Galileo’s measurements were used by Newton as the basis of his laws of motion. In Galileo’s experiments, as a body rolled down the slope it was always acted on by the same force (its weight), and the effect was to make it constantly speed up.
This showed that the real effect of a force is always to change the speed of a body, rather than just to set it moving, as was previously thought. It also meant that whenever a body is not acted on by any force, it will keep on moving in a straight line at the same speed. This idea was first stated explicitly in Newton’s Principia Mathematica, published in 1687, and is known as Newton’s first law. What happens to a body when a force does act on it is given by Newton’s second law. This states that the body will accelerate, or change its speed, at a rate that is proportional to the force. (For example, the acceleration is twice as great if the force is twice as great.) The acceleration is also smaller the greater the mass (or quantity of matter) of the body. (The same force acting on a body of twice the mass will produce half the acceleration.) A familiar example is provided by a car: the more powerful the engine, the greater the acceleration, but the heavier the car, the smaller the acceleration for the same engine.
In addition to his laws of motion, Newton discovered a law to describe the force of gravity, which states that every body attracts every other body with a force that is proportional to the mass of each body.
Thus the force between two bodies would be twice as strong if one of the bodies (say, body A) had its mass doubled. This is what you might expect because one could think of the new body A as being made of two bodies with the original mass. Each would attract body B with the original force. Thus the total force between A and B would be twice the original force.
Proportional 成比例的
伽利略的測量被牛頓用來作為他的運動定律的基礎。在伽利略的實驗中，當物體從斜坡上滾下時，它一直受到不變的外力（它的重量），其效應是它被恆定地加速。
這表明，力的真正效應總是改變物體的速度，而不是像原先想像的那樣，僅僅使之運動。同時，它還意味著，只要一個物體沒有受到外力，它就會以同樣的速度保持直線運動。這個思想是第一次被牛頓在1687年出版的《數學原理》一中明白地敘述出來，並被稱為牛頓第一定律。物體受力時發生的現象則由牛頓第二定律所給出：物體被加速或改變其速度，其改變率與所受外力成比例。（例如，如果力加倍，則加速度也將加倍。）物體的質量（或物質的量）越大，則加速度越小，（以同樣的力作用於具有兩倍質量的物體則只產生一半的加速度。）小汽車可提供一個熟知的例子，發動機的功率越大，則加速度越大，但是小汽車越重，則對同樣的發動機加速度越小。
除了他的運動定律，牛頓還發現了描述引力的定律：任何兩個物體都相互吸引，其引力大小與每個物體的質量成正比。
這樣，如果其中一個物體（例如A）的質量加倍，則兩個物體之間的引力加倍。這是你能預料得到的，因為新的物體A可看成兩個具有原先質量的物體，每一個用原先的力來吸引物體B，所以A和B之間的總力加倍。
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