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'The Ladies Diary': A True Mathematical Treasure - A Mathematical Odyssey

Frank J. Swetz (Pennsylvania State University)

John Tipper died in 1713 and the editorship of the Diary passed through the hands of several individuals:

  • Henry Beighton, 1714-1743;
  • Henry’s wife, Elizabeth Beighton, assisted by Anthony Thacker, 1744;
  • Robert Heath, 1745-1760;
  • Thomas Simpson, 1754-1760;
  • Edward Rollinson, 1761-1773;
  • Charles Hutton, 1774-1818 and
  • Olinthus Gregory, 1819-1840.

Tipper was a dedicated schoolmaster, particularly knowledgeable in astronomy, who exerted great efforts, as editor, in pleasing the women readers. Henry Beighton was an engineer and inventor, more interested in the applications of mathematics. Anthony Thacker was a skilled mathematician and Robert Heath, a military engineer. Rollinson was an avid mathematics problem solver, quite familiar with that aspect of the Ladies Diary. Simpson, Hutton, and Gregory were well-respected mathematicians and instructors of mathematics at the Royal Military Academies. Several of these men were elected Fellows of the Royal Society (FRS) and Charles Hutton was even considered by some to be the greatest English mathematician of his time (Wardhaugh, 2017).

Figure 8. Charles Hutton (1737-1823)

All of these editors were professionals whose work seriously involved them in the study and uses of mathematics. Accordingly, they brought their experiences into their editorship tasks and, with each new editor, the mathematical tenor of the Diary changed: the mathematics became more difficult and the problem situations became more complex and directed towards applications. The ability to grapple with the new forms of mathematical problems was beyond the limited educational preparation and contextual interest of many females. Ostensibly, the periodical was still meant for women, but the mathematical direction it had taken eliminated most female participation in this former area of involvement. Women, as problem solvers, still excelled and dominated at finding the solutions to enigmas and other word puzzles.

In the first few years of the Diary’s existence, mathematical problems reflected the traditional recreational themes: “Guess my age,” “Find the number such that...." However, that soon began to change to more timely, relevant subjects. A chronological survey, sampling mathematical problems from some ensuing years, may be informative for readers.

  Year   Mathematical Question
  1714   From a given cone to cut the greatest cylinder possible.
  1739   Suppose a cask in the form of a middle frustum of a hyperbolic spindle, whose length is 24 inches, bung diameter 30, head diameter 20, and traverse axis of the generating hyperbola 100 inches. Required its content in ale gallons?

Three staves being erected, or set up on end, in some certain place on earth, perpendicular to the plane of the horizon, in the points A, B, and C; whereof that which is at A, is 6 feet long; that in B,18; that in C, 8; the line AB being 33 feet long: It happens on a certain day in the year, that the end of the shadow of the staff A passes through the points B and C; and the staff B through A and C; and of the staff C, through the point A. To find the sun’s declination, and the elevation of the pole or day, and the place where this shall happen. [Both René Descartes and Isaac Newton unsuccessfully grappled with this problem!] (Albree and Brown, 2009, p. 18)

  1759   To determine the curve in which a body must move, so as to continue always at the invariable distance from another body moving uniformly in a right line; the velocity of the former body being also uniform, and exceeding that of the latter, in any given ratio.
  1802   Given the base and height of a cone, it is required to find the height of the greatest parabolic conoid which can be inscribed in the cone?
  1825   Describe equilateral triangles (the vertices being all outward or inward) upon the three sides of any triangle ABC: then the lines which join the centres of gravity of those three equilateral triangles will constitute an equilateral triangle. Required a demonstration. [This is a variation of “Napoleon’s Theorem.”]
  1840   If the lines bisecting the angles of a scalene triangle meet the opposite sides in three points, and each side of the triangles formed by joining these points be produced to meet a line drawn to its adjacent angle parallel to its opposite side, the three points of intersection will be in the one and the same straight line. Required a demonstration.

Table 1. Sample problems from the Ladies Diary

Problem situations became more dynamical, theoretical, and philosophical in nature, with many coming from physics and other applied sciences. This was perhaps a reflection of the prevailing Industrial Revolution impacting Great Britain. Compilations of the Ladies Diary’s mathematical problems and their solution schemes were in great demand. Several were published, the most popular collection being that of Thomas Leybourn. Leybourn (1770-1840) was a British mathematician and teacher at the Royal Military Academy, Sandhurst. He edited and published several mathematical periodicals, but his most popular work was his compilation of the mathematical problems from the Ladies Diary. This valuable resource, which has the answers for the above problems, among many others, can be consulted today via the HathiTrust Digital Archive.

Figure 9. Title page for Volume I (of 4 volumes) of Thomas Leybourn's Mathematical Questions Proposed in the Ladies' Diary, and Their Original Answers, Together with Some New Solutions (1817). (Source: HathiTrust Digital Archive, from a book held by the University of Michigan Library and digitized by Google.)

While the problems themselves offered a challenge for the Diary’s readers, personal satisfaction was brought by the publication of correct solutions for the problems and, especially, by the supplying of demonstrations and explanations of the solution process. This feedback both strengthened the mathematical confidence of the problem solvers and further increased their knowledge of mathematical techniques. As an example, shown below is a problem from the 1720 issue of the Diary as duplicated in Leybourn’s collection (Leybourn, 1817, p. 100). The “Scholium” was added by Charles Hutton, who signed his notes "H".

Figure 10. Problem, or question, and solution from the Ladies Diary of 1720, as it appears on page 100 of Volume I of Leybourn's 1817 Mathematical Questions Proposed in the Ladies’ Diary .... (Source: HathiTrust Digital Archive, from a book held by the University of Michigan Library and digitized by Google.)

Frank J. Swetz (Pennsylvania State University), "'The Ladies Diary': A True Mathematical Treasure - A Mathematical Odyssey," Convergence (August 2018)