If equal are subtracted from equals, the remainders are ____.

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Detailed Solution

If equal are subtracted from equals, the remainders are equals.
It is given that equals are subtracted from equals.
Euclid assumed certain properties, which were not to be proved.
These assumptions are actually ‘obvious universal truths’. He divided them into two types: axioms and postulates.
He used the term ‘postulate’ for the assumptions that were specific to geometry.
Common notions (often called axioms), on the other hand, were assumptions used throughout mathematics and not specifically linked to geometry.
Some of Euclid’s axioms are:
(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, 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.
If equals are subtracted from equals, the remainders are equal.
Therefore, the correct answer is equal.

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