cables-steel cables used for flying trapeze bar fixation.

carabiner-oval-shaped (or drop-shaped) aluminum, steel or titanium ring with a spring-loaded snap link.
The snap link can be equipped with a screw or bayonet lock

catch trap-the bar that the catcher catches from.

catcher-a member of a trapeze act who catches the flyers

catcher's lock-position of the catcher when ready to catch the flyer.

chalk (magnesia)-basic magnesium carbonate (not chalk), available as powder or very friable block.

chalk bag-bag used to store the chalk. Can usually be shut with a small cord. Indeed it's a rock-climbing accessory.

circus tape (tape)-auto-adhesive tape used to wrap trapeze bars (amongst other things). usually a sort of textile tape. Sometimes gauze is used instead of tape.

cloud-swing-u-shaped rope attached at either end by swivels.

coffin-from sitting twist sideways, hold one rope behind head with both hands. Bring legs up and place both feet on opposite rope, toes facing out. Push out in both directions so body is straight, rope to one side of head. You can the take both hands off and stretch them back over head.

crane bar-bar used to suspend trapezes (often fitted with ball bearings).

cutaway-the flyer turns around at the first force out, and then hooks their toes on the bar in a pike.coming back towards the catcher, the flyer breaks, then lets go at the catcher's call and does one full laid out rotation to the catcher who is holding a cutaway bar.

cutaway bar-bar that the catcher holds for the flyer to catch in certain tricks (e.g.: cutaway, reverse knee-hang).

cutaway half-cutaway with a half twist - reverse pike under the bar and then rolling legs up over the bar to do a half twist. like a reverse whip. The flyer jumps off the board and does a "turn-around" at the first force-out. as they're coming back to the platform (facing it) they go into a whip position. They stay that way as the swing back to the catcher. at the top of the catch swing, the catcher yells "hep" and the flyer "punches" their feet into the air (like a handstand) while at the same time turning 1/2 twist to the catchers hands.