One more Preview for the Etymological and Historical Math Dictionary - Graph

Graph has come to have multiple meanings in mathematics, but for most students it relates to the graph of functions on the coordinate axes.  The origin is from the Greek graphon, to write, perhaps with earlier references to carving or scratching. Jeff Miller's web site suggests that the use of graph as a verb may have first been introduced as late as 1898. 
In a post to a history newsgroup, Karen Dee Michalowicz commented on the history of graphing:

It is interesting to note that the coordinate geometry that Descartes introduced in the 1600's did not appear in textbooks in the context of graphing equations until much later.  In fact, I find it appearing in the mid 1800's in my old college texts in analytic geometry.  It isn't until the first decade of the 20th century that graphing appears in standard high school algebra texts. [This matches rise of  graph paper in the same periods].  Graphing is most often found in books by Wentworth.  Even so, the texts written in the 20th century, perhaps until the 1960's, did not all have graphing.  Taking Algebra I in the middle 1950's, I did not learn to graph until I took Algebra II

See my Notes on the History of Graph Paper  here

Math historian Bea Lumpkin has written about the early use of graphs by the Egyptians in what was an early use of what painters call the grid method:

In my article ... I suggest, "It is possible that the concept of coordinates grew out of the Egyptian use of square grids to copy or enlarge artwork, square by square.  It needs just one short, important step from the use of square grids to the location of points by coordinates.  

In the same posting she comments on the finding of graphs in Egyptian finds dating back to 2700 BC: 

"An architect's diagram of great importance has lately been found by the Department of Antiquities at Saqqara.  It is a limestone flake, apparently complete, measuring about 5 x 7 x 2 inches, inscribed on one face in red ink, and probably belongs to the IIIrd dynasty"  Here is the reason that Clark and Engelbach attached great importance to the diagram.  It shows a curve with vertical line segments labeled with coordinates that give the height of points on the curve that are equally spaced horizontally.  The vertical coordinates are given in cubits, palms and fingers.  The horizontal spacing, the authors write "... most probably that is to be understood as one cubit, an implied unit elsewhere."  To clinch their analysis, Clarke and Engelbach observe:  "This ostrakon was found near the remains of a solid saddle-backed construction, the top of which, as far as could be ascertained from its half-destroyed condition, closely approximated tot he curve obtained from the data on the ostrakon. 

This certainly lays claim to the oldest line graph I have ever heard.