Etymology
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am (v.)
first person singular present indicative of be (q.v.); Old English eom "to be, to remain," (Mercian eam, Northumbrian am), from Proto-Germanic *izm(i)-, from PIE *esmi- (source also of Old Norse emi, Gothic im, Hittite esmi, Old Church Slavonic jesmi, Lithuanian esmi), first person singular form of root *es- "to be."

In Old English it formed only present tenses, all other forms being expressed in the W-BASE (see were, was). This cooperative verb is sometimes referred to by linguists as *es-*wes-. Until the distinction broke down 13c., *es-*wes- tended to express "existence," with beon meaning something closer to "come to be."

Old English am had two plural forms: 1. sind/sindon, sie and 2. earon/aron. The s- form (also used in the subjunctive) fell from English in the early 13c. (though its cousin continues in German sind, the 3rd person plural of "to be") and was replaced by forms of be, but aron (see are) continued, and as am and be merged it encroached on some uses that previously had belonged to be. By the early 1500s it had established its place in standard English.
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-i (2)
plural suffix sometimes preserved in English for words from Latin, it is the Latin plural of nouns of the second declension (such as focus/foci, radius/radii).
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I (pron.)

12c., a shortening of Old English ic, the first person singular nominative pronoun, from Proto-Germanic *ek (source also of Old Frisian ik, Old Norse ek, Norwegian eg, Danish jeg, Old High German ih, German ich, Gothic ik), from PIE *eg- "I," nominative form of the first person singular pronoun (source also of Sanskrit aham, Hittite uk, Latin ego (source of French Je), Greek ego, Russian ja, Lithuanian ).

Reduced to i by mid-12c. in northern England, later everywhere; the form ich or ik, especially before vowels, lingered in northern England until c. 1400 and survived in southern dialects until 18c. It began to be capitalized mid-13c. to mark it as a distinct word and avoid misreading in handwritten manuscripts.

The reason for writing I is ... the orthographic habit in the middle ages of using a 'long i' (that is, j or I) whenever the letter was isolated or formed the last letter of a group; the numeral 'one' was written j or I (and three iij, etc.), just as much as the pronoun. [Otto Jespersen, "Growth and Structure of the English Language," p.233]

The dot on the "small" letter -i- began to appear in 11c. Latin manuscripts to distinguish the letter from the stroke of another letter (such as -m- or -n-). Originally a diacritic, it was reduced to a dot with the introduction of Roman type fonts. The letter -y- also was written with a top dot in Old English and early Middle English, during the centuries when -i- tended to be written with a closed loop at the top and thus was almost indistinguishable from the lower-case thorn (þ). In names of U.S. highways (by 1966) it is short for Interstate (adj.).

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-i (1)
as a termination in certain people names (Iraqi, Israeli), it represents the common Semitic national designation suffix -i.
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-i- 
a "connective" element in many words formed with Latin or Greek suffixes, now often felt as part of them (as in -iac, -iacal, -ial, -ian, -ify, -ity, etc.). Properly it forms no proper part of the suffix but is often the stem-vowel of the initial word in the Latin compounds (genial from genius), or a modified form of it. As such forms were very common, -i- was used merely connectively or euphonically in some Latin compounds (uniformis) and in later words made from Latin components in English or French (centennial, editorial).

The Greek equivalent is -o-, which also became an active connective in English, but they now are used indifferently with elements from either language.
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*dhe(i)- 

*dhē(i)-, Proto-Indo-European root meaning "to suck."

It forms all or part of: affiliate; affiliation; effeminate; effete; epithelium; fawn (n.) "young deer;" fecund; fellatio; Felicia; felicitate; felicity; Felix; female; feminine; femme; fennel; fenugreek; fetal; feticide; fetus; filial; filiation; filicide; filioque; fitz; infelicity.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit dhayati "sucks," dhayah "nourishing;" Greek thēlē "mother's breast, nipple," thēlys "female, fruitful;" Latin felare "to suck," femina "woman" ("she who suckles"), felix "happy, auspicious, fruitful," fetus "offspring, pregnancy;" fecundus "fruitful, fertile, productive; rich, abundant;" Old Church Slavonic dojiti "to suckle," dojilica "nurse," deti "child;" Lithuanian dėlė "leech;" Old Prussian dadan "milk;" Gothic daddjan "to suckle;" Old Swedish dia "suckle;" Old High German tila "female breast;" Old Irish denaim "I suck," dinu "lamb."

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*po(i)- 
*pō(i)-, Proto-Indo-European root meaning "to drink."

It forms all or part of: beer; bever; beverage; bib; bibitory; bibulous; hibachi; imbibe; imbrue; pinocytosis; pirogi; poison; potable; potation; potion; symposium.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit pati "drinks," panam "beverage;" Greek pinein "to drink," poton "that which one drinks," potos "drinking bout;" Latin potare "to drink," potio "a potion, a drinking," also "poisonous draught, magic potion;" Old Church Slavonic piti "to drink," pivo "beverage."
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I Ching 
1876, from Chinese, said to mean "Book of Changes."
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I-beam (n.)
1869; see beam (n.). So called for its shape. I-bar is from 1890; also I-rail (1873).
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