Simple question -- why is declination positive in the northern hemisphere?
Seems like it should've been called "inclination" since the word originated north of the equator.
After quite an extensive search of dictionaries and books on astronomical nomenclature I came across this article that has a comprehensive review of celestial coordinate systems. And upon reading page 84 (8/14) I came across the answer to your question.
It would appear that the reason declination is used, as opposed to inclination, is that declination was first interpreted as a "deviation from standard" not an inclination of angular distance from a given point as we know it today.
This "deviation from standard" was first used to describe the motion of the sun along the ecliptic that "deviated" from the then widely accepted notion of all heavenly bodies following the line of the equator. It goes into more detail in the article but it would appear that when translated from Greek to Latin and then Latin to Arabic, the precise meaning of the word changed and evolved so that now the term declination refers to the angular distance of any celestial body.