IN (AREA)
Use in when the place is thought of as a containing area or time period.
Space:
He lives in this house/cave/hole.Time:
He lives in this city/state/province/country/region/galaxy.
The point is in this range/area/space. [a 1, 2 or 3 dimensional container]
He lived in the seventeenth century.
He is in his thirties.
AT (POINT)
Use at when the place is thought of as a point.
Space:
The US president lives at number 1600 Pennsylvania Avenue.Time:
There is a black hole at the center of our galaxy.
It stopped at the end/edge/membrane. [a point where a boundary could be crossed regardless of whether the boundary itself is a point, line or surface]
He lived at the end of the seventeenth century.What is considered a point depends on the scale at which it is viewed. Boundaries in time like the beginning and end of events always have no duration, but a period of a few days could also be seen as a point when viewed on a larger time scale. Hence, we say things like at Christmas time, which is understood as a time of year, and relatively brief on that scale.
The show starts at eight o'clock.
ON (SURFACE)
Use on to indicate contact with a surface. This is usually a two dimensional surface, but on can also be used to indicate contact with a line that is viewed as a boundary, and very occasionally to indicate contact with a point.
Space:
We live on Earth. [contact with a surface]Time:
He lives on the third floor. [contact with a surface]
There are goats living on the mountain. [contact with a surface]
There are spiders living on the ceiling. [contact with a surface]
The cup is on the table. [contact with a surface]
He is on the edge/border. [contact with a line]
He stood on this spot. [contact with a point]
We had lunch on Monday. [imagine the days of the week as stepping stones]Sometimes, you can use more than one preposition depending on whether you want to speak about areas, points or surfaces:
He lives in Pennsylvania Avenue. [understood as a containing area]
He lives on Pennsylvania Avenue. [understood as a contact with a surface]
Very nice articles.We need more on that topics.
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