Some of Euclid’s axioms are:

- Things which are equal to the same thing are equal to one another.
- If equals are added to equals, the wholes are equal.
- If equals are subtracted from equals, the remainders are equal.
- Things which coincide with one another are equal to one another.
- The whole is greater than a part.
- Things which are double of the same things are equal to one another.
- Things which are halves of the same things are equal to one another.

##
**
1
**
^{
st
}
**
Axiom
**

1st axiom says
*
Things which are equal to the same thing are equal to one another.
*

An application of 1
^{
st
}
axiom can be

Area of triangle 1 = Area of triangle 2

& Area of triangle 3 = Area of triangle 2

So, Area of triangle 1 = Area of triangle 3

##
**
4
**
^{
th
}
**
axiom
**

4
^{
th
}
axiom says two things as identical. Then they must be equal.

Since line l
_{
1
}
and l
_{
2
}
are identical.

They are equal

##
**
5
**
^{
th
}
**
Axiom
**

5
^{
th
}
axiom is The whole is greater than a part.

This axiom gives us the definition of greater than

Here,

Area of Blue triangle is greater than the area of green triangle.