On a General Method in Dynamics. E-book. Formato PDF William Rowan Hamilton   -  Forgotten Books, 2017  - 

The law of varying action, or the formula becomes therefore, when expressed by the present more general coordinates or marks Of position.

Elements of Quaternions. E-book. Formato PDF William Rowan Hamilton   -  Forgotten Books, 2017  - 

The volume now submitted to the public is founded on the same principles as the which were published on the same subject about ten years ago: but the plan adopted is entirely new, and the present work can in no sense he considered as a second edition of that former one. The Table of Contents, by collecting into one view the headings of the various Chapters and Sections, may suffice to give, to readers already acquainted with the subject, a notion of the course pursued: but it seems proper to offer here a few introductory remarks, especially as regards the method of exposition, which it has been thought convenient on this occasion to adopt.

Elements of Quaternions. E-book. Formato PDF William Rowan Hamilton   -  Forgotten Books, 2017  - 

In other words, the calculation of 1' and P introduces no differentials higher than the third order but that of R' requires the fourth order of differentials. In the language of modern geometry, the former can be determined by the consideration of four consecutive points of the curve, or by that of two consecutive osculating circles; but the latter requires the consideration of two consecutive osculating spheres, and therefore of five consecutive points of the curve (supposed to be one of double curvature). Other investigations, in the present and immediately following Series (398.