Definition of Dactylonomy

Babylon English
counting on the fingers, counting using the fingers; art of counting by the fingers
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Dactylonomy Definition from Language, Idioms & Slang Dictionaries & Glossaries
Webster's Revised Unabridged Dictionary (1913)
(n.)
The art of numbering or counting by the fingers.
  
Webster's Revised Unabridged Dictionary (1913), edited by Noah Porter. About
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dactylonomy
\dac`tyl*on"o*my\ (?), n. [gr. da`ktylos finger + no`mos law, distribution.] the art of numbering or counting by the fingers.

Grandiloquent Dictionary
Counting using one's fingers