A Dissertation On the Development of the Science of Mechanics Being a Study of

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Later philosophers debated strenuously as to whether this efficacy was propottional to the velocity or to the velocity squared. But it will be perceived from an inspection of the above expressions that a body with double the velocity can overcome a given force through double the time, but through four times the distance. With respect to time, therefore, its efficacy is proportional to velocity; but with respect to dis- tance, or space traversed, its efficacy is proportional to the velocity squa...red.
Before the time of Galileo, force was treated in mechanics only as pressure; after his time the ideals of force, velocity and acceleration as we know them to-day came into use. That either acceleration of motion or change of shape is the imme- diate effect of force is the fact that Galileo perceived and set down as a fundamental and invariable rule of dynamics.
He determines force by the change of velocity, or the ac- celeration it produces, and he may be said to have discovered the law of inertia indirectly.


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