Question

What is the logic behind divedendo-componendo operations.?

Answer 1

Please see below.

Explanation:

Componendo states that if `a/b=c/d`, then `(a+b)/b=(c+d)/d`

This follows as `a/b=c/d=>a/b+1=c/d+1=>(a+b)/b=(c+d)/d`

Similarly dividendo states that if `a/b=c/d`, then `(a-b)/b=(c-d)/d`

This follows as `a/b=c/d=>a/b-1=c/d-1=>(a-b)/b=(c-d)/d`

and dividing former by latter we get

`(a+b)/(a-b)=(c+d)/(c-d)`,

which is componendo-dividendo.