As well as Throwing the diabolo up & down you can also throw it round in a circle. This trick forms the basis for many around the something tricks. It is also a good way of breaking up sequences of Suns, adding spin without losing the circular momentum.
First of all you need to know in which direction round the circle the diabolo should go. While it is possible to throw the diabolo in a circle in either direction, one way will add spin while the other direction will cause the diabolo to slow down & stop. To build up spin throw the diabolo round in a circle in the opposite direction to the way that the diabolo is spinning. So if the diabolo is spinning anticlockwise then you throw it in a clockwise direction.
Begin spinning the diabolo, then turn your subordinate hand inwards so that the tip of the handstick is pointing at the diabolo.
Swing the diabolo towards your subordinate handstick & pull your dominant hand out to the side at the same time. When the diabolo gets close to the tip of your subordinate handstick tighten the string by quickly turning your subordinate wrist outwards, the stick should move like a windscreen wiper blade from pointing inwards to pointing up & out. The diabolo will fly in an arc from your subordinate side over to your dominant. While the diabolo is in the air, turn the subordinate handstick inward again. Also make sure that the string is tight, if the string is loose & flapping around it will be very difficult to reliably catch the diabolo again.
You catch the diabolo just as you would do from a vertical throw, by lining up the tip of the dominant handstick with the diabolo's axle. This time however, keep your dominant hand down below shoulder height. When the diabolo lands on the string, flick your dominant handstick inwards over the top of the diabolo to start it rolling down the string to the subordinate side for another throw.
Keep the diabolo moving round in a circle in this way, the throw draws the top half of the circle while the catch & the roll down the string towards the subordinate hand draws the bottom half. As with all diabolo moves it will take practise to perfect the move. Once you've got it going round smoothly you'll notice that the diabolo picks up a lot of spin during this move. Circular throws combine well with Sun between the arms or an Sun with a stopover.