At the diagram shows, there are two mirrors in the 'eye piece' of a camera lucida: a normal one and a half-silvered (one-way or semi-transparent) one. The object is reflected from first mirror onto the half-silvered one. Your eye sees this reflection and simultaneously looks through this mirror to see the paper too, so it appears that object if on the paper. It's "magic" done with mirrors.
The camera lucida was invented in 1807 by a British scientist, William Hyde Wollaston (1766-1828). Camera lucida is Latin for "light chamber". (Read Wollaston's original patent document.)