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Textbooks and Teachers

Even after the idea of coordinate graphing was in its modern form, it still had to spread. And, of course, one of the major ways that mathematical ideas spread is through math teachers and the textbooks they write. From the 1700s until today, people have been teaching and writing about graphing.

An Italian woman named Maria Gaetana Agnesi wrote one of the first calculus textbooks, called Analytical Institutions. Agnesi started writing the book to teach her little brother about math, but it soon became a much more complete work; it was published in 1748. In her book, Agnesi graphed a curve called the Witch of Agnesi. Her graph labelled the horizontal axis "y" and the vertical axis "x," but otherwise it was just like a modern graph. Here is a picture of her curve:

Another important textbook writer was Gaspard Monge, who was born in France in 1746. As well as making his own discoveries, Monge wrote a geometry textbook that included equations for lines and planes in two and three dimensions.

Professors and their textbooks spread many important mathematical terms and notation. For example, the first person to use the word "graph" was James Joseph Sylvester, who was born in London in 1814. (Sylvester was a teacher, but he had a dangerous temper; once he attacked a student at the University of Virginia with a sword cane, because the student was reading a newspaper during his class.) We know that Sylvester included "graph" in an article in 1878; eight years later, an article in Applied Mechanics remarked, "Students will do well to graph on squared paper some curves like the following . . ."

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