Middle Age techs are more "expensive" than Ancient Age ones, generally. I.E. you must spend more beakers to learn them. So to research at the same pace, you have to start generating more beakers. In order to do that...
1. The Golden Rule of Civ3 is: Population = Power. The more land you grab, the more cities you have, the bigger those cities are, the more people you have in your empire, the more commerce you are going to generate. Also, more indirectly, the more cities you have the more military units that will be covered by base support, thus, your army will cut into your budget less, freeing up more money. if you have 50 cities, even at 50% research you can generate a lot more beakers than a 7-town nation, even if that 7 city nation has its science slider at 90. To give you a rough unscientific illustration
2. Road your tiles. All of them eventually and in due time, but first build roads on the tiles that your citizens are working, and to connect all your cities to resources (especially luxury) and to each other. Also, if you happen to have any hills with gold on them, gold may be only a bonus resource but if you can road it and get a citizen working it, it will generate a lot of gold.
3. It probably goes without saying, but, make sure you're in Republic.
4. The more luxuries you have, the less you have to have your luxury slider cut into your budget.
5. Marketplaces and Libraries can help, but don't just build them willy-nilly, because each one adds 1 to your mantainance costs. They add 50% to your tax and 50% to research respectively. So for example, let's say you have a city that generates 20 total coins per turn, and your slider is set up 4-4-2; you're generating 8 gold, 8 beakers, and 4 luxury per turn. A marketplace and a library will make the total 12 gold and 12 beakers. The marketplace will also generate happy faces which might let you adjust your slider to 6-4-0 (or 4-6-0 since you want to generate research). Now, if a town is corrupt, or small, maybe it's only generating three or four total coins per turn. It'll be something more like 1 gold, 1 beaker, and 1 luxury (rounded off). 50% increase on that isn't much, and with the maintainance cost of the buildings is a break-even proposition [even worse if you weigh the turns spent building those buildings].
There's threads and articles in the war academy that break this down and explain it even better than I do and go into greater detail, but you can hopefully get the gist of things from what I'm saying.
But raw population quantity, getting your science slider as high as you can, and generating as many raw coins as you can are all going to have a bigger impact than a bunch of libraries will.