...It has beenindicated mathematically (by formulae based on conjecture),but never actually solved—for the very good reason that itis impossible to reproduce spacial conditions in earthlylaboratories... 
Various 「Astounding Stories, July, 1931」
... mathematically expressed...
Roman Frederick Starzl 「The Martian Cabal」
...It is mathematically demonstrable thatthis arc of light is precisely what should be seen if Venus has anatmosphere like our earth's...
Richard A. Proctor 「Myths and Marvels of Astronomy」
...It had,however, previously been investigated mathematically by Titius in 1772...
Cecil G. Dolmage 「Astronomy of To-day」
...Laplace mathematically demonstrated that it cannot be uniform andsolid, and survive...
Henry Warren 「Recreations in Astronomy」
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