CON

of

having a circle for its base, and its sides are formed by right lines drawn from the circumference of the base to a point at top being the vertex or apex Or a cone is a solid figure whose base is a circle, and which is produced by the entire re volution of a right angled triangle about its perpendicular leg. See MENSURATION.

the cone.

CONFERVA, see BOTANY.

CONFESSION, in the Romish church, the act of acknowledging crimes and errors of conduct to a priest, in private, to the end that due reprehension may be suffered, and pardon obtained. By the canon-law, the priest who reveals what has been confessed to him, from anger, hatred, or even fear of death, is to be degraded.

CONFESSOR, an inferior saint of the Roman church; one who has resolutely stood forward to confess or avow his faith, and endured torture, if not martyrdom for its sake.

Confessor, a priest, in the Roman church, who has power to receive confessions and grant absolu

tion.

CONGE d'elire, see Bishop.

CONGELATION, may be defined the transition of a liquid into a solid state, in consequence of an abstraction of heat: thus metals, oil, water, &c. are said to congeal when they pass from a fluid into a solid state. With regard to fluids, congelation and freezing mean the same thing.

geals at 32°, and there are few liquids that will not Water concongeal, if the temperature be brought sufficiently low. The only difficulty is to obtain a temperature equal to the effect; hence it has been inferred that fluidity is the consequence of caloric. See FLUIDITY.

CONGREGATIONALISTS, in church history, a sect of Protestants who reject all church government, except that of a single congregation. In other mat ters, they agree with the Presbyterians. See PRESBYTERIANS.

CONIC-SECTIONS are such curve lines as are produced by the mutual intersections of a plane and the surface of a solid cone. In different positions of the plane there arise five different figures or sections, viz. the triangle; the circle; the ellipse; the parabola; and the hyperbola: the last three are peculiarly called Conic Sections, to investigate the properties of which is the business of Conics, and this depends on a knowledge of geometry plane and solid. It will be sufficient to our purpose to describe the lines and to shew how they are produced.

If the cutting plane pass through the vertex of the cone and any part of the base, the section so formed will be a triangle, as V A B, figure 1. Plate CONIC SECTIONS. But if the plane cut the cone parallel to the base, the section will be a circle as ABD fig. 2.

In fig. 3 the section A B C is an ellipse, and it is formed by cutting the cone obliquely through both sides making the angle A z C.

If the cone be cut by a plane parallel to one of its sides, as in fig. 4 the section A D E is a parabola: here the angle b A z is equal to B a z.

The section is an hyperbola when the cutting plane makes a greater angle with the base than the side of the cone makes; thus in fig. 5. the angle Abz is greater than the angle MBZ: and if the plane A D E be continued to cut the opposite cone, this latter section is called the opposite hyperbola to

the former, B e d is opposite to A D E. The vertices of any section are the points in which the cutting plane meets the opposite sides of the cone as A, B, in fig. 5, and 3, and A in fig. 4. Of course the ellipse and opposite hyperbolas have each two vertices, but the parabola has only one. The axis, or transverse diameter of a tion is the line A B fig. 6: B B, fig. 7. And A b fig. 8. The centre C is the middle of the axis. In the ellipse the centre is within the curve, in the hyperbola it is without the curve, but in the parabola the centre is infinitely distant from the

vertex.

conic sec

A diameter is any right line drawn through the centre, and terminated on each side by the curve. All the diameters of the parabola are parallel to the axis, and infinitely long, because there is no termination to the line A B fig. 8. The conjugate to any diameter is the line drawn through the centre and parallel to the tangent of the curve at the vertex of the diameter: thus H I, fig. 6, would be parallel to tangents drawn through A or B, and G F is parallel to tangents drawn through D and E, of course HI is conjugate to A B, and G F is conjugate to DE.

An ordinate to a diameter is a line parallel to its conjugate and terminated by the diameter and curve: thus D K and E L are ordinates to the axis A B, fig. 6, 7, and 8. Ordinates are perpendicular to their axis.

An absciss is a part of any diameter contained between its vertex and an ordinate to it; thus A K, K B are abscisses to the ordinate D K: and D N, N-E are abscisses to the ordinate M N.

In the