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    "source_title": "Encyclopaedia Britannica (1911)",
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    "chunk_id": "1911:cissey:d27cb4eb0362",
    "title": "CISSEY",
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    "verified_text": "cissey, ernest louis octave courtot de (1810-1882), french general, was born at paris on the 23rd of september 1810, and after passing through st cyr, entered the army in 1832, becoming captain in 1839. he saw active service in algeria, and became _chef d'escadron_ in 1849 and lieutenant-colonel in 1850. he took part as a colonel in the crimean war, and after the battle of inkerman received the rank of general of brigade. in 1863 he was promoted general of division. when the franco-german war broke out in 1870, de cissey was given a divisional command in the army of the rhine, and he was included in the surrender of bazaine's army at metz. he was released from captivity only at the end of the war, and on his return was at once appointed by the versailles government to a command in the army engaged in the suppression of the commune, a task in the execution of which he displayed great rigour. from july 1871 de cissey sat as a deputy, and he had already become minister of war. he occupied this post several times during the critical period of the reorganization of the french army. in 1880, whilst holding the command of the xi. corps at nantes, he was accused of having relations with a certain baroness kaula, who was said to be a spy in the pay of germany, and he was in consequence relieved from duty. an inquiry subsequently held resulted in de cissey's favour (1881). he died on the 15th of june 1882 at paris. cissoid (from the gr. [greek: kissos], ivy, and [greek: eidos], form), a curve invented by the greek mathematician diocles about 180 b.c., for the purpose of constructing two mean proportionals between two given lines, and in order to solve the problem of duplicating the cube. it was further investigated by john wallis, christiaan huygens (who determined the length of any arc in 1657), and pierre de fermat (who evaluated the 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 apt a line cutting the circle in p and bt at t; take a point q on at so that aq always equals pt; then the locus of q is the cissoid. sir isaac newton devised the following mechanical construction. take a rod lmn bent at right angles at m, such that mn = ab; let the leg lm always pass through a fixed point o on ab produced such that oa = ca, where c is the 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 axis of x, and consists of two infinite branches asymptotic to the line bt and forming a cusp at the origin. the cartesian equation, when a is the origin and ab = 2a, is y2(2a - x) = x3; the polar equation is r = 2a sin [theta] tan [theta]. the cissoid is the first positive pedal of the parabola y2 + 8ax = 0 for the vertex, and the inverse of the parabola y2 = 8ax, the vertex being the centre of inversion, and the semi-latus rectum the constant of inversion. the area between the curve and its asymptote is 3[pi]a2, i.e. three times the area of the generating circle. the term cissoid has been given in modern times to curves generated in similar manner from other figures than the circle, and the form described above is distinguished as the cissoid of diocles. [illustration] a _cissoid angle_ is the angle included between the concave sides of two intersecting curves; the convex sides include the _sistroid angle_. see john wallis, _collected works_, vol. i.; t.h. eagles, _plane curves_ (1885).",
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