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GEORGE PEACOCK, M. A. É.R.S. F.G.S.
F. Ast. S. AND F.C.P.S.
FELLOW AND TUTOR OF TRINITY COLLEGE,
PRINTED BY J. SMITH, PRINTER TO THE UNIVERSITY.
PUBLISHED BY J. & J. J. DEIGHTON, CAMBRIDGE;'
C. J. G. & F. RIVINGTON; AND WHITTAKER, TREACHER & ARNOT,
REVEREND JAMES TATE, M.A.
MASTER OF RICHMOND SCHOOL, YORKSHIRE,
FORMERLY FELLOW OF SIDNEY SUSSEX COLLEGE, CAMBRIDGE.
I BEG leave to inscribe this Work to you, in the first place, as a tribute of affection to one of my best and dearest friends : in the second place, as an expression of my gratitude for your instructions when I was your pupil, and for your kindness and encouragement at a period of my life when they were invaluable to me: and lastly, as the most public testimony which I can give of the respect which I feel for your learning and for those various happy arts of communicating knowledge to others for which you are so greatly and so justly celebrated.
I trust that you will be pleased to find some topics of discussion in the following Work, which will recall to your mind the subject of many interesting conversations with you, both when I was your pupil, and on subsequent occasions; and I feel gratified in being able to refer some portion of my own fondness for such speculations to the same person to whom I am under so many other obligations.
That you may long live to enjoy health and piness, and to receive the well-merited homage o affection and respect of your friends and of the ration of your numerous pupils, is the prayer of sincere friend and grateful pupil
The Work which I have now the honour of presenting to the public, was written with a view of conferring upon Algebra the character of a demonstrative science, by making its first principles co-extensive with the conclusions which were founded upon them : and it was in consequence of the very particular examination of those principles to which I was led in the course of this enquiry, that I have felt myself compelled to depart so very widely from the form under which they have been commonly exhibited. The object which I proposed to effect is undoubtedly one of great importance, and of no small difficulty, inasmuch as it brought me into immediate contact with the discussion of many subjects of dispute and controversy, which have not hitherto been settled upon satisfactory grounds : and though I am very sensible of the great responsibility which I incur by an attempt of this nature, accompanied as it is by the proposal of so many innovations, yet I shall be perfectly satisfied if I may be considered as having succeeded in removing any difficulties or imperfections from the elements of this beautiful and most comprehensive science.
If the first principles of Algebra had been consistent with themselves, or had led to no difficulties either in the