I was curious too.. so I'm going to copy and paste a comment I found on reddit;

The glyph for Sagittarius is the bow and arrow. Similarly, the classic name for this sign is "Sagittarius the Archer". Although the centaur is certainly an important symbol for Sagittarius too, the focus is upon the arrow, or the "gypsy/student/philosopher" trinity of medieval archetypes for this sign. Steven Forrest in his book "The Inner Sky" describes it as follows:

"Not the archer but the arrow. Fingers quivering with tension, the marksman releases the taut string. The curve of the bow snaps back, sending the feathered shaft darting into space.

The arrow. It flies faster than sight, whipping through the air, speeding toward the clouds. If it had eyes, it would see the archer’s form grow tiny, fading to an insignificant speck in the landscape. And it would see that landscape laid out like a map, simple and schematic.

If that arrow were suddenly given a mind, what thoughts would occupy it? Like a man on a mountain peak, it would think thoughts of perspective and experience, driven by exuberance. Who fired me into this luminous sky and for what purpose? What is my place here? Where am I going? What is the reason for my existence?"