Step 4. Install Ubuntu 14.04: To begin this step, reboot the computer with the Ubuntu 14.04 installation DVD in the optical, or the USB stick in a USB port. Whether you start the installer before booting into the Live desktop or after, click until you get to the step shown in the screenshot below. On my test installation, the installer said, “This computer currently has no detected operating systems. What would you like to do?” We know that there are two operating systems installed on the target HDD, so the only reasonable option to choose at this step, is “Something else.”
Ubuntu 14.04 partition type

So make the right choice and click to the next step.
Ubuntu 14.04 partition methods

That should open the installer’s Advanced Partitioning Tool’s window. You should see the existing Windows 7 and Windows 8 partitions, and the unallocated space you created from Windows 7. In the Ubuntu installer, that space is marked as “free space.” To start creating the three partitions that will be used for installing Ubuntu 14.04, select it, then click on the + button right below it.
ubutrip2

That should open the partition editor. You only need to specify a value for Size and make a selection from the Use as and Mount point menus. For the partitions created in this tutorial, I chose the use the default file system, which is Ext4 journaling file system. If you intend to do the same, then you don’t have to touch the “Use as” menu.
Ubuntu 14.04 partition editor

The first partition will be mounted at /. The minimum required disk space for it is 6.4 GB, so any value higher than that should do. Any value approaching 20 GB is better. OK.
create Ubuntu 14.04 root partition

The /home partition is where all your content will reside, so be generous with disk space here. And make sure that the mount point is set to /home. OK.
create Ubuntu 14.04 home partition

For the Swap partition, select “swap area” from the “Use as” menu. For a 32-bit system, a disk space of 2 GB (2000 MB) is recommended. For a 64-bit system, try 4 GB (4000 MB). OK.
create Ubuntu 14.04 swap partition

With the necessary partitions created, you should see them listed below the Windows 7/8 partitions in the Advanced Partitioning Tool. Before clicking Install Now, you need to select the “device for boot loader installation.” It should not be /dev/sda, but /dev/sda2 or whatever the device name of your system’s EFI partition is.
Triple Ubuntu 14.04

After selecting the appropriate device for boot loader installation, you may continue with the rest of the installation.
Ubuntu 14.04 install GRUB EFI

Step 5. Set the Default Boot Device: After the installation of Ubuntu 14.04 has completed successfully, you should set its boot manager as the default boot device. To see what the others are, access the system’s boot menu. This screenshot shows what the entries on mine were after the installation of Ubuntu. Selecting “Ubuntu” and pressing the Enter key should take you to Ubuntu’s GRUB menu.
UEFI menu Ubuntu GRUB

This is what that looks like on my test system. Aside for an entry for “Ubuntu”, you should see an entry named Windows Boot Manager, which will load the Windows boot menu that you saw at the beginning of this tutorial. Test to make sure that you can boot into all three operating systems.
Ubuntu 14.04 GRUB menu

Finally, boot into your system’s UEFI Setup Utility and set the default boot device to “Ubuntu.” Note that you can also use this guide to triple-boot any Linux distribution with Window 7 and Windows 8 in this manner. If you have a question to ask, try starting a topic at this forum category.