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https://en.wikipedia.org/wiki/Divination is a fairly common form of 'real magic'.
However you will be sadly disappointed if you are expecting something like Luke and Vader force choking each other.
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https://pactwebserial.wordpress.com/ is a story written with a magic system that sounds like what you're describing. In short the magic system is built around the culture and history of the world in a sort of meta way. I feel like the best explanation is reading the first couple chapters.
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You need a copy of Authentic Thaumaturgy, by Isaac Bonewits. He was a modern-day ritual magician, who managed to earn a degree in magic from the University of California.
Authentic Thaumaturgy is his attempt to systematise the underlying rules of historical magic systems: it's written as a tool for creating magic systems for role-playing games. It's available in PDF from its most recent publisher, Steve Jackson Games.
Upvote:3
Not to contradict or compete with Aaron Brick's or John Dallman's posted answers, just helping with some additional resources as food for thought.
Here are three sources that explore magic use in ancient Egypt (a potentially rich source for ideas):
Brandon Sanderson (author of The Wheel of Time series) has a blog where he offers Sanderson's Laws of Magic:
Also, Mythcreants has a blog with resourceful articles, including creating Rational and Ecclectic magic systems, and Limits on Magic among many others.
Also can recommend Orson Scott Card's book How to Write Science Fiction and Fantasy which includes a chapter on creating magic systems.
Also also :-) you might wish to peruse the topic of Alchemy
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Magical practices are either historical or fictionalized. The former are mixed up with religion, as you noted, and will show a lot of regional and epochal variation. The latter have already synthesized and refocused, but don't generally come with footnotes and historical justifications. For example, the magic system in "Monty Python and the Holy Grail" appears to have roots in Anglo-Saxon and Celtic traditions, but saying that doesn't explain why Tim the Enchanter would use explosives or wear ram's horns.
I'm skeptical that any magical practices are or were universal. To create or identify a magic system more strongly linked to historical practices, I think you need to pick a regional/temporal/cultural context as a model and work forward from there. Some of your reading material could include, for example, Magic in the Graeco-Roman world, Magic in the Ancient World, Aztec use of entheogens, and Magical Elements in the Avesta and Nerang Literature. The fact that religion is prominent in magic is an inherent part of historical practices; for your model to be accurate, you might want to incorporate religious elements instead of avoiding them.