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Mathematical Treasure: Isaac Greenwood's Arithmetick

Frank J. Swetz (The Pennsylvania State University)

Isaac Greenwood (1702–1745) graduated from Harvard College in 1721. Six years later, he returned as the first occupant of the Hollis Chair of Mathematics and Natural Philosophy at the College. During his tenure at Harvard, he published Arithmetick Vulgar and Decimal (1729), the first arithmetic book written and published in the English colonies in what is now the Eastern United States, often called Colonial America. Although the book appeared anonymously, its origins are definitely attributed to Greenwood.

Isaac Greenwood's Arithmetick

Page 176 of this book, shown above, contains two typical word problems of the time.

In his Arithmetick, Greenwood chose to use the short scale value for one billion, i.e. 1 billion = 1000 x 1 million, or 109. This standard has been retained by the English speaking countries of the world. The continental countries of Europe use the long scale, i.e. 1 billion = 1 million million, or 1012.

This image is provided courtesy of the Beinecke Rare Book and Manuscript Library, Yale University. You may use it in your classroom; all other uses require permission from the Beinecke Library. The Mathematical Association of America is pleased to cooperate with the Beinecke Library and Yale University to make this image available to a larger audience.

For more information about Isaac Greenwood, see:

"Mathematics Department Timelines: Timeline 1636-1836," available through the Harvard University Mathematics Department:

Leonard, David C., "Harvard's First Science Professor: A Sketch of Isaac Greenwood's Life and Work," available through the Harvard University Library:

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Isaac Greenwood's [i]Arithmetick[/i]," Convergence (August 2012), DOI:10.4169/loci003902