Purpose of $ \frac{f''(z)}{f'(z)}$ while driving "Schwarz- Christoffel Formula"

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I am studying "Schwarz-Christoffel Formula" while driving this formula they are using term $\displaystyle \frac{f''(z)}{f'(z)}$, i have an idea that this term is somewhere is used in Schwarz derivative but still i am not getting a complete picture of why they are using this? i'm also attaching a derivation where they are using this. (The underline part)

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Please Help.