Proof of the Parallelogram of Forces

Abstract

THE objection to Duchayla's proof of the “parallelogram of forces” is, I suppose, admitted by all mathematicians. To base the fundamental principle of the equilibrium of a particle on the “transmissibility of force,” and thus to introduce the conception of a rigid body, is certainly the reverse of logical procedure. The substitute for this proof which finds most favour with modern writers is, of course, that depending on the “parallelogram of accelerations.” But this is open to almost as serious objections as the other. For it introduces kinetic ideas which are really nowhere again used in statics. I should therefore propose the following proof, which depends on very elementary geometrical propositions. The general order of argument resembles that of Laplace.