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The Greek Language has contributed to the English vocabulary in three ways:

1. directly as an immediate donor,
2. indirectly through other intermediate language(s), as an original donor (mainly through Latin and French), and
3. with modern coinages or new Greek.

One can estimate the contribution of Greek words to English in two basic ways. One is to count the proportion of distinct words in the vocabulary (type frequency); another is to count the proportion of words in continuous text (token frequency).

To estimate type frequency, we can use a typical English dictionary of 80,000 words, corresponding very roughly to the vocabulary of an English-speaking adult. Based on this sample, about 5% of the English vocabulary comes from Greek directly, and about 25% indirectly. If modern technical and scientific coinages using Greek roots are also counted, the percentage increases. Conversely, if token frequency in typical running text is used, the percentage decreases.

Since the living Greek and English languages were not in direct contact until modern times, borrowings were necessarily indirect, coming either through Latin (through texts or various vernaculars), or from Ancient Greek texts, not the living language. More recently, a huge number of scientific, medical, and technical neologisms have been coined from Greek roots—and often re-borrowed back into Modern Greek.

Until the 16th century, the few Greek words that were absorbed into English came through their Latin derivatives. Most of the early borrowings are for expressions in theology for which there were no English equivalents. In the late 16th century an influx of Greek words were derived directly, in intellectual fields and the new science.

In the 19th and 20th centuries a few learned words and phrases were introduced using a more or less direct transliteration of Ancient Greek (rather than the traditional Latin-based orthography) for instance nous, hoi polloi.

Finally with the growth of tourism, some words, mainly reflecting aspects of current Greek life, have been introduced with orthography reflecting Modern Greek.

In some cases, a word's spelling clearly shows its Greek origin. If it includes ph or includes y between consonants, it is very likely Greek. If it includes rrh, phth, or chth, or starts with hy-, ps-, pn-, or chr-, or the rarer pt-, ct-, chth-, rh-, x-, sth-, mn-, or bd-, then it is with very few exceptions Greek. One exception is ptarmigan, which is from a Gaelic word, the p having been added by false etymology.

In English, Greek prefixes and suffixes are usually attached to Greek stems, but some have become productive in English, and will combine with other stems, so we now have not only metaphor (good Greek word) and metamathematics (modern word using Greek roots), but also metalinguistic (Greek prefix, Latin stem).

In clusters such as ps- at the start of a word, the usual English pronunciation drops the first consonant; initial x- is pronounced z. Ch is pronounced like k rather than as in "church" (e.g. character, chaos). Consecutive vowels are often pronounced separately rather than forming a single vowel sound or one of them becoming silent (e.g. "theatre" contrast "feat").

The plurals of learned Greek-derived words sometimes follow the Greek rules: phenomenon, phenomena; tetrahedron, tetrahedra; crisis, crises; hypothesis, hypotheses; stigma, stigmata; topos, topoi; but often do not: colon, colons not *cola (except for the very rare technical term of rhetoric); pentathlon, pentathlons not *pentathla; demon, demons not *demones. Usage is mixed in some cases: schema, schemas or schemata; lexicon, lexicons or lexica. And there are misleading cases: pentagon comes from Greek pentagonon, so its plural cannot be *pentaga; it is pentagons (Greek πεντάγωνα/pentagona).

Links:
List of Latin and Greek words commonly used in systematic names
List of Greek words with English derivatives
Romanization of Greek
HOI POLLOI

credits: wikipedia.org