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The Principles of Inertia and Superposition

Galileo was actually the first to write down "Newton's" celebrated First Law, in a form slightly different from Newton's but just as good:^6.15

Galileo's   Principle of Inertia:

 
A body moving on a level surface will continue in the same direction at constant speed unless disturbed.

Note the term "body" employed in order to be deliberately vague about what sort of entities the Principle is meant to apply to. This term is retained in the language of modern Mechanics. It means, more or less, "a massive thing that hangs together." Note also the other ringers, "level surface" and "unless disturbed." Perfectly level surfaces are mighty hard to come by, but Galileo means, of course, a hypothetical perfectly level surface. More serious is the vagueness of "unless disturbed." This can easily be used to make the argument circular: if the body's velocity changes direction or magnitude, it is because it is "disturbed." Well.... Newton invented a new concept to make "disturbance" a little more specific.

The other important insight Galileo saw fit to enshrine as a Principle was

Galileo's   Principle of Superposition:

 
If a body is subjected to two separate influences, each producing a characteristic type of motion, it responds to each without modifying its response to the other.

This, like the other Principle, seems transparently obvious to Modern eyes,^6.16 but without it one would never know how to start applying Galileo's simplified kinematics to the practical problem of trajectories. Again there is a little sloppiness to the Principle that allows for counterexamples; no doubt Galileo had to rely regularly on the most honest of all appeals: "You know what I mean."