Section formula, external ratio

[prashant singh]

I want to know how mathematician got the idea of external division , how they can say that a point can divide a line externally, what's the reason behind this discovery . Why they discovered it.

 

[jedishrfu]

I imagine it came from greek geometry and compass and straight edge construction although I can't find a direct statement to that fact. However there is a notion of constructable numbers in compass and straight edge constructions that may be applicable.

http://www-math.ucdenver.edu/~wcherowi/courses/m3210/lecchap5.pdf

 

[fresh_42]

Why they discovered it.

I assume because of the invariance of the ratios under affine mappings, e.g. parallel projections. These mappings are essential to the constructions @jedishrfu mentioned.