Washington, DC, National Academy of Sciences, 1888. 4to. 62 pp.; 55 text figures. Original printed wrappers.

Offprint, with its own printed wrappers of this in-depth paper, which is the "everything you always wanted to know" about magic squares, cubes, and even magic spheres. Also published in vol. IV (5) of the academy's Memoirs. Frederick Augustus Porter Barnard (1809-1889) "...was an American scientist and educator. From 1838 to 1848 he was professor of mathematics and natural philosophy, and from 1848 to 1854 was professor of chemistry and natural history in the University of Alabama, also, filling the chair of English literature. In 1854 ... he became professor of mathematics and natural philosophy in the University of Mississippi, of which institution he was chancellor from 1856 until the outbreak of the Civil War, when, his sympathies being with the North, he resigned and went to Washington. During his time at Ole Miss, Barnard was 'tried' by the Board of Trustees for taking the testimony of a slave against a student who allegedly assaulted her. He was president of the American Association for the Advancement of Science in 1866" (Wikipedia). Spine slightly chipped, otherwise an excellent, clean copy of this rare treatise.