XVI. Fundamental views regarding mechanics

Abstract

Being encouraged by the friendly interest expressed by English geometricians, I have resumed my former researches, which have been entirely abandoned by me since 1846. While the details had escaped from my memory, two leading questions have remained dormant in my mind. The first question was to introduce right lines as elements of space, instead of points and planes, hitherto employed; the second question to connect, in mechanics, translatory and rotatory movements with each other by a principle in geometry analogous to that of reciprocity. I proposed a solution of the first question in the geometrical paper presented to the Royal Society. I met a solution of the second question, which in vain I sought for in P oinsot’s ingenious theory of coupled forces, by pursuing the geometrical way. The indications regarding complexes of forces, given at the end of the “ Additional Notes,” involve it. X now take the liberty of presenting a new paper, intended to give to these indications the developments they demand, reserving for another communication a succinct abstract of the curious properties of complexes of right lines represented by equations of the second degree, and the simple analytical way of deriving them.