I Section formula, external ratio

prashant singh
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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.
 
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prashant singh said:
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.
 

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