Things which are double of the same things are equal to one another. What does this mean?

Hi!

Here is the answer to your query.

 

Euclid’s axiom states that Things which are double of the same things are equal to one another.

 

Let us consider two identical circles with radii r₁ and r₂ respectively. Suppose their diameters are d₁ and d₂ respectively.

 

 

Since these circles are identical circles, their radii are equal.

∴ r₁ = r₂

Using Euclid’s axiom,

we can say 2r₁ = 2r₂

∴ d₁ = d₂  (Diameter of a circle = 2 × Radius of the circle)

 

Therefore, we can say that when the radii of two circles are equal, then their diameters are also equal. If instead of taking the radii as equal, we say that the diameters of the two circles are equal.

 

Cheers!