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This is a quote by Newton. Grammatically, “diverting myself” modifies “a boy,” so it should be “himself,” right?

I don’t know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

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nicetomeetyouso it should be “himself,” right?

No. The reflexive pronoun refers to the subject.

Newton is writing in first person. He is not describing someone else (a boy) that he knows. He is describing himself as a child.

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Thank you. I am aware that Newton is describing himself as a boy, not some random boy he knows, to compare his trivial existence with a vast mystery of truth, but grammatically “diverting” modifies “a boy.” Even so, the use of “myself” is allowed?
nicetomeetyougrammatically “diverting” modifies “a boy.”

"Myself is the direct object of the verb, "diverting." The subject of the verb is "boy".

I seem to have been only like a boy playing on the seashore, and diverting myself

There are two ways to write this:

1. Newton is an observer of a scene, like a movie, in which he sees a boy entertaining himself. He is detached from this scene and uses "himself" to refer to that boy in the scene. That removes the subject "I" from the action of the boy in the scene.

2. Newton has an inner imagination of himself an earlier time, when he is a young boy. - He uses "myself" because it is his own self-image, an alter ego. It connects the past to the present, showing that this "boy" is still inside of him.

The writer chose to describe the second scenario, not the first.

You’re amazing! Thank you.
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finding a smoother pebble or a prettier shell than ordinary,