PERPENDICULAR
, in Geometry, or Normal. One line is Perpendicular to another, when the former meets the latter so as to make the angles on both sides of it equal to each other. And those angles are called right angles. And hence, to be Perpendicular to, or to make right-angles with, means one and the same thing. So, when the angle ABC is equal to the angle ABD, the line AB is said to be Perpendicular, or normal, or at right angles to the line CD.
A line is Perpendicular to a curve, when it is perpendicular to the tangent of the curve at the point of contact.
A line is Perpendicular to a plane, when it is Perpendicular to every line drawn in the plane through the bottom of the Perpendicular. And one plane is Perpendicular to another, when a line in the one plane is Perpendicular to the other plane.
From the very principle and motion of a Perpendicular, it follows, 1. That the Perpendicularity is mutual, if the first AB is perpendicular to the second CD, then is the second Perpendicular to the first.—2. That only one Perpendicular can be drawn from one point in the same place.—3. That if a Perpendicular be continued through the line it was drawn Perpendicular to; the continuation BE will also be Perpendicular to the same. —4. That if there be two points, A and E, of a right line, each of which is at an equal distance from two points, C and D, of another right line; those lines are Perpendiculars.—5. That a line which is Perpendicular to another line, is also Perpendicular to all the parallels of the other.—6. That a Perpendicular is the shortest of all those lines which can be drawn from the same point to the same right line. Hence the distance of a point from a line or plane, is a line drawn from the point Perpendicular to the line or plane: and hence also the altitude of a figure is a Perpendicular let fall from the vertex to the base.
To Erect a Perpendicular from a given point in a line. —1. When the given point B is near the middle of the line; with any interval in the compasses take the two equal parts BC, BD: and from the two centres C and D, with any radius greater than BC or BD, strike two arcs intersecting in F; then draw BFA the Perpendicular required.
2. When the given point G is at or near the end of the line; with any centre I and radius IG describe an are HGK through G; then a ruler laid by H and I will cut the are in the point K, through which the Perpendicular GK must be drawn.
To let fall a Perpendicular upon a given line LM from a given point N. With the centre N, and a convenient radius, describe an arc cutting the given line in L and M; with these two centres, and any other convenient radius, strike| two other arcs intersecting in O, the point through which the Perpendicular NOP must be drawn.
Note, that Perpendiculars are best drawn, in practice, by means of a square, laying one side of it along the given line, and the other to pass through the given point.
Perpendicular, in Gunnery, is a small instrument used for finding the centre line of a piece, in the operation of pointing it to a given object. See Pointing of a Gun.
Perpetual Motion. See Motion.
Circle of Perpetual Occultation and Apparition. See Circle.
Perpetual, or Endless Screw. See Screw.
