Use the move command.
Select the pad, via, or part you want to move. Type
move (> x y), where x and y are the absolute coordinates you want the part to be moved to.
The most difficult part is choosing an origin on your part. It can be anywhere, but for your linked part I would probably use pin 1 as 0,0. Then make pin 2, select it and type
move (> 0, 10.16), then pin 3 will be 10.16+5.08 for the y coordinate (Eagle unfortunately does not accept basic math inputs).
Recognize the (most common) common denominator.
If you set your grid to 5.08 things will be even easier. Then you can place pin 1, copy from it to make pin 2 and move up by two grid positions. Pin 3 is one more. Pin 7 is seven across, pin 6 is one up from that, etc. Things will continue to move in grid increments, so using the move command to move pin 10 down by 3.68, then drag it over by one grid tick, copy it and move five over for pin 9, etc.