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Lines perpendicular to line l are modeled by chords whose extension passes through the pole of l. Hence we draw the unique line between the poles of the two given lines, and intersect it with the boundary circle; the chord of intersection will be the desired common perpendicular of the ultraparallel lines.
Two intersecting lines. In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line. Distinguishing these cases and finding the intersection have uses, for example, in computer graphics, motion planning, and collision detection.
In United States government, the line-item veto, or partial veto, is the power of an executive authority to nullify or cancel specific provisions of a bill, usually a budget appropriations bill, without vetoing the entire legislative package. The line-item vetoes are usually subject to the possibility of legislative override as are traditional ...
In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the line–line intersection between two distinct lines , which either is one point (sometimes called a vertex ) or does not exist (if the lines are parallel ).
The Line Item Veto Act Pub. L. 104–130 (text) was a federal law of the United States that granted the President the power to line-item veto budget bills passed by Congress, but its effect was brief as the act was soon ruled unconstitutional by the Supreme Court in Clinton v. City of New York. [1]
The de Longchamps point is the point of concurrence of several lines with the Euler line. Three lines, each formed by drawing an external equilateral triangle on one of the sides of a given triangle and connecting the new vertex to the original triangle's opposite vertex, are concurrent at a point called the first isogonal center.
The Line Item Veto Act of 1996 gave the president the power of line-item veto, which President Bill Clinton applied to the federal budget 82 times [8] [9] before the law was struck down in 1998 by the Supreme Court on the grounds of it being in violation of the Presentment Clause of the U.S. Constitution.
However, parallel (non-crossing) pairs of lines are less restricted in hyperbolic line arrangements than in the Euclidean plane: in particular, the relation of being parallel is an equivalence relation for Euclidean lines but not for hyperbolic lines. [51] The intersection graph of the lines in a hyperbolic arrangement can be an arbitrary ...