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# Ec11 a N1cs

## balance, powers, mechanics, machines, motion and simple

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EC11 A N1CS (from the Greek pqyarn, art) that branch of practical mathematics which treats of motion and moving tamers, their nature, laws, effects, &e. This term, in a popular sense, is applied equally to the doctrine of the equi librium of powers, more properly called statics, and to that science which treats of the generation and communication of motion, which constitutes dynamics, or mechanics strictly so called. See FORCE, MOTION, POWER, and STATICS.

This science is divided by Newton into practical and rational mechanics, the former of which relates to the mechanical powers, viz., the lever, balance, wheel and axis, pnbey, wedge, screw, and inclined plane; and the latter, or rational mechanics, to the theory of notion ; showing, when the ffirces or powers are given, how to determine the motion that will re-ult from them ; and, conversely, when the cir cumstances of the motion are given, how to trace the forces or powers from which they arise.

Mechanics, according to the ancient sense of the word, considers only the energy of organs, or machines. The authors who have treated the subject of mechanics systemati cally have observed, that all machines derive their efficacy from a few simple forms and dispositions, which may be given to organs interposed between the agent and the resist ance to be overcome; and to those simple forms they have given the name of mechanical powers, simple powers, or simple machines, The practical uses of the several mechanical powers were nndoubtedly known to the ancients, but they were almost wholly unacquainted with the theoretical principles of this science till a very late period ; and it is therefore not a little surprising that the construction of machines, or the instru ments of mechanics, should have been pursued with such industry, and carried by them to such perffietion. Vitruvius, in his 10th book, enumerates several ingenious machines, which had then been in use from time immemorial. We find, that for raising or transporting heavy bodies, they employed most of the means which are at present commonly used fin. that purpose, such as the crane, the inclined plane,

the pulley, &c.; but with the theory or true principles of equilibrium, they seem to have been unacquainted till the time of Archimedes. This celebrated mathematician. in his Hook of Einiponderants, considers a balance supported on a fulcrum, and having a weight in each scale ; and taking as a ffindamental principle. that when the two arms of the balance are equal, the two weights supposed to be in equilibrio are also of necessity equal, he shows, that if one of the arms be increased, the weight applied to it must be proportionally diminished. Hence he deduces the general conclusion, that two weights suspended to the arms of a balance of unequal length, and remaining in equilibria must be reciprocally proportional to the arms of the balance ; and this is the first trace anywhere to be met with of any theoretical investiffa tion of mechanical science. Archimedes also further observed, that the two weights exert the same pressure on the fulcrum of the balance, as if' they were directly applied to it ; and he afterwards extended the same idea to two other weights sus pended from other points of the balance, then to two ()fliers, and so on ; and hence, step by step, advanced towards the general idea of the centre of gravit v, a point which he behmg to every assemblage of small bodies, and conse quently to every large body, which might be considered as' formed of such an assemblage. This theory he applied to particular cases, and determined the situation of the centre of gravity in the parallelogram. triangle, trapezium, parabola, parabolic trapezium, &c. &c. To him we are also indebted for the theory of the inclined plane, the pulley, and the screw, besides the invention of a multitude of compound machines; of these, however, he has left us no description, and therefore little more than their names remain.

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