Which elements has the LEAST number of dimensions? a. figure
b. line
c. plane
d. point
Passage:
The Elements (excerpt)
Euclid

DEFINITIONS

The

Point 1i. A point is that which has position but no dimensions. A geometrical magnitude which has three dimensions, that is, length, breadth, and thickness, is a solid; that which has two dimensions, such as length and breadth, is a surface; and that which has but one dimension is a line. But a point is neither a solid, nor a surface, nor a line; hence it has no dimensions—that is, it has neither length, breadth, nor thickness.

The
Line 2 ii.
A line is length without breadth. A line is space of one dimension. If it had any breadth, no matter how small, it would be space of two dimensions; and if in addition it had any thickness it would be space of three dimensions; hence a line has neither breadth nor thickness.
3
iii. The intersections of lines and their extremities are points.
4
iv. A line which lies evenly between its extreme points is called a straight or right line, such as AB. If a point move without changing its direction it will describe a right line. The direction in which a point moves in called its "sense." If the moving point continually changes its direction it will describe a curve; hence it follows that only one right line can be drawn between two points. The following Illustration is due to Professor Henrici: "If we suspend a weight by a string, the string becomes stretched, and we say it is straight, by which we mean to express that it has assumed a peculiar definite shape. If we mentally abstract from this string all thickness, we obtain the notion of the simplest of all lines, which we call a straight line."

The
Plane 5 v.
A surface is that which has length and breadth.
A surface is space of two dimensions. It has no thickness, for if it had any, however small, it would be space of three dimensions. 6 I saw.

When a surface is such that the right line joining any two arbitrary points in it lies wholly in the surface, it is called a plane. A plane is perfectly flat and even, like the surface of still water, or of a smooth floor.

Figures
7 vii.
Any combination of points, of lines, or of points and lines in a plane, is called a plane figure. If a figure be formed of points only it is called a stigmatic figure; and if of right lines only, a rectilineal figure.
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viii. Points which lie on the same right line are called collinear points. A figure formed of collinear points is called a row of points.
The Elements (extract)
Euclid

DEFINITIONS

Point

1 me. A point is what has position but there are no dimensions. A geometric magnitude that has three dimensions, that is, length, width, and thickness, is a solid; what has two dimensions, such as length and width, is a surface; and the one with more than one dimension is a line. However, a point is neither a solid, nor a surface, nor a line; therefore, it has no dimensions, that is, it has neither length, width, nor thickness.

Line 2(ii).
A line is the length without width. A line is the space of a dimension. If it had any width, however small, it would be the two-dimensional space; and if it also had any thickness that would be three-dimensional space; therefore, a line is neither the width nor the thickness.
3
iii. Line intersections and their limbs are dots.
4
iv. A line that is equally between its endpoints is called a straight or right line, such as AB. If a point motion without changing its direction will describe a right line. The direction in which a point moves in its so-called "sense". If the moving point continuously changes its direction it will describe a curve; therefore, it follows that only a correct line can be drawn between two points. In the following illustration it is due to Professor Henrici: "If we suspend a weight by a rope, the rope stretches, and we are told that it is straight, so we understand to express that it has assumed a peculiar and defined shape. If mentally abstraction of this whole thickness chain, you get the notion of the simplest of all lines, what we call a straight line."

The
plane 5 v.
A surface is the one with length and width.
A surface is two-dimensional space. It doesn't have a thickness, in case it had any, however small, it would be three-dimensional space. 6 I saw.

When a surface is such that the right line joins two arbitrary points where it is entirely on the surface, it is called an airplane. An aircraft is perfectly flat and uniform, such as the surface of water without gas, or a smooth floor.

Figures 7 vii.

Any combination of points, lines, or points and lines on a plane is called a flat figure. If a dot figure will be formed it is only called a stigmatized figure; and if only of lines on the right, a straight figure.
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viii. Points on the same right line are called aligned points. A figure formed of aligned points is called a row of points.
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