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
2ii. 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.
3iii. The intersections of lines and their extremities are points.
4iv. 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
5v. 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.
6vi. 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
7vii. 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.
8viii. Points which lie on the same right line are called collinear points. A figure formed of collinear points is called a row of points.
What is the author’s MOST LIKELY purpose in writing this text?
Responses
A to educate readers about important factsto educate readers about important facts
B to persuade readers to agree with an opinionto persuade readers to agree with an opinion
C to entertain readers with humorous anecdotesto entertain readers with humorous anecdotes
D to share controversial opinions with the readers