Flooring Tile - laying floor tiles over cement slab.

We are in the process of ripping up carpet in our living room and dining area which is 410 sf. Under the carpet is old tiles that some are missing and some have been removed by previous owner who had begun alot of home improvements before we purchased the house. The house is on a cement slab.
We want to install either ceramic or porcelain tiles and I'm wondering if we can just lay new tiles over old ones, the old ones are very thin, something that was used back in the 40's, I believe the house was built back in 1945.
Is this possible or should we remove all the tiles first??

Thanks in advance for any replies!

1945, rampant use of asbestos. I would have it at least looked at by a pro.

Thats what I was afraid of after reading one of your posts on abestos.
I will have to do that first but, do they really need to be distrubed?? Can the new tiles be laid on top or should I have them removed first?