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Sir ISAAC N E W T O N’s Book IL

shew that a body with a velocity as 2, is able to bend and over-come the resistance of four springs, one of which alone isequivalent to the force of the fame body moving with a velo-city as 1 ; from which they infer that, in the former cafe, theforce is quadruple, tho the velocity be only double of what itis in the latter cafe. In like manner, because a body movingwith a velocity proportional to the diagonal of the rectangle isable to ballance the resistance of two springs proportional tothe sides of the fame rectangle, they thence infer that the forceof a body moving with a velocity as the diagonal is equal tothe sum of the forces of two bodies moving with velocitiesproportional to the sides of the rectangle ; and, because thesquare of the diagonal is equal to the sum of the squares of thetwo sides, they thence infer that the forces of equal bodies areas the squares of their velocities. But in all these arguments(which are the most plausible of any that have been offeredfor their new doctrine, and are most apt to mislead their rea-ders) they do not consider that the force which one body loses,in acting upon another, is not equal to that which it producesor destroys in the other, estimated in any direction at pleasure,but in that only in which the first body acts ; and that body,in consequence of its inertia , not only resists any change in itsquantity of motion, but likewise any change in the direction ofits motion. If any planet revolves in a circle, the gravity of ittowards the centre is employed, during the whole revolution, inchanging the direction of its motion only, without producingthe least augmentation or diminution of the motion itself.But these things will more easily appear after wejiave treatedof the composition and resolution of motion : we only ob-serve here, that, in order to support their favourite doctrine,they embarrass the plain, simple and beautiful theory of motion,in some cases by neglecting the time, and in others by con-. founding

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