Similar methods were devised by Sir Isaac Newton and Colin Maclaurin. In Newton’s method, two angles of constant magnitude are caused to revolve about their vertices which are fixed in position, in such a manner that the intersection of two limbs moves along a fixed straight line; then the two remaining limbs envelop a conic. Maclaurin’s method, published in his Geometria organica (1719), is based on the proposition that the locus of the vertex of a triangle, the sides of which pass through three fixed points, and the base angles move along two fixed lines, is a conic section. Both Newton’s and Maclaurin’s methods have been developed by Michel Chasles. In modern times the study of the conic sections has proceeded along the lines which we have indicated; for further details reference should be made to the article Geometry.
Authorities.—For the ancient geometry of conic sections, especially of Apollonius, reference should be made to T. L. Heath’s Apollonius of Perga (1886); more general accounts are given in James Gow, A Short History of Greek Mathematics (1884), and in H. G. Zeuthen, Die Lehre von dem Kegelschnitten in Alterthum (1886). Michel Chasles in his Aperçu historique sur l’origine et le développement des méthodes en géométrie (1837, a third edition was published in 1889), gives a valuable account of both the ancient and modern geometry of conics; a German translation with the title Geschichte der Geometrie was published in 1839 by L. A. Sohncke. A copious list of early works on conic sections is given in Fred. W. A. Murhard, Bibliotheca mathematica (Leipzig, 1798). The history is also treated in general historical treatises (see Mathematics).
Geometrical constructions are treated in T. H. Eagles, Constructive Geometry of Plane Curves (1886); geometric investigations primarily based on the relation of the conic sections to a cone are given in Hugo Hamilton’s De Sectionibus Conicis (1758); this method of treatment has been largely replaced by considering the curves from their definition in plano, and then passing to their derivation from the cone and cylinder. This method is followed in most modern works. Of such text-books there is an ever-increasing number; here we may notice W. H. Besant, Geometrical Conic Sections; C. Smith, Geometrical Conics; W. H. Drew, Geometrical Treatise on Conic Sections. Reference may also be made to C. Taylor, An Introduction to Ancient and Modern Geometry of Conics (1881).
See also list of works under Geometry: Analytical and Projective.
CONINE, or Coniine (α-propyl piperidine), C8H17N, an alkaloid occurring, associated with γ-coniceine, conhydrine, pseudoconhydrine and methyl conine, in hemlock (Conium maculatum). It is a colourless oily liquid of specific gravity 0·845 (20° C.), boiling at 166° C., almost insoluble in water, soluble in ether and in alcohol. It has a sharp burning taste and a penetrating smell, and acts as a violent poison. It is dextro-rotatory. The alkaloid is a strong base and is very readily oxidized; chromic acid converts it into normal butyric acid and ammonia; hydrogen peroxide gives aminopropylvalerylaldehyde, NH2⋅CH(C3H7)⋅(CH2)3⋅CHO, whilst the benzoyl derivative is oxidized by potassium permanganate to benzoyl-α-aminovaleric acid, C6H5CO⋅NH⋅CH(C3H7)⋅(CH2)3⋅COOH. It combines directly with methyl iodide to form dimethyl coninium iodide, C10H22NI, which by the destructive methylation process of A. W. Hofmann (Berichte, 1881, 14, pp. 494, 659) is converted into the hydrocarbon conylene C8H14, a compound that can also be obtained by heating nitrosoconine with phosphoric an hydride to 80-90° C. On heating conine with concentrated hydriodic acid and phosphorus it is decomposed into ammonia and normal octane C8H18. Conine is a secondary base, forming a nitroso derivative with nitrous acid, a urethane with chlorcarbonic ester and a tertiary base (methyl conine) with methyl iodide; reactions which point to the presence of the ＝NH group in the molecule.
It was the first alkaloid to be synthesized, a result due to A. Ladenburg (see various papers in the Berichte for the years 1881, 1884, 1885, 1886, 1889, 1893, 1894, 1895, and Liebig’s Annalen for 1888, 1894). A. W. Hofmann had shown that conine on distillation with zinc dust gave α-propyl pyridine (conyrine). This substance when heated with hydriodic acid to 300° C. is converted into α-propyl piperidine, which can also be obtained by the reduction of α-allyl pyridine (formed from a-methyl pyridine and paraldehyde). The α-propyl piperidine so obtained is the inactive (racemic) form of conine, and it can be resolved into the dextro- and laevo-varieties by means of dextro-tartaric acid, the 𝑑-conine 𝑑-tartrate with caustic soda giving 𝑑-conine closely resembling the naturally occurring alkaloid. A. Ladenburg (Ber. 1906, 39, p. 2486) showed that the difference in the rotations of the natural and synthetic 𝑑-conine is not due to another substance, iso-conine, as was originally supposed, but that the artificial product is a stereo-isomer, which yields natural conine on heating for some time to 290°-300°, and then distilling.
γ-Coniceine, C8H15N, is a tetrahydro conyrine, i.e. a tetra-hydro propyl pyridine. It may be obtained by brominating conine, and then removing the elements of hydrobromic acid with alkalis. Other coniceines have been prepared. Conhydrine, C8H17NO, and pseudoconhydrine are probably stereo-isomers, the latter being converted into the former when boiled with ligroin. Since conhydrine is dehydrated by phosphorus pentoxide into a mixture of α and β coniceines, it may be considered an oxyconine. Methyl conine, C9H19N or C8H14⋅N(CH3), is synthesized from conine and an aqueous solution of potassium methyl sulphate at 100°.
CONINGTON, JOHN (1825–1869), English classical scholar, was born on the 10th of August 1825 at Boston in Lincolnshire. He knew his letters when fourteen months old, and could read well at three and a half. He was educated at Beverley Grammar school, at Rugby and at Oxford, where, after matriculating at University College, he came into residence at Magdalen, where he had been nominated to a demyship. He was Ireland and Hertford scholar in 1844; in March 1846 he was elected to a scholarship at University College, and in December of the same year he obtained a first class in classics; in February 1848 he became a fellow of University. He also obtained the Chancellor’s prize for Latin verse (1847), English essay (1848) and Latin essay (1849). He successfully applied for the Eldon law scholarship in 1849, and proceeded to London to keep his terms at Lincoln’s Inn. The legal profession, however, proved distasteful, and after six months he resigned the scholarship and returned to Oxford. During his brief residence in London he formed a connexion with the Morning Chronicle, which was maintained for some time. He showed no special aptitude for journalism, but a series of articles on university reform (1849–1850) is noteworthy as the first public expression of his views on a subject that always interested him. In 1854 his appointment, as first occupant, to the chair of Latin literature, founded by Corpus Christi College, gave him a congenial position. From this time he confined himself with characteristic conscientiousness almost exclusively to Latin literature. The only important exception was the translation of the last twelve books of the Iliad in the Spenserian stanza in completion of the work of P. S. Worsley, and this was undertaken in fulfilment of a promise made to his dying friend. In 1852 he began, in conjunction with Prof. Goldwin Smith, a complete edition of Virgil with a commentary, of which the first volume appeared in 1858, the second in 1864, and the third soon after his death. Prof. Goldwin Smith was compelled to withdraw from the work at an early stage, and in the last volume his place was taken by H. Nettleship. In 1866 Conington published his most famous work, the translation of the Aeneid of Virgil into the octosyllabic metre of Scott. The version of Dryden is the work of a stronger artist; but for fidelity of rendering, for happy use of the principle of compensation so as to preserve the general effect of the original, and for beauty as an independent poem, Conington’s version is superior. That the measure chosen does not reproduce the majestic sweep of the Virgilian verse is a fault in the conception and not in the execution of the task. Conington died at Boston on the 23rd of October 1869.
His edition of Persius with a commentary and a spirited prose translation was published posthumously in 1872. In the same year appeared his Miscellaneous Writings, edited by J. A. Symonds, with a memoir by Professor H. J. S. Smith (see also H. A. J. Munro in Journal of Philology, ii., 1869). Among his other editions are Aeschylus, Agamemnon (1848), Choëphori (1857); English verse translations of Horace, Odes and Carmen Saeculare (1863), Satires, Epistles and Ars Poëtica (1869).
CONISTERIUM (from Gr. κόνις, dust), the name of the room in the ancient palaestra or thermae (baths) where wrestlers, after being anointed with oil, were sprinkled with sand, so as to give them a grip when wrestling.
