-As an atheist, I could believe in "numbers", "infinite straight lines", "points" in "space", or that "for any given line and point not on the line, there is one parallel line through the point not intersecting the line"
-I could also, just not believe that last proposition:
Intro on Lobachevsky
-Or go even further: "It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it."
On the hypotheses which lie at the foundation of geometry (1854), by
Bernhard Riemann
-I could believe that the planet Venus has a mass, and an acceleration (moves faster/slower towards or away from, say, "me"). In that case I could believe Venus has a Force F; it's entirely up to me to believe if that Force F is the way it's been described by the ancients, and whether or not there's a relation with constellations further away, like Lion. Maybe I'm a Lionheart too, like that medieval king.
-Then again, since we're speaking about larger distances, I may want to switch to general relativity. Because after all, that's what I've been told to do in these situations. In that case, Venus would have an Energy E equal to it's mass times c^2. Whether that Energy E is exactly..."rinse and repeat".
-I could believe in the validity of causal logic/deductive reasoning...But then I'd have to believe in certain axioms (a troll might call them superstitious beliefs or "dogma"): among others, there's "reflexivity", "transitivity", "monotonicity"... and "Ex falso quodlibet". The last one means that I can deduct anything I want from a contradiction (P&~P, "this sentence is a lie",...).
-I don't know about you, but "anything I want" is a whole lot; reincarnation, god and/or gods, Alice in Wonderland, a "Salvador Dali"-type reality where time is an illusion,... Even "Jesus is god's son and he called his audience brothers and sisters, therefore I'm god's son too".
-To put it in biblical terms: "In the beginning there was the word, and the word was with god, and the word was god." (John 1,1). When I study the word (that's logos, in Greek, hence: "logic"), I study... These are some of the things I could believe in, as an atheist. But I don't.