A turbine engine includes low and high pressure spools. A high power take-off shaft is coupled to the high spool. An auxiliary component, such as a generator, is configured to be driven by the high power take-off shaft at a first speed. The low spool, in part, drives the auxiliary component, for example, by interconnecting the high power take-off shaft to a lower power take-off shaft through a speed summing gearbox. The gearbox drives the auxiliary component and increases the rotational speed of the auxiliary component from the first speed to the second speed. The low power take-off shaft also drives another generator, in one example. The turbine engine can be started by the low pressure generator, for example, in response to a command from a controller, which transforms the generator into a starter motor.