Preface CONTENTS Page V I. Foreign influences leading to the introduction of algebra English influence 1 1 William Churchill Houston, professor of mathematics_ IV. A mathematical notebook from the University of Pennsyl- "Mathematica Compendia". Robert Patterson, professor of mathematics__. 5 5 6 7 8 12 13 15 17 18 18 19 19 20 V. Manuscript material from miscellaneous sources_ "Practical Mathematics ". Nathaniel Bowditch____‒‒ End of the notebook custom. VI. Commencement theses____ A commencement custom__. Account of the custom of printing Latin commence- 22 25 25 26 27 VIII. College records and writings of professors and presidents_ Harvard requirements____. Hugh Jones, professor of mathematics at the College of William and Mary_-_ 46 Thomas Clap, president of Yale College Records of University of Pennsylvania. William Smith, provost of the University of Pennsyl- 48 49 49 Laws and orders at Kings College (Columbia Uni versity) --- 50 IX. Evidences of the use of foreign textbooks.. The Young Mathematician's Guide, John Ward.. X. The first books containing algebra published in the new A Mexican algebra--- 51 51 51 54 55 INDEX. A Dutch algebra-Arithmetica of Cyffer-Konst_ XI. Eighteenth century books on algebra by American au thors----- Algebra in the work of Nicholas Pike___. The American Youth. Consider and John Sterry XII. Algebra and advertisements___ Algebra in the public press_ Private tutors and schoolmasters.. Solutions of algebra problems___ Sale of algebra books- XIII. Summary_. A chronological list of American algebra textbooks Bibliography PREFACE Certain periods in the making of history have been deficient in contemporary chronicles. This is notably true in the history of American education during the eighteenth century. Such history presents lessons to the educator of a later generation. As we follow the growth of the American people from the status of settlers in a new country to that of a distinctive nation with its own life to provide for by training and education, we are led to an understanding of the American character and civilization of our own day. This understanding is necessary for all those who are engaged in the attempt to prepare boys and girls to take their places in the present social structure. The history of education is made up in part of accounts of various subjects which have developed into courses of study. Mathematics of some kind has always been included in such courses. In the American Colonies arithmetic was an important subject for practical reasons. It was needed for trade and commerce. With sailing vessels plying between Europe and America and the only means of communication with the "homeland," navigation and all the kinds of sailing that had to be put to daily use came to be a continuation of the course in arithmetic. Astronomical observations were an important feature in laying out a course at sea, and so astronomy is found in connection with arithmetic. Some elementary trigonometry, logarithms, and geometric constructions played a necessary part in the calculations incident to both navigation and astronomy. With this list the practical uses of mathematics in that day are exhausted. It is the purpose of this study to show that algebra, another branch of mathematics, entered into the American education of the eighteenth century, and to show further that we must seek some other reason for its presence than a practical need for it. The research connected with this work has been made from original sources found in many libraries, both public and private, in the East. It would be a pleasure, if it were possible, to acknowledge in detail the cordial helpfulness that has been extended in every one of these libraries. In particular the writer is indebted to Miss Isadore G. Mudge, reference librarian of Columbia University Library, for her efforts in many directions. To Prof. David Eugene Smith, of Columbia University, who suggested the problem, and whose interest and appreciation have been unfailing, the writer acknowledges inspiration in this study as well as in her whole professional life. Hunter College of the City of New York. LAO GENEVRA SIMONS. INTRODUCTION OF ALGEBRA INTO AMERICAN SCHOOLS IN THE EIGHTEENTH CENTURY Chapter I FOREIGN INFLUENCES LEADING TO THE INTRODUCTION OF ALGEBRA INTO AMERICAN EDUCATION English influence.-Education in the American Colonies for more than a century after its beginnings was an attempt at a reproduction of the education of the countries from which our forefathers came. The influence of foreign universities appears in every aspect of the school life before the American Revolution. The first colleges were modeled entirely on the English universities, so far as the limited resources of the founders allowed. Courses of study, textbooks, and organization were for a long time almost exclusively English. Presidents went to England to raise money to carry on the work on the home field. College professors were either imported from England or Scotland, and in many instances returned there, as was the case with a long line of men at the College of William and Mary, or they traveled to England to obtain the education necessary to fill their positions. Professors educated at Oxford or Cambridge or any other university must have been interested in the application of their foreign experiences on their return and would naturally have transplanted the traditions of the day, so far as it was possible, to the American institutions to which they came. At the same time they were engaged in correspondence with foreign leaders, and so all through the period under consideration reflections of the intellectual life abroad will be apparent. English algebra. From the middle of the seventeenth century works on algebra were being published, and prominent teachers were presenting the subject. In 1707 Sir Isaac Newton's work on algebra and the theory of equations, the Arithmetica Universalis, appeared; and it was followed by an English translation in 1720. With the unparalleled reputation of Newton and the genius of his discoveries this work must have taken a strong hold on the algebraically minded |