What is the origin of the counting prefixes: uni-, bi-/di-, tri-, quad-, etc.?

Solution 1:

You are correct, they are from Latin and Greek, we have simply inherited terms from both. There is a good reference for Latin and Greek roots over at Wikipedia:

Uni meaning one:

un-, uni- one

• language of origin: Latin

• etymology: unus, unius

• examples: unary, union

Bi/Di meaning two:

bi- two

• language of origin: Latin

• etymology: bis, "twice"; bini, "in twos"

• examples: binoculars, bigamy, biscotti

di- two

• language of origin: Greek

• etymology: δι,

• examples: dicot, dipole

Quadr meaning four:

quadr- four

• language of origin: Latin

• etymology: quattuor

• examples: quadrangle, quadrillion

And so on; there are a lot of these and I'm no expert but believe that, although some of the roots from Latin and Greek essentially mean the same, there are some constraints on which ones to use in certain circumstances (see also: hypercorrection.) But don't quote me on that, though, I'll try and look a little information up.

Solution 2:

They do come from both Latin and Greek as follows (along with the rest, up to ten):

uni comes from the Latin unus, meaning "one"
di comes from the Latin dis, meaning "twice" (originally from the Greek prefix di- meaning "two"
tri comes from the Latin tres (Greek treis), meaning three
quadra comes from the Latin quattuor, meaning "four"
quinta/penta comes from the Latin quintus, meaning "fifth" and the Greek pente, meaning "five"
hexa comes from the Greek hex, meaning "six" (Latin is sex)
septa comes from the Latin septem, meaning "seven" (Greek is hepta) m
octa/o comes from the Latin octo (Greek okto), meaning "eight"
nona comes from the Latin nonus, meaning "ninth"
deca/deci comes from the Greek deka, meaning "ten" and from the Latin decimus, meaning "tenth"