Table of Contents
How does Euclid define a straight line?
When geometry was first formalised by Euclid in the Elements, he defined a general line (straight or curved) to be “breadthless length” with a straight line being a line “which lies evenly with the points on itself”.
What is the meaning of a straight line is a line which lies evenly with the points on itself?
Euclid has said “A straight line is a line which lies evenly with the points on itself.” IMHO, this means that a straight line is the line which the points lie evenly pointing to the same slope, they aren’t going down at first then going up again like a curve, they are evenly lying there, the points are even.
In which book can the definition of a plane be found in Euclid’s The Elements?
Throughout Books I through IV and Book VI, the books on plane geometry, there is the implicit assumption of one plane in which all the points, lines, and circles lie. In the books on solid geometry, Books XI through XIII, there is sometimes mentioned a plane of reference, and proposition XI.
How does Euclid define a plane?
In a Euclidean space of any number of dimensions, a plane is uniquely determined by any of the following: Three non-collinear points (points not on a single line). A line and a point not on that line. Two distinct but intersecting lines. Two distinct but parallel lines.
Which has length and breadth only?
We know that the geometrical shapes that have only length and breadth are called 2-dimensional shapes. We come across different types of shapes in our day to day lives. Let us take an example of a rectangle. We know that a rectangle has length as well as breadth.
Who was Euclidean geometry named after?
Euclid (/ˈjuːklɪd/; Greek: Εὐκλείδης Eukleides; fl. 300 BC), sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the “founder of geometry” or the “father of geometry”….
| Euclid | |
|---|---|
| Scientific career | |
| Fields | Mathematics |
Which are the Euclid’s main Elements?
It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines.
What is the basis for all of Euclid’s geometry?
Euclidean geometry, the study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid (c. 300 bce).
What are plane lines?
A line is defined as a line of points that extends infinitely in two directions. A plane extends infinitely in two dimensions. It has no thickness. An example of a plane is a coordinate plane. A plane is named by three points in the plane that are not on the same line.
What is the difference between a straight line and surface?
A straight line is a line which lies evenly with the points on itself. Definition 5. A surface is that which has length and breadth only. Definition 6. The edges of a surface are lines. Definition 7. A plane surface is a surface which lies evenly with the straight lines on itself.
Do lines have to be straight?
One can conclude, then, that lines need not be straight. Perhaps “curve” would be a better translation than line since Euclid meant what is commonly called a curve in modern English, where a curve may or may not be straight.
What are parallel straight lines?
Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction. Postulate 1. To draw a straight line from any point to any point. Postulate 2. To produce a finite straight line continuously in a straight line. Postulate 3.
Why do two straight lines always meet on the same side?
That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. Common notion 1. Things which equal the same thing also equal one another.