CON 



CON 



to a focus has to a perpendicular drawn 

 to the corresponding directrix, a ratio 

 that is constantly the same wherever the 

 point is assumed in the curve; and, in 

 the ellipse, the constant ratio is a ratio 

 of minority (or of a less magnitude to 

 a greater;) in the hyperbola the con- 

 stant ratio is a ratio of majority (or of a 

 greater magnitude to a less ;) and in the 

 parabola the constant ratio is a ratio of 

 equality. 



Let M (fig. 44 and 46) be a point in an 

 ellipse or hyperbola, and draw M F to a 

 focus, and M K perpendicular to the di- 

 rectrix H G, which corresponds to that 

 focus, draw M P perpendicular to the 

 transverse axis, and take C O as in Prop. 

 29. Then 



AC: CF::CP : CO, Pr. 29. 

 Invertendo, CF : CA :: CO : CP ; 

 Therefore, CF : CA :: FO : AP, 19. 5. E. 

 But, CF : C A :: AF . AG, Def. XX. 



Therefore, CF : CA :: AO : GP, 12. 5. E. 

 But, as has been shewn in the demonstra- 

 tion of the last proposition, A O = M F, 

 and G P M K ; therefore 



CF : CA :. MF : MK. 



But the ratio of C F to C A is a constant 

 ratio ; and it is a ratio of minority in the 

 ellipse, and a ratio of majority in the hy- 

 perbola. 



Fig. 45. In the parabola, G A = A F, 

 and 4 A F X A P = M P : , Def. 1. ; but 

 4 A F X A P = G ?- P F>, 8. 2. E ; 

 therefore M P 1 = G P 1 P F 1 ; and 

 M P 1 + P FS or M F 1 = G V-, or M 

 K 1 . Therefore M F = M K. 



CONIFERJE, in botany, the name of 

 one of the orders of Linnxus's frag- 

 ments of a natural method, consisting of 

 [>l:ints, whose, female flowers, placed at a 

 distance from the. male, either on the 

 same or distinct roots, arc formed into a 

 cone. Of this order are the Abies, Cy- 

 prrssiis, &c. 



All the conifers yield a resin which 

 renders most of them evergreen. The 

 fruit in all is biennial, being produced in 

 the spring, but not ripening and drop- 

 ping its seeds until the spring after. The 

 conifers: compose also one of the natural 

 orders ol'.Iussieu. 



CONIL'M, in botany, a genus of the 

 Pt'ntandria Munogyniu class and order. 

 Natural order of Umhellatx. Essential 

 character : partial involucre halved, three- 

 leavcd ; fruit nearly globular, rive- streak- 

 ed, notched on each side. There are 

 five species, of which C. maculaUim, com- 

 mon hemlock, is obviously distinguished 

 by its large and spotted stalk; by the 

 dark-green shining leaves ; and particu- 

 larly ny their disagreeable, smell when 



bruised. The root is biennial, resem- 

 bling that of a small parsnip. The stem 

 is from four to six feet high, hollow , and 

 covered with a bluish powder, which 

 easily wipes off. The leaves which 

 grow near- the bottom of the plant 

 are about two feet in length. Calyx 

 entire ; corolla white, outer petals larg- 

 est ; seeds brownish, resembling those 

 of aniseed. 



CONJUGATE, diameter, or axis of an 

 ellipsis, the shortest of the two dia- 

 meters, or that bisecting the transverse 

 axis. 



CONJUGATE hyperbolas. See CONIC SEC- 

 TION'S. 



CONJUGATION, in grammar, a regu- 

 lar distribution of the several inflexions 

 of verbs in their different voices, moods, 

 tenses, numbers and persons, so as to 

 distinguish them from one another. 



CONJUNCT, or CONJOINT. See the 

 article CONJONT. 



CONJUNCTION, in astronomy, the 

 meeting of two stars or planets in the 

 same degree of the zodiac. This con- 

 junction is either true or apparent. The 

 true conjunction is when a right line, 

 drawn from the eye through the centre 

 of one of the bodies, would pass through 

 that of the other : in this case the bodies 

 are in the same degree of longitude and 

 latitude ; and here the conjunction is also 

 said to be central, if the same line, con- 

 tinued from the two centres through the 

 eye, do also pass through the centre of 

 the earth. 



Apparent conjunction, is when the 

 two bodies do not meet precisely in the 

 same point, but are joined with some 

 latitude. Jn this case a right line, 

 drawn through the centre of the two 

 bodies, would not pass through the cen- 

 tre of the earth, but through the eye of 

 the spectator. 



The moon is in conjunction with the 

 sun, when they meet in the same point 

 of the ecliptic, which happens every 

 month; and eclipses of the sun are al- 

 ways occasioned by the conjunction of 

 the sun and moon in or near the nodes 

 of the ecliptic. 



( <>\ji-.M"riov, in grammar, an unde- 

 clinable word or particle, which serves 

 to join words an/1 sentences together, 

 and thereby shews their relation or de- 

 pendence one upon another. 



CONJ1 UAT10N, strictly means com- 

 bining together by oath, especially with 

 evil spirits, to do a public harm The 

 using of witchcraft, conjuration, &c. 

 was felon} b\ l.Jac. c. 12. but that was 

 repealed by the 9. Geo. II. c. 5. and the 



