On Laws (1800-1849)

"But, as the universe is an extremely complex machine; the arrangement of the various parts of which it is composed, its preservation, and the play and energy of its springs, depend on an infinite number of general as well as particular laws. The most general admit of no exception. The exceptions attach on the detail; their number increases in proportion as the laws are specrfſed and particularized, and thus become more and more limited and restricted by other laws. Hence the exceptions themselves iorm new laws and means employed for a higher end. Apparent disorder in the parts is thus absorbed in the order of the whole, and the small defects gradually vanish in the eye of the philosopher as he proceeds to view nature on a more extended scale." (Johann H Lambert, "The System of the World", 1800

"The law of attraction, which extends its dominion over every atom of matter, suffers nothing within the universe to be in a state of absolute rest: Motion obtains every where; all bodies of whatever description gravitate one towards another; all the wheels in this vast machine are going round; nature tolerates no dead and useless masses. The universe is a whole whose different members or systems can only be combined by reciprocal action and re- action, from which motion results as a- necessary consequence." (Johann H Lambert, "The System of the World", 1800)

"The law of gravitation extends universally over all matter. The fixed stars obeying central forces move in orbits. The milky way comprehends several systems of fixed stars; those that appear out of the tract of the milky way form but one system which is our own. The sun being of the number of fixed stars, revolves round a centre like the rest. Each system has its centre, and several systems taken together have a common centre, Assemblages of their assemblages have likewise theirs. In fine, there is à universal centre for the whole world round which all things revolve." (Johann H Lambert, "The System of the World", 1800)

"[…] we must not measure the simplicity of the laws of nature by our facility of conception; but when those which appear to us the most simple, accord perfectly with observations of the phenomena, we are justified in supposing them rigorously exact." (Pierre-Simon Laplace, "The System of the World", 1809)

"Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy." (Jean-Baptiste-Joseph Fourier, "The Analytical Theory of Heat", 1822)

"The aim of every science is foresight. For the laws of established observation of phenomena are generally employed to foresee their succession. All men, however little advanced make true predictions, which are always based on the same principle, the knowledge of the future from the past." (Auguste Compte, "Plan des travaux scientifiques nécessaires pour réorganiser la société", 1822)

"The business of concrete mathematics is to discover the equations which express the mathematical laws of the phenomenon under consideration; and these equations are the starting-point of the calculus, which must obtain from them certain quantities by means of others." (Auguste Comte, "Course of Positive Philosophy", 1830)

"Geometry is that of mathematical science which is devoted to consideration of form and size, and may be said to be the best and surest guide to study of all sciences in which ideas of dimension or space are involved. Almost all the knowledge required by navigators, architects, surveyors, engineers, and opticians, in their respective occupations, is deduced from geometry and branches of mathematics. All works of art are constructed according to the rules which geometry involves; and we find the same laws observed in the works of nature. The study of mathematics, generally, is also of great importance in cultivating habits of exact reasoning; and in this respect it forms a useful auxiliary to logic." (William Chambers & Robert Chambers, "Chambers's Information for the People" Vol. 2, 1835)