Meaning of "projection" and "to project" in neuroscience What is the exact meaning of the term projection and the verb to project in neuroscience?

I haven't found any neuroscience reference book or dictionary that gives a definition, although those terms are often used in the definitions themselves. For example, the Glossary of Neuroscience (2nd ed.), available at https://www.ncbi.nlm.nih.gov/books/NBK10981/ gives this definition:


  upper motor neuron: A neuron that gives rise to a descending projection that controls the activity of lower motor neurons in the brainstem and spinal cord.


and several others, but "projection" itself is not an entry in the Glossary.

The Oxford English Dictionary gives this definition (#11): 


  Physiol. The spatial distribution, in the brain, or other parts of the central nervous system, of the points to which nerves or nerve impulses go from any given area or organ; const. on, upon, to the receiving part; also concr., a tract of projection fibres.


but it's still a little vague.

I'd be happy if someone could give me a precise definition (and some references to corroborate it). In particular: can I say that a neuron projects to another neuron, to mean that the axon of the first connects to some dendrite of the second?

Cheers!
I think the definition you found from OED is fine. Dictionary definitions are often not really ideal for terms used in biology, you learn more from examples and usage, for example the quote you gave about upper motor neurons.


  can I say that a neuron projects to another neuron, to mean that the axon of the first connects to some dendrite of the second?


Typically yes, though as the OED definition implies, "from any given"/"to the receiving part", projection is typically used for longer-range connections, where the sending and receiving cells are in different nuclei or layers. You would be less likely to describe cells that synapse on each other within one nucleus as projecting, though I also wouldn't say that description is entirely wrong either, and the distance required to be "long-range" can sometimes be short.

You'll note if you go through the Purves' glossary that you linked, all the uses of "projection" refer to long-range connections.