I'm guessing that this is Murray Leinster's "The Fifth Dimension Catapult," originally published in 1931.
The main protagonist is mathematician Tommy Reames, who responds to a telegraph summoning them to the home of Professor Edward Denham. There he meets a man named Von Holtz who informs him that Denham has been trapped for several days in another dimension (sort of) but is still visible via a special viewing scope.
Description of the scope:
The one totally unidentifiable piece of apparatus in the place was one queer contrivance at one side. It looked partly like a machine gun because of a long brass barrel projecting from it. But the brass tube came out of a bulging casing of cast aluminum, and there was no opening through which shells could be fed.
Upon looking through the "dimensoscope":
He was gazing upon a landscape such as should not -- such as could not -- exist upon the earth.
There were monstrous, feathery tree-ferns waving languid fronds in a breeze that came from beyond them. The telescope seemed to be pointing at a gentle slope, ... and halfway up the incline there rested a huge steel globe.
The globe was a kind of capsule built by Denham in which he and his daughter Evelyn had been thrown out of our normal space into a new set of parallel dimensional coordinates. The "fifth dimension" is inhabited by creatures which are named "Ragged Men", as well as the higher-tech inhabitants of a "Golden City" (who have flying machines), and many strange creatures.
Tommy works to figure out how Denham built his catapult (which requires a new material called metallic ammonium), then to save them. There's a subplot involving mobsters who had backed Denham's work.
I should mention that Tommy Reames is described more than once as being atypically athletic for an academic. Also, while the Ragged Men don't seem to be planning to kill Denham, at the climax of the story they are preparing to torture and kill a person from the Golden City in a scene remniscent of a sacrifice. Both Denham and Evelyn are caught while trying to stop this. Reames rescues them by firing a machine gun across dimensions into the mob.
While I don't know for sure, I'm guessing this is the same story mentioned by Organic Marble -- the book in which I read it immediately came to mind when I read your description. However, I'm not sure this is the one you're after. Hopefully, the details I provided will either confirm or definitely disqualify it.
