The Laws of Motion and the Rules of Reasoning in Philosophy

Axioms, or Laws of Motion公理，或运动定律#

Law I

定律一

Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impress'd thereon.

每个物体都保持其静止状态或沿直线匀速运动的状态，除非有外加的力迫使它改变这种状态。

Projectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. A top, whose parts by their cohesion are perpetually drawn aside from rectilinear motions, does not cease its rotation, otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve the motions both progressive and circular for a much longer time.

抛射体只要不受空气阻力的阻滞，不被重力向下拉，就会保持它们的运动。陀螺的各部分由于彼此粘合，不断被拉离直线运动，但只要不受空气阻滞，它就不会停止旋转。行星和彗星这些更大的物体，在更空旷的空间里遇到的阻力较小，能把它们的前进运动和圆周运动保持长久得多的时间。

Law II

定律二

The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd.

运动的变化与所加的动力成正比，并且发生在这个力所沿的那条直线的方向上。

If any force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impress'd altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force) if the body moved before, is added to or subducted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joyned, when they are oblique, so as to produce a new motion compounded from the determination of both.

如果某个力产生一个运动，那么两倍的力就产生两倍的运动，三倍的力产生三倍的运动，不论这个力是一下子同时加上的，还是逐渐地、陆续地加上的。而这个运动（总是与产生它的力同向）如果物体原先已在运动，就要按两者方向相同还是正好相反，加到原来的运动上或从中减去；如果两者方向斜交，就斜向合成，产生一个由两者的方向共同决定的新运动。

Law III

定律三

To every Action there is always opposed an equal Reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

每一个作用总有一个相等的反作用与之相对；或者说，两个物体彼此之间的相互作用总是相等的，并且指向相反的方向。

Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended rope, by the same endeavour to relax or unbend it self, will draw the horse as much towards the stone as it does the stone towards the horse and will obstruct the progress of the one as much as it advances that of the other. If a body impinge upon another, and by its force change the motion of the other; that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, towards the contrary part. The changes made by these actions are equal, not in the velocities, but in the motions of bodies; that is to say, if the bodies are not hinder'd by any other impediments. For, because the motions are equally changed, the changes of the velocities made towards contrary parts are reciprocally proportional to the bodies. This law takes place also in Attractions, as will be proved in the next Scholium.

无论什么东西拉或压另一个东西，也同样被那个东西拉或压。如果你用手指按一块石头，手指也被石头按着。如果一匹马拉着一块拴在绳上的石头，那么马（如果我可以这样说的话）也同样被拉向石头：因为绷紧的绳子同样力图放松、回复原状，它把马拉向石头，就同它把石头拉向马一样多；它阻碍一方的前进，就同它促进另一方的前进一样多。如果一个物体撞击另一个物体，并以它的力改变了那个物体的运动，那么这个物体自身的运动（由于相互压力相等）也会朝相反的方向发生同样的变化。这些作用所造成的变化是相等的，但相等的不是速度，而是物体的运动，也就是说，如果物体没有受到别的阻碍的话。因为运动的变化既然相等，那么朝相反方向发生的速度变化就与物体成反比。这条定律也适用于吸引，这将在下一个附注中证明。

Rules of Reasoning in Philosophy哲学中的推理规则#

Rule I

规则一

We are to admit no more causes of natural things, than such as are both true and sufficient to explain their appearances.

寻求自然事物的原因，不得超出那些既真实又足以解释其现象的原因。

To this purpose the philosophers say, that Nature do's nothing in vain, and more is in vain, when less will serve; for Nature is pleas'd with simplicity, and affects not the pomp of superfluous causes.

为此，哲学家们说，自然不做徒劳的事；少用就够了的时候多用，便是徒劳；因为自然喜欢简单，不爱用多余的原因来装点门面。

Rule II

规则二

Therefore to the same natural effects we must, as far as possible, assign the same causes.

因此，对于同样的自然结果，我们必须尽可能归之于同样的原因。

As to respiration in a man, and in a beast; the descent of stones in Europe and in America; the light of our culinary fire and of the Sun; the reflection of light in the Earth, and in the Planets.

比如人和兽的呼吸；欧洲和美洲石头的下落；我们灶火的光和太阳的光；地球上和行星上光的反射。

Rule III

规则三

The qualities of bodies, which admit neither intension nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.

物体的那些既不能增强也不能减弱的性质，又是我们实验所及范围内一切物体都具有的，就应当被看作一切物体的普遍性质。

For since the qualities of bodies are only known to us by experiments, we are to hold for universal, all such as universally agree with experiments; and such as are not liable to diminution, can never be quite taken away. We are certainly not to relinquish the evidence of experiments for the sake of dreams and vain fictions of our own devising; nor are we to recede from the analogy of Nature, which uses to be simple, and always consonant to itself. We no otherwise know the extension of bodies, than by our senses, nor do these reach it in all bodies; but because we perceive extension in all that are sensible, therefore we ascribe it universally to all others also.

因为物体的性质只能通过实验为我们所知，所以凡是与实验普遍相符的，我们都应当认为是普遍的；而那些不会减少的性质，也就永远不会被完全去掉。我们当然不应当为了梦想和我们自己杜撰的空虚臆造，而放弃实验的证据；也不应当背离自然的类比，因为自然总是简单的，总是与自身一致的。我们对物体广延的认识，无非来自感官，而感官并不能触及所有物体；但由于我们在一切可感知的物体中都觉察到广延，我们便把广延普遍地归于其余一切物体。

That abundance of bodies are hard we learn by experience. And because the hardness of the whole arises from the hardness of the parts, we therefore justly infer the hardness of the undivided particles not only of the bodies we feel but of all others. That all bodies are impenetrable, we gather not from reason, but from sensation. The bodies which we handle we find impenetrable, and thence conclude impenetrability to be an universal property of all bodies whatsoever. That all bodies are moveable, and endow'd with certain powers (which we call the vires inertiae) of persevering in their motion or in their rest, we only infer from the like properties observ'd in the bodies which we have seen. The extension, hardness, impenetrability, mobility, and vis inertiae of the whole, result from the extension, hardness, impenetrability, mobility, and vires inertiae of the parts: and thence we conclude the least particles of all bodies to be also all extended, and hard and impenetrable, and moveable, and endow'd with their proper vires inertiae. And this is the foundation of all philosophy.

许多物体是硬的，这是我们从经验中得知的。又因为整体的硬度来自部分的硬度，我们便有理由推断：不仅我们摸得到的那些物体，而且其余一切物体的不可分割的微粒，都是硬的。一切物体都不可入，这一点我们不是从推理中得来，而是从感觉中得来。我们所接触的物体，我们发现它们是不可入的，由此断定不可入性是一切物体的普遍性质。一切物体都能运动，并且具有某种保持其运动或静止的能力（我们称之为惯性），这只是我们根据所见物体的类似性质推断出来的。整体的广延、硬度、不可入性、可动性和惯性，来自部分的广延、硬度、不可入性、可动性和惯性；由此我们断定，一切物体的最小微粒也都有广延、坚硬、不可入、可动，并具有各自的惯性。这就是全部哲学的基础。

Moreover, that the divided but contiguous particles of bodies may be separated from one another, is matter of observation; and, in the particles that remain undivided, our minds are able to distinguish yet lesser parts, as is mathematically demonstrated. But whether the parts so distinguish'd, and not yet divided, may, by the powers of nature, be actually divided and separated from one another, we cannot certainly determine. Yet had we the proof of but one experiment, that any undivided particle, in breaking a hard and solid body, suffer'd a division, we might by virtue of this rule, conclude, that the undivided as well as the divided particles, may be divided and actually separated to infinity.

此外，物体中分开了但仍相邻的微粒可以彼此分离，这是观察得到的事实；而在那些尚未分开的微粒中，我们的心智还能分辨出更小的部分，这是数学上已经证明了的。但是，这些这样分辨出来而尚未分开的部分，能否凭自然的力量真正被分开、彼此分离，我们无法确定。不过，只要有一个实验证明：在打碎一个坚硬的固体时，有某个不可分割的微粒发生了分裂，我们就可以凭这条规则断定：不仅已分开的微粒，而且未分开的微粒，都可以被分割，并真正分离下去，以至无穷。

Lastly, If it universally appears, by experiments and astronomical observations, that all bodies about the Earth, gravitate towards the Earth; and that in proportion to the quantity of matter which they severally contain; that the Moon likewise, according to the quantity of its matter, gravitates towards the Earth; that, on the other hand, our Sea gravitates towards the Moon; and all the Planets mutually one towards another; and the Comets in like manner towards the Sun; we must, in consequence of this rule, universally allow, that all bodies whatsoever are endow'd with a principle of mutual gravitation. For the argument from the appearances concludes with more force for the universal gravitation of all bodies, than for their impenetrability; of which among those in the celestial regions, we have no experiments, nor any manner of observation. Not that I affirm gravity to be essential to bodies. By their vis insita I mean nothing but their vis inertiae. This is immutable. Their gravity is diminished as they recede from the Earth.

最后，如果实验和天文观测普遍表明：地球周围的一切物体都被吸向地球，并且与它们各自所含的物质的量成正比；月球也按其物质的量被吸向地球；另一方面，我们的海洋被吸向月球；所有行星彼此相互吸引；彗星也同样被吸向太阳；那么，根据这条规则，我们就必须普遍承认：一切物体都具有相互吸引的本原。因为从现象得出的论证，对于一切物体的普遍引力，比对于它们的不可入性更有说服力；关于天体中的物体的不可入性，我们既没有实验，也没有任何形式的观察。我并不是断言重力是物体的本质属性。我说物体的固有之力，指的只是它们的惯性，而惯性是不变的。它们的重力则随着离开地球而减小。

Rule IV

规则四

In experimental philosophy we are to look upon propositions collected by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.

在实验哲学中，我们必须把由现象经一般归纳得出的命题看作完全真实的，或者非常接近真实的，而不管可以设想出怎样相反的假说；直到出现了别的现象，使这些命题变得更加精确，或者出现例外。

This rule we must follow that the argument of induction may not be evaded by hypotheses.

我们必须遵守这条规则，以免归纳的论证被假说架空。