ball (n.1) Look up ball at Dictionary.com
"round object," Old English *beal, from or corresponding to Old Norse bollr "ball," from Proto-Germanic *balluz (cognates: Old High German ballo, German Ball), from PIE root *bhel- (2) "to blow, inflate, swell" (see bole).

Meaning "testicle" is from early 14c. Ball of the foot is from mid-14c. A ball as an object in a sports game is recorded from c.1200; To have the ball "hold the advantage" is from c.1400. To be on the ball is 1912, from sports. Ball-point pen first recorded 1946. Ball of fire when first recorded in 1821 referred to "a glass of brandy;" as "spectacularly successful striver" it is c.1900.
ball (n.2) Look up ball at Dictionary.com
"dancing party," 1630s, from French, from Old French baller "to dance," from Late Latin ballare "to dance," from Greek ballizein "to dance, jump about" (see ballistics). Hence, "very enjoyable time," 1945, American English slang, perhaps back to 1930s in black slang.
ball (v.) Look up ball at Dictionary.com
1650s, "make into a ball," from ball (n.1). Sense of "to become like a ball" is 1713; that of "to copulate" is first recorded 1940s in jazz slang, either from the noun sense of "testicle" or "enjoyable time" (from ball (n.2)). Related: Balled; balling.