On another world 52 symbols (2 unique sets of 26 elements) correspond to the standard "Anglo-Saxon" alphabet with both being used relatively equally.
In this instance the frequency of a corresponding element differs by only one if at all, and by "coincidence" any character appearing more than once alternates exactly from one set to the other when it appears next.
For those who have a fondness for letter frequencies, I offer this table:
A-Z Letter Frequencies in the unencrypted text:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Total
7 1 5 3 12 1 3 5 16 1 0 4 3 12 9 6 0 9 7 11 2 1 1 0 3 0 122
The following statement does, for example, address Desargues' Theorem (but not specifically due to a certain peculiarity it has):
mUY oqb kydIzvuZWdEM uT khzwfXoWCb
RfdcbZyL zrXxh uE IQWyv Mgrl oqmZ eN
uEofhXlQTVWER Zqb sdyiv kzuTo mEB UWTf
uE dTb WDcfiuQZbYL WEJfhM uov ImWy
Please offer a translation.
Note: Only for ease of presentation (and readability rather than have strange symbols) have the upper and lower cases of the standard alphabet been used, and for that matter, each set of 26 elements contains a mix of uppercase and lowercase.