How to download minecraft on my other computer if i already bought it on a different computer?

I got a new computer since my old one is getting slow and has started to mess up. I was wondering how i could download minecraft on my new computer without having to pay again for it.

If you're using Windows, click this link and you will be able to download it.
https://s3.amazonaws.com/...ecraft.exe
Mac
https://s3.amazonaws.com/...ecraft.dmg
Linux/All with Java
https://s3.amazonaws.com/...ecraft.jar

You will have to sing in again. You did not have to buy a new account to play it again. All you had to do was go to http://www.minecraft.net/...t/download and download it.
Also, if you want to transfer your worlds:
Windows:
goto %appdata% and move your.minecraft fodler to your new computer
Linux:
/home/[your username]/ then copy your.minecraft folder.
If you're using Mac, sorry I do not know how. If you know where it is stored, copy it from there to your new computer.

Wow that answer is way too complicated. If you have already bought it, just log into the minecraft website and download it again. For mac or windows, it works if you are switching from one to the other. If you want to transfer your world, do what this guy says: %appdata% and go to.minecraft copy it, put it on a flash drive, then go back to it on your new comp and put into the SAVES folder.