BEFORE the end of the sixteenth century, mechanical science had never gone beyond the problems which treat of the equilibrium of bodies, and had been able to resolve these accurately, only in the cases which can be easily reduced to the lever. Guido Ubaldi, an Italian mathematician, was among the first who attempted to go farther than Archimedes and the ancients had done in such inquiries. In a treatise which bears the date of 157'7, he reduced the pulley to the lever, but with respect to the inclined plane, he continued in the same error with Pappus Alexandrines, supposing that a certain force must be ap plied to sustain a body, even on a plane which has no inclination.
Stevinus, an engineer of the Low Countries, is the first who can be said to have passed beyond the point at which the ancients had stopped, by determining accurately the force necessary to sustain a body on a plane inclined at any angle to the horizon. He resolved 4 also a great number of other problems connected with the preceding, but, nevertheless, did not discover the general principle of the composition of forces, though he became ac quainted with this particular case, immediately applicable to the inclined plane.
- The remark, that a chain laid on an inclined plane, with a part of it hanging over at top, in a perpendicular line, will be in equilibrio, if the two ends of the chain reach down exactly to the same level, led him to the conclusion, that a body may be supported on such a plane by a force which draws in a direction parallel to it, and has to the weight of the body the same ratio that the height of the plane has to its length.
Though it was probably from experience that Stevinus derived the knowledge of this proposition, he attempted to prove the truth of it by reasoning a priori. He supposed the two extremities of the chain, when disposed as above, to be connected by a part similar to the rest, which, therefore, must hang down, and form an arch. If in this state, says he, the chain were to move at all, it would continue to move for aver, because its situation, on the whole, never changing, if it were determined to move at one instant, it must be so determined at every other instant. Now, such perpetual motion, lie adds, is impossible, and therefore the chain, as here supposed, with the arch hanging below, does not move. But the force of the arch below draws down the ends of the chain equally, because the arch is divided in the middle or lowest point into two parts similar and equal. Take away these two equal forces, and the remaining forces will also be equal, that is, the tendency of the chain to descend along the inclined plane, and the opposite tendency of the part hanging perpendicularly down, are equal, or are in equilibrio with one another. Such is the
reasoning of Stevinus, which, whether perfectly satisfactory or not, must be acknowledged to be extremely ingenious, and highly deserving of attention, as having furnished the first solution of a problem, by which the progress of mechanical science had been long arrested. The first appearance of his solution is said to have had the date of 1585 but his works, as we now see them, were collected after his death, by his countryman Albert Girard, and published at Leyden in 1634. Some discoveries of Stevinus in hydrostatics will be hereafter mentioned.
. The person who comes next in the history of mechanics made a great revolution in the physical sciences. Galileo was born at Pisa in the year 1564. He early applied himself to the study of mathematics and natural philosophy ; and it is from the period of his dis coveries that we are to date the joint application of experimental and geometrical reason ing to explain the phenomena of nature.
As early as 159.2 he published a treatise, della Scienza Mechanica, in which he has given the theory, not of the lever only, but of the inclined plane and the screw ; and has also laid down this general proposition, that mechanical engines make a small force equi valent to a great one, by making the former move over a greater space in the same time than the latter, just in proportion as it is less. No contrivance can make a small weight put a great one in motion, but such a one as gives to the small weight a velocity which is as much greater than that of the large weight, as this last weight is greater than the first. These general propositions, and their influence on the action of machinery, Galileo pro. seeded to illustrate with that clearness, simplicity, and extent of view, in which he was quite unrivalled ; and hence, I think, it is fair to consider him as the first person to whom the mechanical principle, since denominated that of the virtual velocities, had occur. red in its full extent. The object of his consideration was the action of machines in motion, ,and not merely of machines in equilibria or at rest ; and be showed, that, if the effect of a force be estimated by the weight it can raise to a given height in a given time, this effect can never be increased by any mechanical contrivance whatsoever.