Р362
ПОЛОЖА (less often ПОЛОЖЙВ(ШИ)) РУКУ НА СЕРДЦЕ сказать, ответить, утверждать и т. п. (
Verbal Advthese forms onlyadvoften used with imper
fixed WO (to say sth. , respond, declare sth. etc) absolutely sincerely
hand on (upon) heart
with one's hand on (upon) one's heartin (with) all sincerityin all honesty
the corresponding modern form is the perfective verbal adverb «положив».