In Old English, believe was geliefan, which traces back to the Germanic galaubjan, where laub is the root for "dear" (so "believe" is "to hold dear"). Laub goes back to the Proto-Indo-European root for "love," leubh.
We got furlough from the Dutch verlof, which traces back to the same Germanic laub root as in believe. It is also related to the sense of leave meaning allowance or permission ("get leave," "go on leave"). The "leave" in a furlough is given with pleasure, or approval, which is how it connects back to love.
Old English Frigedæg was named for Frigg, the Germanic goddess of love (and counterpart to the Roman Venus). According to the OED, frīg was also a noun for "strong feminine" love.
Venom comes from the Latin venenum, which shares a root with love-goddess Venus, and originally referred to a love potion.
The root of amateur is Latin amare, "to love." An amateur practices a craft simply because they love it.
The Latin caritas, which ended up as charity in English, was a different kind of love than amor, implying high esteem and piety, rather than romance and passion. It was used to translate the Ancient Greek agape, the word used in the New Testament to express godly love.
Greek had another word for love, philia, that — in contrast to agape and eros (sexual love) — meant brotherly or friendly love. It's used in many classical compounds to signify general fondness or predilection for things. Philosophy is the love of sophos, wisdom.
Love of anthropos, humanity.
You might know it as the "city of brotherly love," but you might not know that the tagline is right there in the name. It's love for adelphos, brother.
The name Philip comes from the compound phil- + hippos, love of horses.
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