Kim Kardashian & Kanye West -- First Video Of The PROPOSAL

Here it is ... the video of Kanye West begging Kim Kardashian in the most grandiose way possible to become his lawful wedded wife.

Kanye and Kim were planted on the infield at AT&T Park in San Francisco Monday night when he got down on his knee and popped the question, while an orchestra played in the background.

The hug that ensues tells the story ... Kim said yes, she got a 15-carat diamond ring and they went off into the sunset and drank a lot.