Answer:
Per is a Latin preposition that means "through" or "by means of". Per (pronounced like "purr") is also an English preposition that can mean "for each", "to each", "by means of", or [lastly, annoyingly] "in accordance with"; somewhat interchangeably with the [even more annoying] "as per". In the example expressions here, it conveys "because of the rationale presented at/by".
