ON THE PRINCIPLES OF DEMONSTRATIVE MATHEMATICS BY THE REV. PHILIP KELLAND, A. M., F. R. SS. L. & E. PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF EDINBURGH, EDINBURGH: ADAM AND CHARLES BLACK; MDCCCXLIII. THE following pages contain the substance of Lectures annually delivered to my classes in the University of Edinburgh. The necessity for confining myself within the narrowest possible limits, has compelled me to have recourse to a system, of strict condensation, the effect of which is in some cases, I fear, too apparent. Due allowance being made for this circumstance, I trust that these Lectures will be found not altogether an unacceptable addition to our mathematical literature. The subjects discussed are of vital importance; and, whatever may be thought of the manner of treating them, the simple exhibition of the promi nent features of the different branches of the science, combined with the references I have given, will, it is hoped, be found useful to the more ad iv vanced student. The views which I have developed have been adopted after much thought and mature consideration. If in any instance they are erroneous, I am confident that those who are best able to set me right will be most ready to pardon the error. In discussing the principles of mathematical science, it is impossible not to have come in collision with some of those who have previously written on them. With respect to authors of former days, it is sufficient to observe that I have not hesitated freely to canvass their opinions; such names as Barrow are too illustrious in the annals of literature to suffer from my strictures. Of the opinions of living authors I have spoken more guardedly. It has been my anxious desire to contend simply for truth; and although I have urged my own views with decision, I have felt all the diffidence which a proper respect for the judgment of others cannot fail to produce. To the students (whether in Cambridge or in Edinburgh) who have attentively followed my Lectures, who have exhibited their interest in the 4 subjects discussed by so many voluntary essays, over and above the exercises exacted from them, who have manifested towards me on all occasions the warmest reciprocity of affection ; I cannot suffer this opportunity to pass without an expression of my gratitude for their kindness, and of my interest in their welfare and happiness. The friend who has given his valuable and able assistance in conducting these sheets through the press has my best thanks. P. KELLAND. EDINBURGH, March 16. 1843. |