What is the pre-computer version of Photoshop's blending modes? Before computers, to blend two pictures into one, I'd imagine the painter would have used some sort of mirror setup to reflect the one picture onto a mirror containing the reflection of the other picture. Does that sound right? 
What about different blending modes that Photoshop has, like "Difference," "Pin Light," etc. What are the pre-computer origins of these?

Example of blending modes
I think the origins lie in many places. In photograms and photocompositing, each image component is burned-in over the initially white surface and the edges can be blended by using to umbra of the shadow of the hands or stencil controlling the burn. 

Blending tones is an important technique in drawing with pastels. I think a lot of the blending tools come from the color blending realm, perhaps even more than from the collage and photogram realm. So even things liking mixing paints have their computer analogue, which can then be applied to edges due to the converge of the two sub-topics.