What is the origin of the phrase "off by heart"?

LEARN BY HEART - "How does it happen we say we learn things 'by heart' instead of 'by head'? It's because of a mistaken analysis of anatomical functions made by the ancient Greeks. They placed the seat of thought in the heart." LEARN BY ROTE - "What is the reason we use the phrase 'learn by rote' to indicate learning by repetition? This phrase means 'to learn by the wheel' - from 'rota,' the L*tin word for 'wheel.' The allusion is to turning the thought over and over in the mind or saying it over and over again, in much the same way as a wheel goes around." From "Why do we say it? The stories behind the words, expressions and cliches we use," (no author listed), Castle Books, Edison, N.J., 1985.

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