Elements of Vector Algebra

Excerpt from Elements of Vector Algebra

This little book was written at the instance of Messrs. Adam Hilger, and, in accordance with their desire, it contains just what is required for the purpose of reading and handling my Simplified Method of Tracing Rays, etc. (Longmans, Green & Co., London, 1918). With this practical aim in view, all critical subtleties have been purposely avoided. In fact, it is scarcely more than a synoptical presentation of the elements of Vector Algebra covering the needs of those engaged in geometrical optics. At the same time, however, it is hoped that this booklet will serve a more general purpose, viz. to provide everybody unacquainted with the subject with an easy introduction to the use of Vector Algebra.

It is scarcely necessary to explain that the deductions given in this book are based on Euclid's axioms, notably with the inclusion of his postulate of parallels - upon which the equality of vectors is most essentially based. Those readers who are desirous of seeing how the formal rules here given can be generalized so as to be valid independently of the axioms of congruence and of parallels, may consult the author's Projective Vector Algebra (Bell & Sons, 1919), and a sequel to it published in Phil. Mag. for July, 1919, pp. 115-143. It is, however, advisable for the student to become first thoroughly familiar with the euclidean vector algebra as here presented.

I take the opportunity of expressing my sincere thanks to Messrs. Hilger for enabling me to make this further contribution towards the promotion of the more general use of this powerful and convenient language of vectors, and to the Publishers for the care they have bestowed upon this little book.

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