Collections : [University of Michigan William L. Clements Library]

Adam R. Barr of Conestoga Township, Pennsylvania, created this mathematics exercise book or cipher book of mathematical operations, rules and theorems, and example problems. Sections labeled with calligraphic lettering include the Single Rule of 3, Double Rule of 3, Simple Interest, Insurance, Commission, Barter, Fellowship, Exchange, Vulgar Fractions, Decimal Fractions, and others.

Adam R. Barr of Conestoga Township, Pennsylvania, created this mathematics exercise book or cipher book of mathematical operations, rules and theorems, and example problems. Sections labeled with calligraphic lettering include the Single Rule of 3, Double Rule of 3, Simple Interest, Insurance, Commission, Barter, Fellowship, Exchange, Vulgar Fractions, Decimal Fractions, and others.

This arithmetic copybook was compiled by an anonymous student in the nineteenth century. It includes rules and examples for addition, subtraction, multiplication, and division, as well as practical examples relating to money and weights and measures.

Barbary Aplin's Cyphering Book contains examples and explanations of arithmetic operations, and genealogical information about the Applin, Sparks, and Coxe families of New Jersey.

The Barbary Aplin Cyphering Book contains examples and explanations of arithmetic operations, and genealogical information about the Applin, Sparks, and Coxe families of New Jersey. The first 10 pages of the book are arithmetic rules, proofs, problems and solutions, and tables. Although the manuscript inscription on the cover is "Barbary Aplin's Cyphering Book," Elizabeth Sparks signed her name on page five, suggesting that she may have contributed to the volume.

Eight additional pages contain sparse genealogical notes regarding the Applin, Sparks, and Coxe families of New Jersey, including birth and death dates for several members of the families. Also of interest is a brief note regarding the deaths of Mary and Hanna Sparks in 1824, accompanied by a small swatch of cloth.

The fourth page of the volume includes a young person's drawings of plants, a person, buildings, a fence, and a bird.

Daniel Conover composed this mathematics exercise book containing definitions, problems, solved examples, rules, cases, and remarks. Subjects covered include practical geometry, mensuration of superficies, conic sections, mensuration of solids, and cylindrical rings.

Daniel Conover composed this mathematics exercise book containing definitions, problems, solved examples, rules, cases, and remarks. Subjects covered include practical geometry, mensuration of superficies, conic sections, mensuration of solids, and cylindrical rings. Short sections relate to the application of the principles to the work of artificers, bricklayers, masons, carpenters and joiners, slaters and tilers, plasterers, painters and glaziers, pavers, as well as the construction of roofs and measuring timber. Conover illustrated examples of geometric shapes and angles, some painted with watercolors. A watercolor painting of a building also appears in the volume.

This currently unidentified student's cypher book contains mathematical rules and examples largely in the service of commerce. Entries relate to the addition of money, addition of Troy weight, addition of dry measure, subtraction, a numeration table, a multiplication table, the Golden Rule (i.e. the rule of three), and similar concepts. Currency in this volume is almost exclusively British coinage, but at least one problem references conversion of British pounds into the (newly created) U.S. dollar. The covers of the volume are (apparently re-used) canvas, possibly sailcloth. The cypher book was owned by the Higgins family of Cape Cod, Massachusetts, and it contains names of Higgins family members, but the author is yet undetermined.

The Isam Leonard Arithmetic Book includes mathematical rules, questions, practical examples, and solved exercises covering subtraction, multiplication, division, addition, reduction, fractions, decimals, the single rule of three direct, inverse and compound proportions, and simple interest. The volume includes calligraphic lettering and designs. One undated, unsigned pencil drawing of the "Old Mill at Iffley" is tipped into the volume.

The Isam Leonard Arithmetic Book includes mathematical rules, questions, practical examples, and solved exercises covering subtraction, multiplication, division, addition, reduction, fractions, decimals, the single rule of three direct, inverse and compound proportions, and simple interest. The volume includes calligraphic lettering and designs. One undated, unsigned pencil drawing of the "Old Mill at Iffley" is tipped into the volume. Colored, floral-patterned paper (wallpaper) is pasted onto the front and back covers.

Elements of Navigation, a manuscript adaptation of John Robertson’s work of the same name, provides instruction and practical exercises in arithmetic, geometry, trigonometry, geography, astronomy, and navigational principles (781 pages). The volume is heavily illustrated with mathematical diagrams. It also contains a 1785 copy of a ship log for a 1772 voyage from England to Madeira, (21 pages).

"Elements of Navigation," a manuscript adaptation of John Robertson’s work of the same name, provides instruction and practical exercises in arithmetic, geometry, trigonometry, geography, astronomy, and navigational principles (781 pages). The volume is illustrated with mathematical diagrams. It also contains a 1785 copy of a ship's log for a 1772 voyage from England to Madeira (21 pages). The book is divided into 14 primary chapters, 11 of them preceded by an ink or watercolor illustration of buildings, ships, and places, such as the watercolor drawings "The Desire in a Storm" and "A west View of Islington, old Church." (See below for complete list.) Several chapters are further divided into sections, and most chapters or sections are followed by problems, questions, case studies, answers, and explanations. Please see the box and folder listing below for a table of contents.

The volume begins with explanations of basic mathematical principles, including arithmetic operations, decimals and fractions, roots and powers, notation, and "Tables of English Money, Weights, and Measures" (pp. 9 verso-10 verso). This chapter is followed by theorems and problems of geometry and trigonometry. The subsequent section on geography contains prose explanations of the discipline's foundations, such as the shape of the Earth, the concept of latitude and longitude, and the currently known world. Remarks on the continents are accompanied by tables showing major countries, principal cities, rivers, and mountains. The tables for North and South America are split, and individual states within the United States are identified as "countries," as are California, New Mexico, Old Mexico, Louisiana, Canada, New Britain, New Wales, and others. Introductory geographic material also includes content on winds, tides, and bodies of water. A segment on "chronology" introduces several scales for measuring time, and explains the reasoning behind concepts such as the leap year and the "Golden Number" (pp. 147-147 verso).

The remainder of the work focuses on the art of maritime navigation. Several topics include: the calculation of compound courses, oblique and windward sailing, sailing in currents, and globular sailing. The sections devoted to each topic are comprised primarily of rules or theorems, exercises, and illustrations of practical applicability. A chapter on "spherics" introduces spherical geometry and trigonometry. Two chapters on astronomy explain concepts in "star astronomy," "terrestrial astronomy," and "spherical astronomy," such as the composition of the Solar System, planetary movements, and mathematical applications. The final 80 pages contain information on the art of sailing and expand on principles previously discussed. These pages include instructions on how to calculate the location of a ship at sea, make necessary observations, and correct a ship's course, among other similar topics.

The final 21 pages consist of a log from an unknown ship traveling from England to Madeira in 1772, transcribed by James West in 1785. Between July 2 and July 11, the log contains notes on the weather, wind direction, and general remarks of occurrences on board as the ship prepared for its journey at Deptford, London. On one occasion, the author mentioned a sailor being disciplined for drunkenness (July 3). Between July 12 and July 28, the log documents the weather, wind direction, ship's location, use of various sails, and other information compiled throughout the course of each day. The ship arrived at Madeira on July 28. The log is followed by a brief note by James West concerning the location of Funchal, Madeira.

The non-mathematical illustrations separating the book's chapters are done in ink or watercolor, and depict rural scenes and sailing ships.

• [View of a village, with a man fishing in a river], p. 2
• [View of a river, with a cylindrical building in the foreground and a church in the background], p. 76
• [View of an arched gateway, with attached buildings and bridge], p. 114
• [View of a stone building with a high-peaked roof, alongside a body of water], p. 138
• "The Victor in a calm sea," p. 187
• [Oval-framed view of two persons sitting beside a river, with a ship and fortifications in the background], p. 202
• "The Desire in a Storm," p. 223
• [Oval-framed view of a small sailing vessel on shore beside a stone building], p. 241
• "A west View of Islington, Old Church," p. 267
• "Teneirs House," p. 319
• "At Abingdon 1782," p. 349

The royal coat of arms of the British monarch is imprinted on the volume's front and back covers.

This collection is made up of 2 volumes that Marianna Chandler Lanman composed while studying at Mrs. Rowson's Academy for Young Ladies in Boston, Massachusetts, around 1814. One concerns arithmetic, focusing on practical applications in bookkeeping, conversion, and monetary transactions; the other contains copied poems, calligraphic alphabets, and graphic illustrations.

This collection is made up of 2 volumes that Marianna Chandler Lanman composed while studying at Mrs. Rowson's Academy for Young Ladies in Boston, Massachusetts, around 1814. One concerns arithmetic, focusing on practical applications in bookkeeping, conversion, and monetary transactions; the other contains copied poems, calligraphic alphabets, and graphic illustrations. Lanman dedicated both volumes to her parents.

Lanman composed the first volume, entitled "Practical Arithmetic[:] Comprising All the Rules for Transacting Business" (10"x16", 60 pages), at Mrs. Rawson's Academy in 1814. Its sections, each labeled in calligraphy, concern mathematical operations, rules and theorems; weights and measures; and practical applications of mathematical principles. Many of the later pages concern subjects such as the calculation of simple and compound interest, the value of "federal money" against "lawful money" (state currencies), commission charges, and bookkeeping. The explanatory text is accompanied by finished exercises and problems. The volume also includes tables of weights and measures and an index.

The second volume, "Specimens of Penmanship" (16"x10", 23 pages), is undated. Lanman copied poetry and proverbs on the book's odd-numbered pages; most concern subjects such as happiness, rural living, and gratitude. The title of a poem on the "Pleasures of retired Life" is written on a drawing of a ribbon (p. 19). One poem, entitled "Virtue's Tears Embalm the Brave," is dedicated to the memory of American casualties of the War of 1812 (p. 21). The volume contains several drawings: a hermit in his home (p. 3), a bald eagle among patriotic decorations (p. 21), a sailing ship (p. 21), and a line drawing of a bird with the word "industry" in its feathers (p. 23). The volume also includes examples of cursive, German, and Old English alphabets.

In 1820, Robert Galbreath created this cypher book, sold by Bennet & Walton of Philadelphia, Pennsylvania. It includes rules, examples, and exercises for vulgar fractions, raising of powers, square and cube roots, measurements, gravity, and applied mathematics for walling, masonry, paving, shingling, plastering, and digging. The volume has several pen-and-ink drawings of geometrical objects related to math problems.

In 1820, Robert Galbreath created this cypher book, sold by Bennet & Walton of Philadelphia, Pennsylvania. It includes rules, examples, and exercises for vulgar fractions, raising of powers, square and cube roots, measurements, gravity, and applied mathematics for walling, masonry, paving, shingling, plastering, and digging. The volume has several pen-and-ink drawings of geometrical objects related to math problems.

In 1820, Robert Galbreath created this cypher book, sold by Bennet & Walton of Philadelphia, Pennsylvania. It includes rules, examples, and exercises for vulgar fractions, raising of powers, square and cube roots, measurements, gravity, and applied mathematics for walling, masonry, paving, shingling, plastering, and digging. The volume has several pen-and-ink drawings of geometrical objects related to math problems.

In 1820, Robert Galbreath created this cypher book, sold by Bennet & Walton of Philadelphia, Pennsylvania. It includes rules, examples, and exercises for vulgar fractions, raising of powers, square and cube roots, measurements, gravity, and applied mathematics for walling, masonry, paving, shingling, plastering, and digging. The volume has several pen-and-ink drawings of geometrical objects related to math problems.