What is this old Hermagis brass lens marked “Objectif Cinéma”?

This appears to be a Hermagis lens from Paris, most likely a cinema projection lens rather than a taking lens for a camera.

The markings help decode it:

• “OPTn” likely stands for opticien (optician/optical maker).
• “Bte S.G.D.G.” abbreviates breveté sans garantie du gouvernement, a historical French patent disclaimer.
• “Objectif Cinéma” means cinema/projection lens.

So the inscription is essentially saying it’s a patented Hermagis cinema lens made in Paris.

If you want to learn more about the optics themselves, you can estimate focal length by projecting a distant object (or the sun very carefully) onto a surface and measuring the distance at focus. That gives a rough focal length, though real lenses are not perfect “thin lenses,” so it’s only approximate.

Given your later notes, it’s also very possible that two separate parts were stuck together, so some markings may belong to different components. But based on the inscription alone, the main identification is: an antique Hermagis cinema/projection lens.