"Question 7 Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the question is not about the fifth postulate.)
Class 9 - Math - Introduction to Euclid's Geometry Page 86"
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244
Fig.is in the attachment]
According to axiom 5, we have the whole is greater than the part which is a universal truth.
Let a line segment PQ=8cm.
Consider a point R in its interior such that PR= 5cm
Clearly, PR is a part of the line segment PQ and R lies in its interior so PR is smaller than PQ.
Hence, the whole is greater than its part and this is true for anything in any part of the world.
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Hey there!
Fifth axiom :- " The whole is always greater than its part. "
It is universal truth because it was proved in all the cases.
The main thing required to prove is When a bigger number is subtracted from smaller number, the result is always less than zero.
We shall try to prove it by Taking a whole 3 & a part 1/3.
Now subtract 1/3 from 3
So 3-1/3=8/3 is greater than zero.
Hence we proved the whole is greater than the part.
Fifth axiom :- " The whole is always greater than its part. "
It is universal truth because it was proved in all the cases.
The main thing required to prove is When a bigger number is subtracted from smaller number, the result is always less than zero.
We shall try to prove it by Taking a whole 3 & a part 1/3.
Now subtract 1/3 from 3
So 3-1/3=8/3 is greater than zero.
Hence we proved the whole is greater than the part.
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