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Mathematics is not only real, but it is the only reality. [The] entire universe is made of matter, obviously. And matter is made of particles. It's made of electrons and neutrons and protons. So the entire universe is made out of particles. Now what are the particles made out of? They're not made out of anything. The only thing you can say about the reality of an electron is to cite its mathematical properties. So there's a sense in which matter has completely dissolved and what is left is just a mathematical structure.

Gardner on Gardner: JPBM Communications Award Presentation. MAA FOCUS, v. 14, no. 6, December 1994.

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Mathematical Treasure: Matthew Wood's Copybook

In 17th and 18th century Britain, some people took pride in compiling their own handwritten books.  These copybooks represented a personal view toward the subjects under consideration.  They were often ornately decorated and embellished with calligraphy.  Matthew Wood compiled such a book in 1699 and titled it “Numeration: treatise on arithmetic.”  On his introductory page, he told the reader,

Seven friends supremely excellent are the stars in wisdom’s firmament. Whereof arithmetic is one most worth.

Here he was referring to the seven liberal arts of the medieval curriculum.

On the page shown above, titled "Numeration," Wood noted that:

Numeration is the very entrance into Arithmeticks.  It teaches the art of numbering, so that by it you may know the value of any figures.

He then graphically demonstrated the increase of place value as the tens denominations of numbers increased. Numeration at this time was considered a separate mathematical operation in arithmetic. Note that on this chart there is no term “billion”, but rather “1000 million”.

On the page above Wood gave examples of using addition and subtraction in the same problem to determine value given and value received. He recorded monetary results in pounds : shillings : pence; thus 220 : 13 : 04 reads as 220 pounds, 13 shillings, and 4 pence. Besides instruction in arithmetic, the book also contains numerous tables for monetary, liquid, and weight conversions.  Most likely, the work was intended for use by a merchant.

For another example of a 17th century copybook, see the Convergence page, "Mary Serjant's Copybook."

For examples of 18th century British copybooks, see the Convergence article, “Learning Geometry in Georgian England,” by Benjamin Wardhaugh (August 2012).

(These two images are provided courtesy of the Beinecke Rare Book and Manuscript Library, Yale University. You may use them 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 these images available to a larger audience.)

Swetz, Frank J., "Mathematical Treasure: Matthew Wood's Copybook," Loci (September 2012), DOI: 10.4169/loci003931