I am writing an e-mail to a potential business partner and want to express how our partnership could benefit the both of us. The above saying by Aristoteles came to mind but it sounds much to elaborate for a business context. Is there a similar saying/phrase like this?
The usual term in business contexts is Synergie - "synergy". It describes a Win-win-Situation (also a common phrase in business in german) where both partners profit from joint effort.
Outside of business contexts, in philosophy and often in the humanities, you will find the term "Emergenz", coined to describe exactly the phenomenon that an entity is more than the sum of its parts - see en:wikipedia: Emergence and de:wikipedia: Emergenz.
Your long version could be suitable for e.g a speech after a contract was signed and is celebrated by both parties.
For mail, I would prefer examples like:
Die Vereinbarung wäre zu unserem gegenseitigen Nutzen.
Die Vereinbarung wäre zu unserem gegenseitigen Vorteil.
Die Vereinbarung wäre ein Gewinn für alle Beteiligten.