Question

Chapter 2. Euclid's Proof of the Pythagorean Theorem THE "TRIANGLE INEQUALITY" IN THE ELEMENTS 14. (a) Do the proof of Proposition 1.18. Note that it hinges on the Exterior Angle Theorem. (b) Do the proof of Proposition 1.19. This is a "double reductio ad absurdum" argument - that is, it shows that of the three possibilities AC > AB, AC = AB, and AC < AB, two lead to contradictions. (c) Now prove Proposition I.20: "In any triangle, two sides taken together in any manner are greater than the remaining one" - the Triangle Inequality the Epicureans thought was patently obvious even to an ass.

          Chapter 2. Euclid's Proof of the Pythagorean Theorem
THE "TRIANGLE INEQUALITY" IN THE ELEMENTS
14. (a) Do the proof of Proposition 1.18. Note that it hinges on the Exterior Angle Theorem.
(b) Do the proof of Proposition 1.19. This is a "double reductio ad absurdum" argument -
that is, it shows that of the three possibilities AC > AB, AC = AB, and AC < AB, two
lead to contradictions.
(c) Now prove Proposition I.20: "In any triangle, two sides taken together in any manner are
greater than the remaining one" - the Triangle Inequality the Epicureans thought was
patently obvious even to an ass.

Chapter 2. Euclid's Proof of the Pythagorean Theorem
THE "TRIANGLE INEQUALITY" IN THE ELEMENTS
14. (a) Do the proof of Proposition 1.18. Note that it hinges on the Exterior Angle Theorem.
(b) Do the proof of Proposition 1.19. This is a "double reductio ad absurdum" argument -
that is, it shows that of the three possibilities AC > AB, AC = AB, and AC < AB, two
lead to contradictions.
(c) Now prove Proposition I.20: "In any triangle, two sides taken together in any manner are
greater than the remaining one" - the Triangle Inequality the Epicureans thought was
patently obvious even to an ass.

Added by Ashley C.

Question

Please give Ace some feedback