " control " in this, its literal, meaning)

control from a See also:

• POLITICAL

political officer stationed at See also:

• UMBALLA

Umballa, and styled the See also:

• AGENT (from Lat. agere, to act)

agent of the See also:

• GOVERNOR (from the Fr. gouverneur, from gouverner, O. Fr. governer, Lat. gubernare, to steer a ship, to direct, guide)

governor-See also:

• GENERAL
• GENERAL (Lat. generalis, of or relating to a genus, kind or class)

general for the Cis-Sutlej states . After the first Sikh See also:

• WAR
• WAR (O. Eng. werre, Fr. guerre, of Teutonic origin; cf. O.H.G. werran, to confound)

War the full See also:

• ADMINISTRATION (Lat. administrare, to serve)

administration of the territory became vested in this officer . In 1849 occurred the See also:

• ANNEXATION (Lat. ad, to, and nexus, joining)

annexation of the Punjab, when the Cis-Sutlej states commissionership, comprising the districts of Umballa, Ferozepore, See also:

• LUDHIANA

Ludhiana, See also:

• THANESAR (=" place of the god ")

Thanesar and See also:

• SIMLA

Simla, was incorporated with the new See also:

• PROVINCE
• PROVINCE (Lat. provincia; perhaps a contraction of providentia)

province . The name continued to be applied to this See also:

• DIVISION (from Lat. dividere, to break up into parts, separate)

division until 1862, when, owing to Ferozepore having been transferred to the See also:

• LAHORE

Lahore, and a part of Thanesar to the Delhi division, it ceased to be appropriate . Since then, the See also:

• TRACT (from Lat. tractare, to treat of a matter, through Provencal tractat and Ital. trattato)

tract remaining has been known as the Umballa division . See also:

• PATIALA, or PUTTIALA

Patiala, See also:

• JIND

Jind and See also:

• NABHA

Nabha were appointed a See also:

• SEPARATE

separate political agency in 1901 .

Excluding See also:

• BAHAWALPUR, or BHAWALPUR

Bahawalpur, for which there is no political agent, and See also:

• CHAMBA

Chamba, the other states are grouped under the commissioners of Jullunder and Delhi, and the See also:

• SUPERINTENDENT

superintendent of the Simla See also:

• HILL
• HILL (0. Eng. hyll; cf. Low Ger. hull, Mid. Dutch hul, allied to Lat. celsus, high, collis, hill, &c.)
• HILL, A
• HILL, AARON (1685-175o)
• HILL, AMBROSE POWELL
• HILL, DANIEL HARVEY (1821-1889)
• HILL, DAVID BENNETT (1843–1910)
• HILL, GEORGE BIRKBECK NORMAN (1835-1903)
• HILL, JAMES J
• HILL, JOHN (c. 1716-1775)
• HILL, MATTHEW DAVENPORT (1792-1872)
• HILL, OCTAVIA (1838– )
• HILL, ROWLAND (1744–1833)
• HILL, SIR ROWLAND (1795-1879)

hill states .