Emulation is the desire of something, engendered in us by our conception that others have the same desire.
Explanation--He who runs away, because he sees others running away, or he who fears, because he sees others in fear; or again, he who, on seeing that another man has burnt his hand, draws towards him his own hand, and moves his body as though his own were burnt; such an one can be said to imitate another's emotion, but not to emulate him; not because the causes of emulation and imitation are different, but because it has become customary to speak of emulation only in him, who imitates that which we deem to be honourable, useful, or pleasant.

As to the cause of emulation, cf.III.xxvii.and note.

The reason why this emotion is generally coupled with envy may be seen from III.
xxxii.

and note.
XXXIV.

Thankfulness or Gratitude is the desire or zeal springing from love, whereby we endeavour to benefit him, who with similar feelings of love has conferred a benefit on us.