THE AUTHOR'S PREFACE

it would have the power of the striker to the resistance of the struck body in the same proportion as the velocity of the striker has to the velocity of the struck body, which is against his hypothesis. For they have a reciprocal proportion: namely, if the power of the striker were of one degree and the resistance of the struck body of 100 degrees, the velocity of the striker ought to be set at one hundred times the velocity of the struck body for the reciprocal proportion to be verified; yet it would have to be one-hundredth of the velocity of the resistance. If the percussive power of one degree and its velocity were the same thing, then, if the percussive power differs in the whole heavens A Latin idiom, toto coelo differre, meaning to differ completely. from motion and impetus, what, I ask, will it be? Perhaps the force and energy of weight? But from this it follows that bodies which are deprived of gravity, or do not exercise it while they strike another resisting body, have no percussive power; and therefore this kind of power, being nothing, no matter how much it is multiplied by the acceleration of motion, would never become a quantity, nor could it overcome nothingness. But in transverse or upward percussion, done perpendicularly to the horizon, a hammer does not act with gravity, because the effort of gravity is exerted by tending downward, and it cannot exercise any force while it is moved upward; therefore, it would have no percussive power, and would not propel or strike resisting bodies placed above, which is repugnant to the evidence of the senses. If, therefore, the percussive power is not a faculty of motion, nor the force of weight, it remains that it must be bodily mass. Although this may seem incredible, or at least unknown, it will nevertheless be shown in the progress of this work that in percussion, bodily masses do not respond reciprocally to their velocities. For even if a hammer is moved most vehemently before it inflicts a percussion, and before it is brought to the contact of the struck body and overcomes the resistance of the stationary body, yet in the act of percussion, the hammer cannot retain its original velocity; for it is forced to move with the same velocity simultaneously with the struck body, since one cannot conceive of two bodies touching each other and agitated simultaneously, whose subsequent and propelling body moves faster than the preceding impacted one. Thus, either the velocity of the hammer before it inflicts the percussion is compared with the velocity acquired by the struck body—and then that will have a greater proportion to this velocity than the mass of the struck body has to the mass of the striker, for they have the same proportion as the sum of the bodies, the struck and the striker, to the striker, as will be demonstrated in its place—or the striker and the struck are compared when they are carried with one and the same velocity in the act of percussion, and it is clear that the velocities will not have the same