Given two straight lines constructed on a straight line (from its extremities) and meeting in a point, there cannot be constructed on the same straight line (from its extremities), and on the same side of it, two other straight lines meeting in another point and equal to the former two respectively, namely each to that has the same extremity with it.

Click the figure bellow to see the illustration.

Read more at:

Euclid's Elements Book I, Proposition 7

## Monday, February 22, 2010

### Euclid's Elements Book I, Proposition 7

Subscribe to:
Post Comments (Atom)

let us assume that the construction is possible then triangle ABC is congruent to triangle DBC by SSS criterion. so angle ABC = angle DBC by cpct. this implies that angle ABD equals 0 degrees. or the points A and D are not distinct. they are coincident. thus the existence of another such point D on the same side of the segment BC is impossible which satisfies the given conditions. so our assumption is wrong. hence there exists no such point on the same side of the segment BC as point A.

ReplyDeleteQ. E. D.