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Geocentric and early heliocentric models of cosmos were different at the very core of theory, but they did share some elements: circular orbits, epicycles, uniform speed of celestial bodies.

What words/phrases can be used to refer to these things that they had in common?

In my native language I could say "obszar wspólny", which could be literally translated to "common area", "shared field" or similar. But scientific theories obviously does not have any "area" that you can measure and I am unsure whether metaphorical meaning of word functions in English.

Is "commonalities" ("commonalities of geocentric and heliocentric models") good enough?

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  • "Shared assumptions", "Common Principles", "Common Foundation" etc
    – Dan Bron
    Nov 23, 2014 at 23:26

4 Answers 4

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Common ground is the English equivalent of the idiom you mention.

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Commonalities could work. It isn't bad. There's overlap too, but that's still not perfect.

You could rephrase to something like the theories shared ideas. It's a good question.

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commonality/ies

Geocentric and early heliocentric models of cosmos were different at the very core of theory, but showed certain commonalities.

You could also use one of these:

  • Geocentric and early heliocentric models of cosmos have the following similarities...

  • Geocentric and early heliocentric models of cosmos have the following characteristics in common...

  • Geocentric and early heliocentric models of cosmos share a few characteristics but are, in fact, two distinct...

similarity - point, feature, or detail in which two items are alike. The Free Dictionary

characteristic - a special quality or trait that makes a person, thing, or group different from others. Merriam-Webster

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As noted in previous answers, commonalities is a word you could use; from en.wiktionary, commonality has a sense “shared attribute or characteristic”. But I'd prefer wording that refers to common elements or shared aspects. For example:
• The theories have these elements in common: ...
Aspects shared by the two theories include ...

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