According to Euclid’s Elements, Book I, “Parallel straight lines are those straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.” Euclid defines about parallel lines at last of his definition of Book I which he uses to prove a lot of his proposition. He proves two lines are parallel lines in proposition 27 and uses parallel lines properties in every proposition after that. Therefore, this paper seeks to discover why Euclid introduce about parallel lines in his proposition, and how parallel lines properties help him to delve deeper in his proposition.
Parallel lines make a lot of angles equal to one another. If a straight lines falls on two lines parallel …show more content…
In Euclid’s Elements, the proposition from 1 to 26 were all about lines and triangles then he starts to talk about parallel lines and again he does some proposition from triangle in later parts of books. In proposition 16, he states that, “In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles.” In proposition 32, he states, ‘In any triangle if one sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles. Both propositions are dealing about exterior, interior angles and triangle things, but he still does not complete triangle at first and come to parallel lines. It is because Euclid provides the reason and way of construction for he does everything in his elements, he waits until proposition 31 to draw a line parallel to given line and proposition 29 to say two alternate angles in the parallel lines are equal. If Euclid has not uses his parallel line concepts, it would be difficult to prove his proposition 32, which conveys important properties of
Parallel lines make a lot of angles equal to one another. If a straight lines falls on two lines parallel …show more content…
In Euclid’s Elements, the proposition from 1 to 26 were all about lines and triangles then he starts to talk about parallel lines and again he does some proposition from triangle in later parts of books. In proposition 16, he states that, “In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles.” In proposition 32, he states, ‘In any triangle if one sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles. Both propositions are dealing about exterior, interior angles and triangle things, but he still does not complete triangle at first and come to parallel lines. It is because Euclid provides the reason and way of construction for he does everything in his elements, he waits until proposition 31 to draw a line parallel to given line and proposition 29 to say two alternate angles in the parallel lines are equal. If Euclid has not uses his parallel line concepts, it would be difficult to prove his proposition 32, which conveys important properties of