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rising and setting of stars

Certain types of rising and settings must be inferred instead of observed, because the star is obscured by sunlight. These are used only by astronomers.

the cosmical rising: the star and the sun rise together. The star, of course, is obscured by the sun.
the cosmical setting: the star sets as the sun sets.
the true acronychal rising: the star rises as the sun sets.
the true acronychal setting: the star sets as the sun rises.

Perceptible risings and settings

These risings and settings can be observed directly, and it is these which have played a part in calendars.

the heliacal rising: the first visible, though brief, appearance of a star on the eastern horizon before sunrise. On the previous morning, sunlight made the star invisible. When the rising of a star is spoken of, it is usually the heliacal rising that is meant. In ancient Egypt, the helical rising of Sirius coincided with the annual rising of the Nile at Memphis.
the heliacal setting: the last visible setting of a star in the evening twilight. On the following evening, the star will pass below the horizon while there is still too much sunlight for it to be seen.
the apparent acronychal rising: the last visible rising of a star in the evening twilight. On the following evening, the star will rise while there is still too much daylight for it to be seen.
the apparent cosmical setting: the first visible setting of a star in the morning twilight. On the previous morning, the star didn't quite reach the western horizon before sunlight made it invisible.

The actual times of these events, for 7 selected stars, can be calculated from volume 1 of Sight Reduction Tables for Air Navigation.