The name 'Eve' comes from the Hebrew word חַוָּה or 'Chava,' a form of the word for life, which is why she is called 'the mother of all living.' She represents the church, and is called 'mother' because this was the first Church of all, and 'living' because of its faith in the Lord, who is life itself.

(Odkazy: Arcana Coelestia 287-291, Genesis 3:20)

355. Verse 5 And for Cain and his gift He had no respect; and Cain's anger was set ablaze and his face' fell.

'Cain', as has been stated, means faith separated from love, or the kind of doctrine which allows faith to be separated. 'His gift for which He had no respect' means, as previously, that his worship was unacceptable. 'Cain's anger was set ablaze and his face ¹ fell' means a change as to interiors; 'anger' means the fact that charity had departed, and 'face' the interiors, which are said 'to fall' when they undergo change.

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