I am sure you can rent out projectors (possibly from a school or even the libraries), but it would probably be cheaper to just go buy one. You can find one at Michael's for about $40.
The overhead projector was invented in the 1960's.
Renting a projector can cost anywhere from about $150 to $900. It all depends on what kind of projector you want to rent and how long you expect to rent it for.
The projector can reach a pretty high temperature if left on for a while. So I think the main danger of an overhead projector is simply the heat. ;)
One can rent a projector from ATS Rentals. Another place to rent a projector is Rentex. Rentex is known for their rentals of computer and audio visual needs.
My guess is that with LCD and DLP projector coming down in price, we will be seeing less and less of the overhead. When a video projector is used with an interactive whiteboard or tablet the possibilities are limitless.
You don't need a slide projector or an overhead projector.
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You can rent a LCD projector at lcdprojectorrentals.com. This online company will deliver the projector 24 hours before your event and promises easy return shipping.
This is referred to as an opaque overhead projector, or sometimes simply as an "opaque projector." This is in contrast to the regular overhead projector which must have transparencies to project, an opaque projector can project an image of opaque objects such as the paper pages of a book.
The only real similarity that I can think of is they both project images onto a wall or projector screen.
Renting a projector can be done by looking through Yellow Pages or online in your area. Some electronic outlets will rent projectors, but mostly you will find that professional video companies are the most likely source. They too can be found by looking through Yellow Pages or online in your area. Search for "Rent Projector" using Google or the Yahoo search engines.