Saturday, 4 August 2018

CBSE Class 9 - Maths - Introduction To Euclid's Geometry - Axioms, Theorem and Other terms (#cbsenotes)(#eduvictors)

Introduction To Euclid's Geometry - Axioms, Theorem and Other terms


(Note: Following list is compiled from a very old book 'Elements of Geometry by Ledegenre' and other NCERT textbooks)

Important terms to remember:

1. An axiom is a self-evident proposition (an assumption which is a self-evident truth).

2. A theorem is a truth, which becomes evident by means of a train of reasoning called a demonstration or proof. Theorems are proved, using axioms, previously proved statements and deductive reasoning.

3. A problem is a question proposed, which requires a solution.

4. A lemma is a subsidiary truth, employed for the demonstration/proof of a theorem, or the solution of a problem.


5. The common name, proposition, is applied indifferently, to theorems, problems, and lemmas.

6. A corollary is an obvious consequence, deduced from one or several propositions.

7. A scholium is a remark on one or several preceding propositions, which tends to point out their connection, their use, their restriction, or their extension. 

7. A hypothesis is a supposition, made either in the enunciation of a proposition or in the course of a demonstration/proof.

8. A conjecture is a conclusion or proposition based on incomplete information, for which no proof has been found.


List of a few Euclid's Axioms are:

1. Things which are equal to the same thing, are equal to each other.

2. If equals are added to equals, the wholes will be equal.

3. If equals are taken from equals, the remainders will be equal.

4. If equals are added to unequals, the wholes will be unequal.

5. If equals are taken from unequals, the remainders will be unequal.

6. Things which are double of the same thing, are equal to each other.

7. Things which are halves of the same thing are equal to each other.

8. The whole is greater than any of its parts.

9. The whole is equal to the sum of all its parts.

10. All right angles are equal to each other.

11. From one point to another only one straight line can be drawn.

12. Through the same point, only one straight line can be drawn which shall be parallel to a given line.

13. Magnitudes, which is applied to each other, coincide throughout their whole extent, are equal.

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