There's a mishmash of highly dangerous misunderstanding going on here.
NO electric range, apartment (20") or full (30") size notwithstanding, should be connected to anything less than a #8 wire. No. 10 wire is simply not heavy enough to carry the potential amperage an electric range can draw.
And a certain size breaker is not specified because it will make the range operate better; it has nothing to do with that.
Electrical conductors (wires) OPERATE a range and the breaker to which the wires are connected PROTECT the wires.
You can play with all the math you want to, but you can't escape the fact that a #10 wire is rated to carry a maximum of 30 amps and will not be protected by a breaker which won't snap until more than 40 amps hit it. A #10 wire will burn up (and burn your house down) before that 40-amp breaker even thinks about snapping.
And limiting each use to only one or two burners or just the oven will not bypass the potential for disaster. Burners burn out and when they do they can create dead shorts, causing uncontrolled amperage to run wild. When that happens, the only thing that can keep that wire from burning up inside your walls is a breaker rated at no more amperage than the maximum the wire is able to carry safely.
Apartment-size ranges require at least a #8 wire and full-size ranges require a #6 wire. You might get by with #8 and a 40-amp breaker on a full-size range, but it wouldn't be my choice.
Bite the bullet and rewire the thing for the size range you'll be connecting to.
Or forget the range and just get a hotplate for that #10 wire -- with a 30-amp breaker.
Unless, of course, you enjoy watching house fires.
EDIT: You don't necessarily have to rip out walls and cabinets. You can probably figure a route for surface-mount electrical conduit or the higher-priced Wiremold and run the new wire along baseboards, walls, etc., to a new -- and properly sized -- range outlet. And just leave the old #10 circuit for other uses.
[This message has been edited by HBB (edited August 20, 2002).]