matics at Harvard. It is in many respects the work that would be of four exercises is probably representative of his course in mathemathematical thesis, graduated in that year, and so this group type of work. Samuel Willard, whose signature is affixed to this This last set of 1787 will be discussed as an illustration of this and their Solutions," and the fourth is again "Algebraic Problems."

Theses presented to the mathematics department at Harvard College in 1787

The next problem, "To find the Cube root of any proposed quantities, a usage occurring in Ward's Young Mathematician's Guide.* eighteenth century. Here a and e are used for the unknown quanof Pennsylvania, was accorded problems so universally in the in connection with the notebooks from Harvard and the University The treatment of the algebra problem is that which, as pointed out expected from a good secondary school pupil of the present day.

4 John Ward.

The Young Mathematician's Guide, London, 1709; and later editions.

"Algebraical solutions of problems" from the thesis presented by Luther Richardson to the mathematics department of Harvard College in 1799 95337°-24

tity," might have been copied from that same work. The third problem employs six-place logarithms, but shows no use of interpolation. It combines a knowledge of geometric facts with certain trigonometric relations. The fourth problem is the real applied work and shows the use of the law of sines. In the original the diagram is colored with excellent taste.

Evidence drawn from the commencement theses goes to show that this work by Samuel Willard does not cover all of the mathematical instruction at Harvard in 1787, for the theses of that year include a number of statements concerning fluxions. It may represent the required work, while the more difficult courses were open only to exceptional students.

Other sets of algebraic problems show such differences as would arise from the need of the professor of mathematics to vary his subject matter and from the inclinations of the individual pupils. Francis Cabot Lowell, on October 30, 1792, presented two problems which show a love for long mechanical operations. In one the value of the unknown is given in a number containing 38 digits. In the other, the equation 454-1800x3 +21564x2 - 324000324000 is brought to a successful solution by a method of approximation, but there is a great deal of tedious work before that end is attained. The persistence of the Oughtred symbols for inequality is shown by their use in a paper of 1793. Work of an involved nature and even of an advanced character is that on the paper of Luther Richardson in 1799.

Such direct evidence as the foregoing mathematical theses is worth more in an account of the mathematics in American colleges during the eighteenth century than all the statements about that subject in catalogue or college president's report. It warrants the conclusion that algebra had obtained an established place in the curriculum, which place it has filled from that time until the present day.

5 Ibid, p. 238 (1719).

Chapter VIII

COLLEGE RECORDS AND WRITINGS OF PROFESSORS AND PRESIDENTS

Algebra in manuscripts and printed works.-P.eferences to algebra in the manuscript and printed works of college presidents and professors, as well as in regulations and laws governing courses of study, constitute another link in the chain of evidence showing the recognition granted to the subject during the eighteenth century.

Harvard requirements.-The earliest laws for Harvard College were prepared in 1642 by President Dunster and included the study of mathematics but with no mention of specific branches.1 These laws governed the Harvard curriculum with no material changes during the seventeenth century. In the early part of the eighteenth century a professorship in mathematics was established by Thomas Hollis. The first definite requirement of algebra at Harvard is included in the principles on which the chair was founded. These principles are set down thus:

Rules and Orders relating to a Professor of the Mathematics, of Natural & Experimental Philosophy in Harvard College in Cambridge in New England, appointed by Mr. Thomas Hollis of London Merchant.

1. That the Professor be a Master of Arts and well acquainted with the several parts of the Mathematics & Experimental Philosophy.

2. that his Province be to Instruct the Students in a System of Natural Philosophy & a course of Experimental in which to be comprehended, Pneu maticks, Hydrostaticks, Mechanicks, Staticks, Opticks, &c in the Elements of Geometry to-gether with the doctrine of Proportions the Principles of Algrebra (sic) Conic Sections, plain & Sperical (sic) Trigonometry with the general principles of Mensuration, Plain & Solids, in the Principles of Astronomy & Geometry, viz, the Doctrine of the Spheres the use of the Globes, the motions of the Heavenly Bodies according to the different Hypotheses of Ptolomy (sic) Tycho Brahe & Copernicus with the general Principles of Dialling the Division of the World into its various Kingdoms with the use of the Maps, &c.*

The second rule is the only one which bears directly on the subject in hand. It shows that the principles of algebra were accepted as a necessary part of the instruction in mathematics as early as the date on this paper, 1726. Isaac Greenwood, the first man who was

1 Louis Franklin Snow. The College Curriculum in the United States, p. 25. [no place], 1907.

2 Harvard College Papers, Vol. I, 1650-1763, Jan. 18, 1726. Harvard University Library. There are 13 rules.

called upon to live up to this fine set of rules, may have had something to do with formulating them. He was one of five men to respond to a call from Mr. Hollis to furnish plans for his projected chair of mathematics. The two Harvard notebooks on algebra already set forth attest the success of Greenwood in fulfilling the requirement to teach algebra.

These rules guided the professor of mathematics at Harvard for many years. Not until 1787 are there any more specific directions adopted for his control. A committee appointed to revise the course of instruction voted on August 16, 1787, with respect to the sopho

mores

that at eleven o'clock on Friday they attend the Professor of Mathematics to be instructed in Algebra, and to be carried forward to other branches of the Mathematics if the time allow.

And again on October 16, 1788,5 that future Hollis professors of mathematics were to carry the classes forward by private lectures, in Algebra as far as through affected quadratic equations and infinite series. Algebra, then, receives specific mention in all the laws and regulations formulated at Harvard in the eighteenth century.

Hugh Jones at William and Mary.-The College of William and Mary," the second oldest college in the United States, was founded in 1693 at Williamsburg, Va., and the charter provided at the outset for a president and six professors. The published records until recently named the Rev. Hugh Jones as the first professor of mathematics. An earlier name in the faculty of the college is that of Mr. Le Fevre, as shown by the following extracts from the letters of Governor Spotswood, of Virginia: 7

To Mr. BLATHWAYT:

VIRGINIA, July 28, 1711.

SIR: I have not had the honor of any from you since my last, but having seen a Letter that you writt to Collo. Diggs in behalf of Mr. Le Fevre, I very gladly embraced the Opportunity of doing hon'r to your Recommendation by getting the Governor of the College to receive him as a Mathematick Professor . . .

To the B'P OF LONDON:

VIRGINIA, May 8th, 1712.

... I gave your Lord'p an account of Mr. Le Fevre's admission into the College upon your Lord'p's recommendation, and am now to acquaint you that after a Tryal of three-quarters of a year he appeared so negligent in all the

3 Josiah Quincy, The History of Harvard University, Vol. I, p. 399, Boston, 1860.

4 L. F. Snow, College Curriculum, p. 84, Quoted from Col. Book 8, p. 243.

5 Ibid., p. 270 ff.

6 The researches of Dr. Lyon Gardiner Tyler, for 31 years the president of William and Mary, have been most helpful in the study of that college. They are published in The William and Mary Quarterly.

The Official Letters of Alexander Spotwood, Lieutenant Governor of the Colony of Virginia, 1710-1722. Now First Printed from the Manuscript in the Coilections of the Virginia Historical Society with an introduction and notes by R. A. Brock ... I, pp. 103, 156, Richmond, 1882.