316 



SCIENCE 



[N. S. Vol. LIII. No. 1370 



ciation again held a conference in the History of 

 Science at its Washington meeting.2 



This year (1920) a similar movement was insti- 

 tuted by the scientists, and the president of the 

 American Association for the Advancement of Sci- 

 ence, through the councU, appointed an organizing 

 committee consis-ting of the following scholars : 



Dr. William W. Welch, Johns Hopkins University, 

 Dr. A. P. Carman, University of Illinois, 

 Dr. Felix Neumann, Washington, D. C. 

 Dr. George Sartou, Carnegie Institution, 

 Dr. William A. Loey, temporary chairman. North- 

 western University, 

 Dr. Henry G. Gale, University of Chicago, 

 Dr. C. Judson Herrick, University of Chicago, 

 Frederick E. Brasch, secretary, John Crerar Li- 

 brary, Chicago. 



Through the efforts of this committee the policy 

 of the History of Science section was established. 

 The principal fact to be noted, however, in con- 

 junction with this policy, was the adoption of a 

 plan whereby the function of the program com- 

 mittee was such as to offer the utmost freedom in 

 cooperating and coordinating with existing sec- 

 tions in the American Association. In view of the 

 unique position of the History of Science section 

 relative to the older seotions, the relation is such 

 that conflicts of interest are great. Therefore, in 

 order to advance the work and interest of the His- 

 tory of Science, and, at the same time, minimize 

 this conflict — ^also to meet the growing interest of 

 a large number of scholars both in the technic and 

 history of their respective sciences, the following 

 policy has been approved: 



The program shall be flexible, so that such 

 papers as are technical (example — ^mathematics) in 

 historical treatment be given in sections where they 

 will be most appreciated, and the more general 

 historical papers be given in the special section 

 (History of Science). It is also the opinion of the 

 committee, that papers for this section shall be 

 given by invitation. 



This plan was thought most feasible, and has 

 subsequently proven a success, as was evident at 

 the tirst conference during American Association 

 for the Advancement of Science week. 



Consequently, the first joint session was held 

 with Section A (American Mathematical Society 

 and the Mathematical Association of America). 

 Papers were presented by well known scholars 

 in the History of Mathematics. The first was 

 by Dr. Louis C. Karpinski, of the University of 

 Michigan, who presented a most interesting topic, 



2 Science, N. S., Vol. LIII., p. 122, February 

 4, 1921. 



namely: "Geometrical development of analytical 

 ideas. ' ' 



The purpose of this paper is to show that many 

 of the fundamental concepts of analysis had their 

 progenitors in ideas developed by the Orientals, the 

 Greeks, the Arabs, and the Europeans, to the time 

 of Newton, along geometrical lines. The alge- 

 braical problems of the first degree equation in 

 one unknown, the quadratic and the cubic, were all 

 early solved by geometrical means; many of the 

 dominating "motif" problems and theories of 

 geometry lead directly to the quadratic and the 

 cubic. The problem of the pentagon, of the tri- 

 section of the angle, of the duplication of the cube, 

 of the conic sections of the regular polygons of 

 seven and nine sides, and even of the squaring of 

 the circle, all contributed to the geometrical de- 

 velopment of analytical ideas. 



With the Arabs first came the quite complete 

 appreciation of the algebraical and geometrical 

 correspondences, which culminated, of course, in 

 the work of Descartes, with whom modern mathe- 

 matics begins. 



The second paper was given by Dr. David Eugene 

 Smith, of Columbia University — "The earliest 

 mathematical work printed in the New World, "s 



It was supposedly known that the earliest 

 mathematical work printed in America was that 

 by Isaac Greenwood, first HoUis professor of 

 mathematics and natural philosophy at Harvard 

 College (1727-1738). It was printed in Boston, 

 1729. However, it thus appears through Dr. 

 Smith's efforts that the first mathematical book 

 printed in America was one printed in Mexico 

 City, 1556. Of this work, known as the ' ' Sumario 

 Compendiso, ' ' there remain perhaps only four 

 copies. The book consists of one hundred and 

 three folios, generally numbered. The author, 

 Juan Diez, undertook the work primarily for the 

 purpose of assisting those who were engaged in 

 buying of gold and silver from Mexico, for the 

 moneyed class of Spain. The principal text con- 

 sists of tables relating to the purchase price of 

 various grades of silver, and of gold, and to mone- 

 tary affairs of various kinds. The mathematical 

 text consists of twenty-four pages of problems of 

 arithmetic and algebra. Aside from the great 

 historical importance and rarity this book pos- 

 sesses, it also has an interesting place in the early 

 history of education in America. 



In the second joint meeting the third paper 

 was presented by Dr. Plorian Cajori, of the Uni- 

 versity of California. His topic, "The evolution 

 of algebraic notations," was illustrated by slides. 

 Due to the extremely technical character of this 

 topic, which involved so many symbols and signs, 

 and the tracing of the evolutionary character of 

 the notation by a long and painstaking detail 

 study, it is not possible to give an adequate ab- 



3 A full account of this paper is to be found in 

 The American Mathematical Monthly, 28: 10-15, 

 January, 1921. 



