Greek or Latin numerical prefix?

Why do some English words (e.g., pentagon, decahedron) have prefixes derived from the Greek numerals, while other English words (e.g., quinquereme, decennial) have prefixes derived from the Latin numerals?

It is hard to give a complete answer to this question, but two points are worth making:

• There is a tendency for numerical prefixes to come from the same language as the stem of the word: if the stem has a Greek origin, numerical prefixes tend to derive from the Greek numerals, and if the stem has a Latin origin, numerical prefixes tend to derive from the Latin numerals. So we have 'pentagon' and 'decahedron' because the stems -gon and -hedron have a Greek origin: -gon is from the Greek word gonia (which means 'angle') - a pentagon is a figure with five angles; and -hedron is from the Greek word hedra (which means 'seat' or 'base') - a decahedron is a figure with ten plane surfaces. In the same way we have 'quinquereme' and 'decennial' because the stems -reme and -ennial have a Latin origin: -reme is from the Latin word remus (which means 'oar') - a quinquereme is a ship which is propelled by five banks of oars on each side; and -ennial is from the Latin word annus (which means 'year') - 'decennial' means 'lasting for, or happening, every ten years'.

• There is a tendency for English words in the areas of science, mathematics, and technology to have a Greek rather than a Latin origin. This tendency is, again, illustrated by the pairs 'pentagon' and 'decahedron', on the one hand, and 'quinquereme' and 'decennial', on the other.

However, these points must not be exaggerated. What they refer to are no more than tendencies. It is easy to find examples of Greek numerical prefixes with Latin stems (e.g., pentangle, pentavalent) and of Latin numerical prefixes with Greek stems (e.g., nonagon, quadriplegia). (Incidentally, the prefix quadra-/quadri- derives from the Latin quattuor (four): quadriplegia - -plegia is from the Greek plege (a blow or stroke) - is a condition in which there is paralysis of all four limbs.) Equally, there are many scientific, mathematical, or technological terms which have a Latin rather than a Greek origin - e.g., quadrilateral, quadrivalent, quinquefoliate.

See also Greek and Latin words for numbers, Prefixes in units of measurement, Prefixes for very high numbers, and Prefixes in words for geometrical figures.