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From manual "the basic casualties are doubled for artillery". But I cant find any artillery damage bonus in my detailed battle reports

Is manual wrong?

I think this is an old COG rule that was superseded by the scale (i.e. division / brigade) modifiers.  Just ignore that line in the manual.  When you play at division level, artillery get +50% bonus, other units +100%; there should be a line in the report for this.

Thank you for explanation. But where I can read in detail about this modifiers?

They are just scale modifiers -- to represent the fact that division combat turns are proportionally longer than brigade level.  I'm not sure there is any place that discusses them in detail.