Is there a proof of the following statement?
The book can be found on: https://mirror.thelifeofkenneth.com/lib/electronics_archive/GraySearle-ElectronicPrinciples_text.pdf

On page 556 in PDF / page 553 in book, the section starts with:  


  To find the general relationship between a1/a0 and the network elements, we consider a linear active network that contains n capacitors and no other 
  energy storage.
  For simplicity, we develop the relation for a1/a0 for the three- 
  capacitor network of Fig. 15.3a, recognizing that the PROOF can be readily 
  generalized.


This generalization of the proof can be demonstrate by induction, as @Neil_UK suggests, by adding another capacitor in Figure 15.3 and appending the equation for the next capacitor to eq. 15.23a and following equations.