Seven Axioms
Seven Axioms
Euclid seven axioms :
These 'common notions' refer to magnitidues of some kind. The first common notion could be applied to plane figures. For example, if an area of a triangle equals the area of a rectangle and the areas of the rectangle equals that of a square, then the area of the triangle also equal the area of the square.
Magnitudes of the same kind can be compared and added, but magnitudes of different kinds cannot be added to a rectangle, nor can angle be compared to a pentagon.
The 4th axiom given above seems to say that if two things are identical (that is, they are the same), then they are equal. In other words, everything equals itself. It is the justification of the principle of superposition. Axiom (5) gives us the definition of greater than. For example , if a quantity B is a part of another quantity A, then A can be written as the sum of B and so third quantity C. Symbolically, A>B means that there is some C such that A = B + C.
Example : Two district lines cannot have more than one point in common.
Proof: Here we are given two lines L and m. we need to prove that they have only one point in common.
For the time being, let us suppose that the two lines intersect in two distinct points, say P and Q. So, youhave two lines passing through two distinct points P and Q . But this assumption clashes with the axiom that only one line can pass throught two distinct. points. So, the assumption that we started with , that two lines can pass thorugh two distinct points is wrong.
From this, what can we conclude? We are forced to conclude that two distinct lines cannot have more than one point in common.
Students / Parents Reviews [20]
It was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
Eshan Arora
8thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
Aman Kumar Shrivastava
10thI have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
Yatharthi Sharma
10thThe experience was nice. I studied here for three years and saw a tremendous change in myself. I started liking subjects like English and SST which earlier I ran from. Extra knowledge gave me confidence to overcome competitive exams. One of the best institutes for secondary education.
Aman Kumar Shrivastava
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Shivam Rana
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Prisha Gupta
8thIn terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...
Aman Kumar Shrivastava
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Aman Kumar Shrivastava
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Om Umang
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Barkha Arora
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Yogansh Nyasi
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Archit Segal
7thWe started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.
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10thMy experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
