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the Romans would put a bronze pan on a metal stand.
eggs that are cooked different from other ones - Perhaps you mean "poached eggs," which are cooked in boiling water without the shell. The idea is that the egg-white becomes a pocket for the yolk.
Yes, fish may be cooked by boiling.
Many dried beans must be soaked overnight in cold water prior to cooking. After soaking, the beans can be cooked in boiling water. If the beans fall apart, you are cooking them too long.
A vast majority of Japanese food is "cooked," often either by frying, grilling, or boiling.
Pasta should be cooked in lots of boiling water.
poached egg
With direct simmering, the food is immersed in slowly boiling liquid and cooked until it is done. With indirect steaming, the food is place on a rack above the boiling liquid and cooked by the steam from that liquid.
The red potato is usually cooked by boiling, frying (sliced), grilling, or steaming. Their skin is too thin to commonly be baked.
You boil the shelled mussels in boiling water and they are cooked when the shells split open.
Parboiling is cooking food in boiling water until it is partly cooked, to parboil noodles, drop them into boiling water, when partly cooked remove them and refresh in ice cold water to stop them cooking any more. Finish them off later, either in more boiling water, or add them to a stir fry or a bowl of soup. As they are already partly cooked they will be ready in no time.
Cooking pasta is an example of boiling. Ironically, boiled eggs are not an example of boiling (since they should actually be cooked at a simmer).