Defn: At right angles to a given line or surface; as, the line ad is perpendicular to the line bc.
Defn: A spiral whose polar equation is r2th = a; that is, a curve the square of whose radius vector varies inversely as the angle which the radius vector makes with a given line.
Line of levels, a connected series of measurements, by means of a level, along a given line, as of a railroad, to ascertain the profile of the ground.
The same method applies to a given line to be divided into various proportions, as shown in this lower figure.
AE and BC at right angles to a given line, AB, and from A, drawing the diagonal AC at 45° till it cuts BC at C, and then through C drawing EC parallel to AB.
Through a point P one line p can be drawn, which is with regard to a given conic conjugate to a given line q, viz.
The axiom is equivalent to Euclid's Axiom 12, for it follows from either that through any point only one line may be drawn parallel to a given line.
We prove, for example, that the angles opposite the equal sides of a triangle are equal, a fact that is probably quite as obvious as the postulate that but one line can be drawn through a given point parallel to a given line.
It is also fairly accurate to run a line at any angle to a given line by sighting along two pins stuck in a protractor.
This involves the ranging of a line, and the running of a line at right angles to a given line, both of which have been described in Chapter IX.
To construct, on a given line, a polygon similar to a given polygon.
To describe, on a given line, a segment of a circle capable of containing a given angle.
To find the equations of a right line, 1º which passes through two given points, 2º which passes through a given point and which is parallel to a given line.
We speak of it as "a point" and not as "points," because in the geometry studied by Euclid we assume only one line through a point parallel to a given line.
Find the order of infinity of all the lines of space that cut across a given line; across two given lines; across three given lines; across four given lines.
The above list will hopefully provide you with a few useful examples demonstrating the appropriate usage of "given line" in a variety of sentences. We hope that you will now be able to make sentences using this group of words.
