Geometrical Problems

Geometrical Problems is a mathematical textbook by Henry Latham, the nineteenth century English mathematician and Cambridge tutor. Latham was associated with Trinity Hall, Cambridge, and produced several textbooks on mathematics aimed primarily at the Cambridge undergraduate audience during the period when the Mathematical Tripos was the central intellectual qualification for ambitious young men at the university.

The book belongs to the substantial body of nineteenth century English mathematics textbooks that supported the Cambridge teaching system. The Mathematical Tripos in the nineteenth century placed enormous emphasis on problem solving, and the various textbooks produced by Cambridge tutors during the period were essentially designed to drill students through the standard types of problem that would appear on the examination papers. Geometrical Problems collects together a substantial body of geometrical problems with worked solutions and commentary, organized by topic and by difficulty in the manner that had become standard for Cambridge mathematical preparation.

The problems cover the geometrical topics that the Tripos syllabus required students to master. There are problems in plane Euclidean geometry of the kind that had been part of the syllabus since the eighteenth century, problems in solid geometry, problems involving the conic sections, and problems requiring the combination of geometrical and algebraic methods. The presentation is in the careful logical style of nineteenth century English mathematics, with each problem stated precisely, each step of the solution justified, and each conclusion supported by reference to earlier results or to standard theorems.

Latham’s textbook was used at Cambridge during the second half of the nineteenth century and was reprinted in several editions. It belongs to a tradition of mathematical pedagogy that was eventually displaced by the broader, more conceptual approach to mathematics that began to develop at Cambridge and elsewhere in the late nineteenth and early twentieth centuries under the influence of writers like Whitehead and Russell. For modern readers the book is mostly of interest as a document of how Cambridge mathematics was actually taught during a particular period and of how the Tripos system shaped the production of mathematical textbooks.

The book is mostly of historical interest now. It pairs naturally with the other Cambridge mathematical textbooks of the same period, particularly those by Todhunter and Routh.