Etymology
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lacto- 

before vowels, lac-, word-forming element used in chemistry and physiology from 19c. and meaning "milk," from Latin lac (genitive lactis) "milk," from Proto-Italic *(g)lagt-, from PIE root *g(a)lag- "milk." This and the separate root *melg- (source of milk (n.)) account for words for "milk" in most of the Indo-European languages. The absence of a common word for it is considered a mystery. Middle Irish lacht, Welsh llaeth "milk" are loan words from Latin.

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-ine (1)

also -in, adjectival word-forming element, Middle English, from Old French -in/-ine, or directly from Latin suffix -inus/-ina/-inum "of, like," forming adjectives and derived nouns, as in divinus, feminus, caninus; from PIE adjectival suffix *-no- (see -en (2)).

The Latin suffix is cognate with Greek -inos/-ine/-inon, and in some modern scientific words the element is from Greek. Added to names, it meant "of or pertaining to, of the nature of" (Florentinus), and so it also was commonly used in forming Roman proper names, originally appellatives (Augustinus, Constantinus, Justinus, etc.) and its descendants in Romanic languages continued active in name-forming. The Latin fem. form, -ina, was used in forming abstracts (doctrina, medicina). Relics of the attempt to continue a distinction between Latin -ina and -inus account for the English hesitation in spelling between -in and -ine.

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