When starting a computer, why is this called "booting it"?

When you switch on the computer, the memory is empty, except for a very small program. This is just clever enough to load a slightly larger program in from the disk. This is just clever enough to load the whole operating system in. The Operating System then takes control. This process was likened by the early computer scientists to 'lifting yourself up by your own bootstraps', a term which was later shortened to 'bootstrap loading' and later still to 'booting up'.