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Greek
kalli-‘beautiful’
-graphia‘writing’
combined
combined
English
calligraphy
‘The art of beautiful handwriting.’
The story of calligraphy
Calligraphy contains Greek elements for beauty and writing. The dictionary records French or Greek as the source of the English formation. The scored components are clear even though the immediate borrowing route is not presented as uniquely settled.
This view explains the components. They are pieces of one construction, not consecutive borrowing stages.