write 7 Euclid's axioms.
Answers
heya!
1.Things which are equal to the same thing are equal to one another.
2.If equals are added to equals,the wholes are equal.
3.If equals are subtracted from equals,then the remainders are equal.
4.Things which coincide with one another are equal to one another.
5.The whole is greater than the part.
6.Things which are double of the same things are equal to one another.
7.Things which are halves of the same things are equal to one another.
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Answer:
(1) Things which are equal to the same thing are equal to one another.
Example : For example, if an area of a triangle equals the area of a rectangle and the area of the rectangle equals that of a square, then the area of the triangle also equals the area of the square.
(2) If equals are added to equals, the wholes are equal.
Example : For example, a line cannot be added to a rectangle, nor can an angle be compared to a pentagon.
(3) If equals are subtracted from equals, the remainders are equal.
Example : For example, a line cannot be subtracted to a rectangle,nor can an angle be compared to a pentagon.
(4) Things which coincide with one another are equal to one another.
Example : Segment AB = Segment BA ; ∠A = ∠A .
(5) The whole is greater than the part.
Example : If a quantity B is a part of another quantity A, then A can be written as the sum of B and some third quantity C. Symbolically, A > B means that there is some C such that A = B + C.
(6) Things which are double of the same things are equal to one another.
Example : If 2x = 2y then x = y.
(7) Things which are halves of the same things are equal to one another.
Example : If ½ x = ½y then x = y.