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A curve or surface which is tangent to each member of a system of curves or surfaces, the form and position of the members of the system being allowed to vary according to some continuous law. Thus, any curve is the envelope of its tangents. push the envelope. It is used to refer to the maximum performance available at…

igonometrical functions, or Circular function, the lengths of arcs relative to the sines, tangents, etc. Thus, AB is the arc whose sine is BD, and (if the length of BD is x) is written sin - 1x, and so of the other lines. See Trigonometrical function (below). Other transcendental functions are the exponential functions…

ntial galvanometer. See under Differental, a. -- Sine galvanometer, Cosine galvanometer, Tangent galvanometer (Elec.), a galvanometer in which the sine, cosine, or tangent respectively, of the angle through which the needle is deflected, is proportional to the strength of the current passed through the instrument.…

which the point of sight is taken at the center of the sphere, and the principal plane is tangent to the surface of the sphere. "The gnomonic projection derives its name from the connection between the methods of describing it and those for the construction of a gnomon or dial." Cyc. of Arts & Sciences.…

A nonplane curve whose tangents are all equally inclined to a given plane. The common helix is the curve formed by the thread of the ordinary screw. It is distinguished from the spiral, all the convolutions of which are in the plane.

point of the one corresponds one and but one point in the other, and vise versa. Thus, a tangent line rolling on a circle cuts two fixed tangents of the circle in two sets of points that are homographic.

gh the eye of the spectator and at right angles to the vertical at a given place; a plane tangent to the earth's surface at that place; called distinctively the sensible horizon.

ctions which have relations to the hyperbola corresponding to those which sines, cosines, tangents, etc., have to the circle; and hence, called hyperbolic sines, hyperbolic cosines, etc. -- Hyperbolic logarithm. See Logarithm. -- Hyperbolic spiral (Math.), a spiral curve, the law of which is, that the distance from t…

A certain conic section supposed to be drawn in the tangent plane to any surface, and used to determine the accidents of curvature of the surface at the point of contact. The curve is similar to the intersection of the surface with a parallel to the tangent plane and indefinitely near it. It is an ellipse when the curv…

curve, measured from a given point of it, to a movable point, has to the angle which the tangent to the curve at the movable point makes with a fixed line. -- Intrinsic value. See the Note under Value, n.

the form of the figure 8, with both parts symmetrical, generated by the point in which a tangent to an equilateral hyperbola meets the perpendicular on it drawn from the center.

A horizontal line or plane; that is, a straight line or a plane which is tangent to a true level at a given point and hence parallel to the horizon at that point; -- this is the apparent level at the given point.

line in a space in which forces are acting, so drawn that at every point of the line its tangent is the direction of the resultant of all the forces. It cuts at right angles every equipotential surface which it meets. Specifically (Magnetism), a line in proximity to a magnet so drawn that any point in it is tangential…

A logarithm of the cosine or cotangent. [Obs.] Kepler. Hutton.

e locus of the feet of perpendiculars let fall from a fixed point upon the straight lines tangent to a given curve, or upon the planes tangent to a given surface. -- Pedal note (Mus.), the note which is held or sustained through an organ point. See Organ point, under Organ. -- Pedal organ (Mus.), an organ which has p…

The right line drawn through the two points of contact of the two tangents drawn from a given point to a given conic section. The given point is called the pole of the line. If the given point lies within the curve so that the two tangents become imaginary, there is still a real polar line which does not meet the curve…

representing the sphere, the spherical surface being projected upon the surface of a cone tangent to the sphere, the point of sight being at the center of the sphere. -- Cylindric projection, a mode of representing the sphere, the spherical surface being projected upon the surface of a cylinder touching the sphere, th…

drawn from the center of a circle through one end of a circular arc, and terminated by a tangent drawn from the other end; the number expressing the ratio line of this line to the radius of the circle. See Trigonometrical function, under Function.

ne end by a joint, each arm marked with several scales, as of equal parts, chords, sines, tangents, etc., one scale of each kind on each arm, and all on lines radiating from the common center of motion. The sector is used for plotting, etc., to any scale.

er in a direction parallel to their plane of contact; -- also called shearing stress, and tangential stress.