How did the development of clocks and automata relate to the ideas of determinism and reductionism?
The clock was being compared to the universe because of its regularity and precision. Just like the clock when it is set in motion, one can predict the operations of the clock. The same logic was applied to the universe because of its precision. One could predict the future depending on past events. This was called determinism.
Another thing that was common was the fact that one could easily disassemble the clock or any machine and gain insight into its functioning, and develop another machine, which could be more sophisticated. This was called reductionism.
An automaton was a machine that resembled a human or an animal in its function and appearance. In ancient days human automata were designed to serve wine, play musical instrument among other things with precision and regularity.
The clock and automata related to the idea of determinism as they both were machines. They would perform a specific function that the maker knew, through which he could determine every act of his invention.
Similarly the clock and the automata related to the idea of reductionism. Both of them could be dismantled to know its functioning, and could be re-created again with the same precision and regularity.