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Charles Green mathematical notebooks
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Held at: University of Delaware Library Special Collections [Contact Us]181 South College Avenue, Newark, DE 197175267
This is a finding aid. It is a description of archival material held at the University of Delaware Library Special Collections. Unless otherwise noted, the materials described below are physically available in their reading room, and not digitally available through the web.
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Charles Green, the creator of these notebooks of mathematical exercises, was likely born in Christiana Hundred, Delaware, in 1825, the son of William and Maria Green. Green had several siblings, including James and Mary, whose names also appear in these notebooks. Green studied carpentry and was alternately described in federal censuses as a carpenter and a manufacturer of kegs. Many of the mathematical exercises in the second volume of his notebooks relate to carpentry, masonry, and the gauging of casks. Green died in Greenville, Delaware, in 1891.
Most of the exercises in Green’s notebooks were copied from an 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 by John Bonnycastle. The first American edition of Bonnycastle’s work was published in Philadelphia in 1812. Green occasionally made reference to “Ryan’s edition,” suggesting that he was using a later edition annotated by James Ryan, whose name appeared alongside Bonnycastle’s on the book by 1834. Green’s notebooks very closely follow the lessons in the 1834 edition of An Introduction to Practical Geometry and Mensuration.In addition to geometry, Green used trigonometric functions in several of his exercises involving circles. Green described using the “versed sine” to make many of his calculations. The “versed sine” or “versine” was historically considered one of the most important trigonometric functions, and was especially useful in estimating distance in navigation. It was defined as being equal to 1cos(θ).
Bonnycastle, John and James Ryan. 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.Biographical and Genealogical History of the State of Delaware. Vol. 1. Chambersburg, PA: J.M. Runk & Co, 1899. 1850 Federal Census (accessed via Ancestry.com on November 16, 2016)1870 Federal Census (accessed via Ancestry.com on November 16, 2016)1880 Federal Census (accessed via Ancestry.com on November 16, 2016)Jim Wilson, University of Georgia website, “The Forgotten Trigonometric Functions, or how Trigonometry was used in the Ancient Art of Navigation (Before GPS!)” (accessed November 15, 2016) http://jwilson.coe.uga.edu/EMAT6680Fa2013/Lively/Forgotten%20Trig/The_Forgotten_Trigonometric_Functions.pdfInformation derived from the collection.
Charles Green of Brandywine Hundred, Delaware, created these notebooks of mathematical rules and exercises around 18401841 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 faintlylined, 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.
Item 0099: Shelved in SPEC MSS 0097
Purchase, May 1992
Processed and encoded by Elizabeth JonesMinsinger, January 2017.
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 University of Delaware Library Special Collections
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 University of Delaware Library, Special Collections
 Finding Aid Date
 2017 January 9
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1 volume
1 volume