euclid's definitions

Question: Though Euclid did not require his fifth postulate to prove his first 28 theorem, why is this postulate most significant? Answer: Euclid and many other mathematicians thought that the fifth postulate can be proved by using just the four postulates and the a..

Question 1 - Question: Give a definition for a) parallel lines b) perpendicular lines Are these other terms that need to be defined first? Answer: a) Given any straight line and a point not on it, there exists one and only one line which passes through that point and never intersects the ..

Question: Which of the following statements are true and which are false? Give reasons for your answers. i) Only one line can pass through a single point. ii) There are infinite number of lines which pass through two distinct points. iii) A terminated line can be produced indefinitely on both ..

Question: If A, B and C are three points on a line, and B lies between A and C, then prove that AB + BC = AC. Answer: In the given figure AC coincides with AB + BC. According tone of Euclid's axioms, things which coincide with one another, are equal to one another. Acco..