384 THE MATHEMATICAL PRINCIPLES [BOOK III. RULES OF REASONING IN PHILOSOPHY, RULE I. We are I'o admit no more causes of natural things than such as are both true and sufficient to explain their appearances. To this purpose the philosophers say that Nature does nothing in vain, and more is in vain when less will serve ; for Nature is pleased with sim plicity, and affects not the pomp of superfluous causes. RULE II. Therefore to the same natural effects we must, as far as possible, assign the same causes. 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 reflec tion of light in the earth, and in the planets. RULE III. The qualities of bodies, which admit neither intension nor remission oj 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. 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 ; nnd 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 other way 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. 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 im penetrable, and thence conclude impenetrability to be an universal property of all bodies whatsoever. That all bodies are rnoveable, and endowed with certain powers (which we call the vires inertias] of persevering in their mo tion, or in their rest, we only infer from the like properties observed in the