I get the impression from your action of asking the question more than once, as well as your inability to supply more relevant information the second time through that you not only don't appreciate the answer and information you already got... but that you might be one of those people who just simply rejects any advice that doesn't support an opinion you already hold.
Forget this endeavor, and buy yourself a Mac compatible webcam
That's my advice. Why? Because in my opinion, this project is beyond your capabilities, and the expense of getting it to work will be higher than the expense of buying a webcam.
Now... how can I say THAT? Well, for starters, your initial thought of going BNC to VGA.... because you believed that the VGA port on your computer might be an input. I'm not calling you dumb for thinking that... just pointing out that since you did think in that direction, that's an indication that this project might be above you.
However. What kind of camera is it? I'm asking about the make and model. Do you have a power source for it? You know... an external VAC adapter. Just a few examples on that page there to point out that your camera will most probably require something like that... something that converts 120v AC power, to 24v AC.... or 15v AC.... or 18v AC.... or some other voltage that I would know about if you had included the make and model of the camera... which you would have included either time you posted your question if you had the appropriate level of knowledge to most likely succeed with a project like this. At any rate... the power source is just step 1.
As has been pointed out, you will need a video capture device, and a converter to change the BNC cable to something compatible with your video capture device... most likely a BNC to RCA converter as was mentioned. Now. I'm not trying to say something new here... like I said, this was already pointed out. However, this is good and solid advice. I get the impression that because you asked your question AGAIN that you did not like this advice. I'm sorry you did not like it.
At any rate, you are now looking at purchasing a power supply, some dual element cabling to run between the power supply and the camera, a BNC to RCA converter, and a MAC video capture device with an RCA connection. Add all that up, and 99 times out of 100 it will cost you more than a Mac compatible USB Webcam. Thus... my initial advice in bold, repeated here for effect...
Forget this endeavor, and buy yourself a Mac compatible webcam