Though the words are linked through two simple connections. Books used to be big and heavy, so rather than travelling market stalls the first shops for books were in fact stationary - stationarius. And writing implements, paper and the like began to be sold at these stationary stores. Various sites will explain the history.

Stationary and Stationery

Mnemonic from the entertaining and informative book Made to Stick.

Make your idea sticky

The sun behind you, the rain in front of you, and the angle is due to the refraction of light in the raindrops.

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The position of a rainbow is predictable