perience and observation, and are not to be found without a diligent comparison, and scru pulous examination of facts. Of such an examination, neither Aristotle, mor any other of the ancients, ever conceived the necessity, and hence those laws remained quite unknown throughout all antiquity.
When the laws of motion were unknown, the other parts of natural philosophy could make no great advances. Instead of conceiving that there resides in body a natural and universal tendency to persevere in the same state, whether of rest, or of motion, they believ ed that terrestrial bodies tended naturally either to fall to the ground, or to ascend from it, till they attained their own place ; but that, if they were impelled by an oblique force, then their motion became unnatural or violent, and tended continually to decay. With the heavenly bodies, again, the natural motion was circular and uniform, eternal in its course, but perpetually varying in its direction. Thus, by the distinction between natural and violent motion among the bodies of the earth, and the distinction between what we may call the laws of motion in terrestrial and celestial.bodies, the ancients threw into all their reasonings upon this fundamental subject. a confusion and perplexity, from which their philosophy never was delivered.
There was, however, one part of physical knowledge in which their endeavours were at tended with much better success, and in which they made important discoveries. This was in the branch of Mechanics, which treats of the action of forces in equilibrio, and producing not motion but rest ;—a subject which may be understood, though the laws of motion are unknown.
The first writer on this subject is Archimedes. He treated of the lever, and of the centre of gravity, and has shown that there will be an equilibrium between two heavy bodies connect ed by an inflexible rod or lever, when the point in which the lever is supported is so placed between the bodies, that their distances from it are inversely as their weights. Great in, genuity is displayed in this demonstration ; and it is remarkable, that the author borrows no principle from experiment, but establishes his conclusion entirely by reasoninga priori. He assumes, indeed, that equal bodies, at the ends of the equal arms of a lever, will ba lance one another ; and also, that a cylinder, or parallelopiped of homogeneous matter, will be balanced about its centre of magnitude. These, however, are not inferences experience ; they are, properly speaking, conclusions deduced from the principle of the sufficient reason.
The same great geometer gave a beginning to the science of Hydrostatics, and discover ed the law which determines the loss of weight sustained by a body on being immersed in water, or in. any other fluid. His. rests on a prinCiple, which he lays down as a postulatum, that, in.water„ the .parts which .are less pressed are gimp ready to .yield
in any direction to those that are more pressed, and. from this, by the .application.of maths.. matical reasoning, the whole theory of floating bodies is derived. The above is the same principle on which the modern writers on hydrostatics proceed :; • they give it not. as a pos tulatum, but as constituting the definition of a 'fluid.
Archimedes, therefore, is the person who first made. the application .of mathematics to natural philosophy. No individual, perhaps, ever laid the foimdation.of more great. disco-. veries than that geometer, of whom Wallis has said with so .much . truth, " Vir stupendss sagacitatis, qui prima fundaments posuit inventionum fere onnium in glans promovendis. fetes nostra gloriatur." The mechanical inquiries, begun. by the geometer of .Syracuse„ were extended. by Ctesi bins and Hero ;• by Anthemius. of Tulles ; and, lastly,. by Pappus Alexandrines.. Ctesi?, bins and Hero were the first. who analyzed mechanical engines, reducing them all to. comm. binations of .five simple, mechanical contrivances, to which they..gave: the nanle;Df.AuvaMg, or Powers, the same which they retain at the present moment.
Even in mechanics, however, the success of these inveitigations,was. limited; and failed in those cases wherethe reaolution.of forcea.is necessary, that.principle being then. entire, ly unknown. Hence the force necessary to sustain .a .body on an inclined plane,; is reedy determined by Pappus, and serves to, mark a point to which the,mechanieal3theoriea, of antiquity did not extend.' In another department of physical knowledge, Astronomy, the..endeavauz of:1h* an- . eients. were .also 'accompanied with success.. I do, not, here speak of their astronomical the., ones, which were, indeed, very defective, but of their discovery of the.apparent motions of , the heavenly bodies, from the observations begun by Hipparchus, and continued .by Ptole., my. In this their success was great ; and. while the earth was supposed to be at rest, and while the instruments.of observation had. but a very limited degree of ,accuracy, a nearer approach to the truth was probably not within the power. of human ingenuity. Mathema. _ tical reasoning was very skilfully applied,, and no men whatever,. .in the same circumstances,. are likely•to have performed more than the ancient astronomers.. They succeeded,. bo, cause they were observers, and examined carefully the motional which theytreated of.. The philosophers, again, who studied the motion of terrestrial bodies, either did not observe at all,, or observed so slightly, that they could obtain knowledge, and in:general they knew just enough of.the.facts to.bemislml.by them.