This is the way the project started (in, during) the early 1970s. The creators of the Internet decided to attempt to

telephone line, which allowed data to be transmitted between computers at different universities. This network of connected computers became known as the ARPANET.

The project started in the early 1970s, which means it began at some point during that decade. So, in this case, the correct preposition to use is «during».

The creators of the Internet decided to connect universities, and they did this by using computers. They used computers as the means or tool to achieve their goal of connecting universities. Therefore, the correct preposition to use in this context is «by».

The creators of the Internet believed that they could connect computers within these universities through telephone lines. The word «within» implies that the computers would be physically located inside the universities. So, the correct preposition to use here is «within».

Researchers at the universities could quickly share significant amounts of information while working on the same project. They would use the connected computers to exchange data and collaborate on their work. The phrase «working on» indicates that the researchers were actively involved in a task or project. Therefore, the correct preposition to use here is «on».

Finally, the computer was connected to a telephone line. This means that the computer and the telephone line were linked or joined together. So, the correct preposition to use here is «to».

To summarize, the sentence should be written as follows:

«This is the way the project started during the early 1970s. The creators of the Internet decided to attempt to connect universities by using computers. They had the belief that they could connect computers within these universities through telephone lines. Researchers at the universities could quickly share significant amounts of information while working on the same project. The computer was connected to a telephone line.»