A measurement perpendicular to the celestial equator, above or below it, is called Declination .
Declination is measured in degrees.
Subtract your latitude from 90 degrees. This result is your co-latitude. The co-latitude of 40 degrees north is 50 degrees. If your co-latitude plus the declination of the star is greater than zero, then it will rise above your horizon at least sometime during the year. Another way to think of this is if the sum of your latitude and the absolute value of a southerly declination is less than 90, then it's visible.