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HISTORICAL VIEW OP THE

investigated in cases which were reducible to this. Wehave also observed, that the doctrine of the inclinedplane was unsuccessfully attempted by Pappus. Nofurther investigation appears to have been tried till thesixteenth century, when Cardan considered the problemin a more distinct light ; though what he advancedon the subject was no more than a plausible conjecture.

Guido Ubaldi, an Italian mathematician , also at-tempted the problem of the oblique action of forceswith imperfect success in 1577- He considers chieflythe wedge; and comparing the direction in which ittends to produce motion with the direction in whichthe body thus acted on really moves, he observes thatthere is between these directions “ a certain repug-nance,” which is greater as the angle of the wedge ismore obtuse. He hence infers that the wedge willproduce its effect the more easily the more acute it is,hut without obtaining the exact proportion of the force.He also observes rightly, that the screw may be consi-dered as a wedge wrapped round a cylinder.

It has been stated that the problem of the inclinedplane had been solved by Jordanus in the thirteenthcentury, and that the solution is given in Tartalea’sedition of his works in 1565. The discussion, how-ever, is so vague and obscure, and so mixed up withthe peripatetic views, that It cannot be admitted ashaving a valid claim to be a real demonstration.

The individual who really first solved the problem ofoblique forces on solid principles, was Simon Stevin ofBruges , whose works were published Soon after 1600.He not only deduced correctly the ratio of the power tothe weight on the inclined plane, hut, on the same princi-ples, resolved forces so as to obtain their effect in dif-ferent directions, and solved a number of importantproblems relating to them. The principle of his rea-soning was highly original and simple. He supposed aperfectly flexible, uniform chain, joined at its ends, andhanging upon the inclined plane down its perpendicularside, and in a festoon below. However free the mo-