There are similar words in German language, like »Kogel« (round top of a Hill), »Kogge« (broad but short sailing ship), and all of them belong to a family of words round the word »Keule« (cudgel) which is a stick with a thick, round end, and the Englisch word cudgel in fact also is related to this family. In other languages there are similar words for »Kugel«: Danish kugle and Dutch kogel.
So, from it's etymology a »Kugel« is something that is round and hard.
A Kugel can be:
- A mathematical sphere plus it's content.
Sei K eine Kugel mit dem Radius r und E eine Ebene, die K tangential berührt.
- A hard object that is shaped like a sphere.
Die Kugel am oberen Ende eines menschlichen Oberschenkelknochens hat die Größe eines Tischtennisballs.
- A bullet.
Die Kugel prallte am Geländer ab und traf dann den Schützen selbst.
The meaning »bullet« comes from medieval times, when the first guns was invented. The bullets of guns in those times was shaped like balls, and they was hard, so they was named »Kugel«. Later the shape changed, but the name stayed.
Sometimes you can read, that the German word »Ball« (as well as the englisch »ball«) has it's origin in the greek word βάλλειν (ballein) which means »to throw«. But this is wrong. The word »Ballistik« (the science of throwing) comes from βάλλειν, but not »Ball«. The true etymology is a little bit complicated, but very interesting:
The Middle High German word and the Old High German are the same: »bal«, and this is also the Dutch word. The English word »ball«, the French »balle« and the Swedish »boll« have all the same origin, as well as the english »ballock« which literally means »little ball« but means testicle. They all come from the Indogermanic word »bhel«. And »bhel« means: to swell, to well up, to bulge, to blow up.
So »Ball« (in German as well as in English) means: A thing that is blown up.
And so also the english »balloon« and the German »Ballon« have the same etymologic root as »Ball« and »ball«.
Also intersting is, that the indogermaic word »bhel« also transformed to the greek word φάλλος (phallos), which is the greek word for the penis, and this is also something that can swell.
But there is another word that comes from »bhel«: The German words »blähen« (to belly) and »blasen« (to blow). The original meaning of both word was: to swell something, to make it bigger (primarily, but not exclusively, by blowing it up with air). And this meaning is still vivid in the word »blasen« when it is used in the meaning of fellatio.
So, under this aspect (»Ball« = a thing that is blown up) it becomes much clearer what »Ball« can mean:
- A device in sports, that is filled with air, but does not need to be in the shape of a sphere.
Im amerikanischen Football wird ein ovaler Ball verwendet.
Derived from this usage many round sports devices are called »Ball«, even if they are not really blown up. It is rare, but the balls used in Billard and Bowling sometimes are also in German called »Bälle«, but more common still is »Billardkugel« and »Bowlingkugel«.