Charles Green mathematical notebooks

Charles Green of Brandywine Hundred, Delaware, created these notebooks of mathematical rules and exercises around 1840-1841 to aid his study of practical geometry.

Green probably created these exercises between 1840 and 1841. On the first page of Volume 1, he noted that he had completed these exercises on February 25, 1841. Green inscribed the first page of Volume 2 with the notation “The property of Charles Green of Brandywine February 26th the year of our Lord Ad 1841,” suggesting that he began the second volume immediately after completing the first. The first volume also included entries from James and Mary Green, along with the dates December 17, 1840, and April 1841.

Green’s notebooks cover a wide range of mathematical topics and include many examples demonstrating practical applications. He began Volume 1 with a section on the measurement of lines and angles, as well as rules regarding triangles and other polygons. Green then studied the “mensuration of superficies,” or, the measure of surfaces. Most examples related to calculating the area of various plane figures, but also included how to determine the leg measurements of right triangles. Green then worked with conic sections and other geometric solids. Most of the examples towards the end of Volume 1 related to calculating volume, which Green termed “solidity.”

In Volume 2, Green continued his study of geometric solids, including examples related to regular bodies and cylindrical rings. He then began a section entitled “Of Artificer’s Work” in which he described how masons, roofers, bricklayers, and other artisans calculated their use of materials and costs. He ended this section with “miscellaneous questions” involving real world applications, including paving a semicircular plot, painting a conical church spire, and gilding a ball at the top of St. Paul’s Cathedral. In the final section of this volume, Green included an appendix on the gauging of casks and kegs and information on calculating the power generated by simple and complex machines.

Both of Green’s notebooks closely follow the problems, rules, and examples included in John Bonnycastle and James Ryan’s 1834 edition of An Introduction to Practical Geometry and Mensuration. To Which Are Added A Treatise on Gauging and also the Most Important Problems in Mechanics. (Philadelphia: Kimber & Sharpless, 1834). Green copied most of their text verbatim, but occasionally referred back to previous examples and possibly other editions of the book.

Both of the volumes are bound with marbled paper over boards and have leather spines. They have wove paper pastedowns and flyleaves, although Volume 2 is missing its endleaf. Both volumes contain faintly-lined, wove paper leaves with handwritten text in black, blue, red, and green ink and pencil. Volume 1 contains 82 leaves. Volume 2 contains 68 leaves, of which the last 14 are blank.