How Do You Derive Equations from Diagrams?

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When deriving equations, do you look at the diagrams and derive the equations from there. Could you please tell me how you would derive the equations?
 
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The algorithm for deriving equations is quite similar to the algorithm for proving theorems. Write down true statements until you're satisfied with what you've done. Of course, there are many heuristic refinements, but you'll have to figure those out on your own with practice practice practice!