The relation between 4 jhana and 7 factors development?

First of all, my English is not so good. Please forgive me if i make some mistakes in grammar.
As you all know, Buddha teach us both 4 jhana and 7 factors of enlightment. Jhana start with the abandon of 5 hindrances. 7 factors start with 4 kinds of mindfulness. If they are all sadmahi, concentration, why Buddha teach us in 2 way? Are there any relations between these 2 kinds of practice?

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My present-day understanding is that the 7 factors of enlightenment are an exposition of the link between the 7th and 8th limbs of the Noble Eightfold Path: between Right mindfulness and Right concentration, Right mindfulness leading to Right concentration.

The 6th factor of enlightenment (concentration) could be either any of the 4 jhanas or the 4th jhana. While the 7th factor of enlightenment (equanimity) could be the equanimity of the 4th jhana (though one could argue that it could also be the equanimity of the 3rd but the 4th jhana seems definitely the most prone to enlightenment in the suttas).

So to reply specifically to your questions, I would say that they are not two different ways but different expositions of one method; the jhanas being the results of a number of conditions being fulfilled.

If you don’t know it already, I would recommend reading SN54.13 which is a delightful exposition of the links between mindfulness of breathing, the four establishment of mindfulness, the 7 factors of enlightenment and the true knowledge and liberation. A very inspiring sutta :anjal:

Please bear in mind that this only my present-day understanding.

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I agree with most of what @Yasoja has said except that I think it starts earlier. Mindfulness, determining defilements, and effort begins at the 6th Step- in Right effort. Right effort is the foundation for Right mindfulness - which must be developed devoid of craving or aversion. We know that the Four foundations lead to lessening of discursive thought, calmness and becomes the foundation for Right concentration.

With metta

IMO (in my opinion),
The 4 jhanas,
the 4 iddhi-pada,
3 ways of samadhi, (such as described in AN 8.63)
7 bojjh-anga

Are all describing the same process of how the mind moves from 4 satipatthana into greater clarity and stillness. What gets confusing is it’s not clear where the boundaries between all of these paradigms are. So my conclusion is to treat all of them as approximate models, and not try to nail down each specialized samadhi term into a specific narrow meaning, otherwise you’ll drive yourself crazy. For example, the words jhana (as a verb and noun) and satipatthana are used in the EBT to where you really can’t completely separate them from each other on their duties and boundaries.

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