[Grammar] preposition "at" following an intransive or transitive verb

[vil]

Dear teachers,
Would you be kind enough explain to me the mysterious “magic power” of the preposition “at” following an intransitive, respectively a transitive verb.

1.1. Presently a vagrant poodle dog came idling along, sad at heart, lazy with the ... he went to the beetle and began a wary attack on it again; jumping at it from ...
…the poodle jumped at the beetle then smelt it..

1.2. the dog snatched at the beetle

2.1. He snatched the paper.

2.2. He snatched at the paper but it had already caught fire.

3.1. She caught my arm.

3.2. She caught at my arm.

Thank you for your efforts.

Regards

V.

[Soup]

1.1. ... at the beetle
=> in the general direction of the beetle

1.2. ... the dog snatched at the beetle
=> To make grasping or seizing motions


2.1. He snatched the paper.
=> To grasp or seize hastily, eagerly, or suddenly

snatch - Definitions from Dictionary.com


3.1. She caught my arm.
=> To catch (hastily, eagerly, or suddenly)

3.2. She caught at my arm.
=> To make grasping motions

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Correction
Would you be kind enough to explain to me the mysterious “magic power” of the preposition “at” following transitive and intransitive verbs?

[vil]

Hi Soup,

There is my version of a likely explanation of the matter in question:

In the first sentence (1.1.) the preposition “at” follows an intransitive verb and shows direction e.g.

He aimed at the bird, the poodle ran at the beetle, also to ride at, to fire at etc. (this fits in well with your statement)

When the preposition “at” follows transitive verbs (1.2.) it also shows direction, but the action denoted by the verb is generally unsuccessful.e.g.


I got to my feet, still not looking at her, I started back towards the window, when she caught at my arm but I moved aside.

catch at = snatch, grasp, (reach out o’s hand for, reach for/ after, try to, as in
“The beggars kept catching at their coats.” Also see grasp at straws.
grasp at straws = also, clutch at straws. Make a desperate attempt at saving oneself.

For example, “He had lost the argument, but he kept grasping at straws, naming numerous previous cases that had little to do with this one.”

This metaphoric expression alludes to a drowning person trying to save himself by grabbing at flimsy reeds.

Would you be kind to confirm the present inquiry?

Thank you for your relevant correction.

Regards

V.

[Soup]

I agree on both accounts.

Well done.

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Correction

This is my version of a likely explanation for the matter in question: