AustraliayoudaoicibaDictYouDict
from Latin Terra Australis (16c.), from australis "southern" + -ia. A hypothetical southern continent, known as terra australis incognita, had been proposed since 2c. Dutch explorers called the newfound continent New Holland; the current name was suggested 1814 by Matthew Flinders as an improvement over Terra Australis "as being more agreeable to the ear, and an assimilation to the name of the other great portions of the earth" ["Voyage to Terra Australis"]. In 1817 Gov. Lachlan Macquarie, having read Flinders' suggestion, began using it in official correspondence. The ultimate source is Latin auster "south wind," hence, "the south country."

The Latin sense shift in australis, if it is indeed the same word other Indo-European languages use for east (see aurora), for which Latin uses oriens (see orient), perhaps is based on a false assumption about the orientation of the Italian peninsula, "with shift through 'southeast' explained by the diagonal position of the axis of Italy" [Buck]; see Walde, Alois, "Lateinisches etymologisches Wörterbuch," 3rd. ed., vol. 1, p.87; Ernout, Alfred, and Meillet, Alfred, "Dictionnaire étymologique de la langue latine," 2nd. ed., p.94. Or perhaps the connection is more ancient, and from PIE root *aus- "to shine," source of aurora, which also produces words for "burning," with reference to the "hot" south wind that blows into Italy. Thus auster "(hot) south wind," metaphorically extended to "south."
handsome (adj.)youdaoicibaDictYouDict
c. 1400, handsom "easy to handle, ready at hand," from hand (n.) + -some (1). Sense extended to "fit, appropriate" (1550s, implied in handsomely), then "having fine form, good-looking, agreeable to the eye" (1580s). Meaning "generous, on a liberal scale" (of rewards, etc.) first recorded 1680s.
[Americans] use the word "handsome" much more extensively than we do: saying that Webster made a handsome speech in the Senate: that a lady talks handsomely, (eloquently:) that a book sells handsomely. A gentleman asked me on the Catskill Mountain, whether I thought the sun handsomer there than at New York. [Harriet Martineau, "Society in America," 1837]
Related: Handsomeness. For sense development, compare pretty (adj.). Similar formation in Dutch handzaam "tractable, serviceable."
prosper (v.)youdaoicibaDictYouDict
mid-14c., from Old French prosperer (14c.) and directly from Latin prosperare "cause to succeed, render happy," from prosperus "favorable, fortunate, prosperous," perhaps literally "agreeable to one's wishes," traditionally regarded as from Old Latin pro spere "according to expectation, according to one's hope," from pro "for" + ablative of spes "hope," from PIE root *spe- "to flourish, succeed, thrive, prosper" (see speed (n.)).
rationality (n.)youdaoicibaDictYouDict
1620s, "quality of having reason;" 1650s, "fact of being agreeable to reason," from French rationalité, from Late Latin rationalitas "reasonableness, rationality" (also source of Spanish racionalidad, Italian razionalita), from Latin rationalis (see rational).
unsavory (adj.)youdaoicibaDictYouDict
also unsavoury, early 13c., "tasteless, insipid," from un- (1) "not" + savory (adj.). Meaning "unpleasant or disagreeable to the taste" is attested from late 14c.; of persons, from c. 1400. Related: Unsavoriness.
well (adv.)youdaoicibaDictYouDict
"in a satisfactory manner," Old English wel "abundantly, very, very much; indeed, to be sure; with good reason; nearly, for the most part," from Proto-Germanic *welo- (cognates: Old Saxon wela, Old Norse vel, Old Frisian wel, Dutch wel, Old High German wela, German wohl, Gothic waila "well"), from PIE root *wel- (2) "to wish, will" (cognates: Sanskrit prati varam "at will," Old Church Slavonic vole "well," Welsh gwell "better," Latin velle "to wish, will," Old English willan "to wish;" see will (v.)).

Also used in Old English as an interjection and an expression of surprise. The adjective was in Old English in the sense "in good fortune, happy," from the adverb; sense of "satisfactory" is from late 14c.; "agreeable to wish or desire" is from mid-15c.; "in good health, not ailing" is from 1550s. Well-to-do "prosperous" is recorded from 1825.