The Principles of Arithmetic: Analyzed and Practically Applied; For Advanced Students

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Excerpt from The Principles of Arithmetic: Analyzed and Practically Applied; For Advanced Students

As my name appears in connection with that of the late Dr. Joseph Ray, on the title-page of this work, it is proper to account for the circumstance by referring briefly to matters personal in their nature. As an author, Dr. Ray is known to the public at large, through the medium of his excellent mathematical publications. As an able and faithful teacher, his merits are deeply impressed on those who have been so fortunate as to come within reach of his immediate instructions and example. In every line of duty he was conspicuous for unremitting industry, and in all the relations of life, his first desire was to be of service to others.

To me, his memory is endeared by many acts of friendship and confidence, extending over a period of twenty years, sixteen of which were spent with him as pupil and colleague, in Woodward College and High School.

In his last illness, Dr. Ray expressed a wish that I should prepare for publication, his Higher Arithmetic, then unfinished, and directed his manuscripts and materials to be handed to me for chat purpose.

In performing the part thus assigned to me, I have endeavored to preserve the spirit and pursue the course indicated in the other Arithmetics of this series. With this view, the language of the author has been retained without material change as far as the manuscript was complete and ready for publication. Whenever a change has been made, it has been done with great caution and with an anxious desire to carry out the general plan of the work. New matter has been occasionally introduced when it deemed necessary to render a demonstration more clear and conclusive, or the treatment of a subject more full and satisfactory.

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