Q:

"Second," "Minute," and "Hour"

Would anyone happen to know where the terms for the units of time came from, and why? I know "minute," which also means something extremely small, comes from the latin meaning "small," but then why is it not the smallest unit of time? 
Also, is there any relation between the time unit "second" and the ordinal number "second"?

A:

"Hour" comes from Old French "hore", 1/12 of a day.  "Minute", from Latin "minuta", "small" (think of it pronounced as "mine-yute").  "Second" is more complicated: 
"Medieval Latin secunda, short for "secunda pars minuta" - "second diminished part," the result of the second division of the hour by sixty (the first being the "prime minute," now called the minute)"
Note that angular measure has degrees, minutes (1/60 of a degree) and seconds (1/60 of a minute).   They usually write "minutes of arc" and "seconds of arc" so as not to confuse them with the time units.
There could be a connection between the time "second" and the ordinal "second", from the "second diminished part" (in the quote above).
The ordinal "second" comes from Latin "secundus: following, next in time or order"

