Principles of Pilates:

1. concentration of mind and body
2. control of movement
3. your center, core, or powerhouse
4. fluidity of movement
5. precision of movement
6. breath

You may find many more throughout research but this is a good list to get started.

The 8 limbed path to Yoga
(as described in the Yoga Sutra's of Patanjali)

1. yamas (restraints/the 'shall nots')
2. niyamas (observances/behaviors)
3. asana (physical poses)
4. pranayama (breathwork)
5. pratyahara (withdrawal of senses)
6. dharana (concentration/holding steady)
7. dhyana (meditation)
8. samadhi (complete absorption)