The Newtonian telescope was developed by guess who? Isaac Newton!!! The Newtonian design is the most common telescope built by amateurs. In the Newtonian n the light comes in the top of the the tube, travels down to the Primary mirror where it is reflected back in a cone, then just below the top of the cone the photons are tilted at a ninety degree angle into the eyepiece and consequently, your eye.
Cassegrain type telescopes are significantly more difficult to build, because they require a hole bored in the middle of the primary mirror and a curved secondary. Some of the most popular types of Cassegrain are the the Shmidt-Cass such as a Celestron 8 inch and the Makstov Cassegrain such as a Meade ETX both of which differ slightly in their optical components from the pictured Cassegrain.