ELEMENTS

OF

QUATERNIONS.

BY THE LATE

537-54

SIR WILLIAM ROWAN HAMILTON, LL. D., M. R. I. A.,

D. C. L. CANTAB.;

FELLOW OF THE AMERICAN SOCIETY OF ARTS AND SCIENCES;

OF THE SOCIETY OF ARTS FOR SCOTLAND; OF THE ROYAL ASTRONOMICAL SOCIETY OF LONDON: AND OF THE
ROYAL NORTHERN SOCIETY OF ANTIQUARIES AT COPENHAGEN:
CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE;

HONORARY OR CORRESPONDING MEMBER OF THE IMPERIAL OR ROYAL ACADEMIES OF ST. PETERSBURGH,
BERLIN, AND TUBIN; OF THE ROYAL SOCIETIES OF EDINBURGH AND DUBLIN ;

OF THE NATIONAL ACADEMY OF THE UNITED STATES;

OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY; THE NEW YORK HISTORICAL SOCIETY:

THE SOCIETY OF NATURAL SCIENCES AT LAUSANNE; THE PHILOSOPHICAL SOCIETY OF VENICE:
AND OF OTHER SCIENTIFIC SOCIETIES IN BRITISH AND FOREIGN COUNTRIES;

ANDREWS' PROFESSOR OF ASTRONOMY IN THE UNIVERSITY OF DUBLIN ;
AND ROYAL ASTRONOMER OF IRELAND.

EDITED BY HIS SON,

WILLIAM EDWIN HAMILTON, A. B. T. C. D., C. E.

TO THE

RIGHT HONORABLE WILLIAM EARL OF ROSSE,

CHANCELLOR OF THE UNIVERSITY OF DUBLIN,

This Volume

IS, BY PERMISSION, DEDICATED,

BY

THE EDITOR.