In Book III, Proposition 16 of the Elements Euclid defines the tangent to a circle:

"The straight line drawn at right angles to the diameter of a circle from its extremity will fall outside the circle, and into the space between the straight line and the circumference another straight line cannot be interposed."

Modern translation: The tangent line through a point on a curve is the closest line to the curve at that point.

Bill

In a message dated 10/15/2010 9:54:59 P.M. Eastern Daylight Time, nswenson@masterschool.org writes:

One of my students hit me today with a question I couldn't answer, so I thought I would ask you brilliant people out there for some help. The definition that we have been using for a tangent line is, "A line which intersects the curve at exactly one point." However, the function they were dealing with was a cubic function. They had to determine the points at which there were horizontal tangents. Her reasoning was that there were no horizontal tangents, since any line that hit the graph horizontally would cross at more than one point. How do I need to redifine tangent line to eliminate this very insightful answer? ==== Course related websites: http://apcentral.collegeboard.com/calculusab http://apcentral.collegeboard.com/calculusbc --- To search the list archives for previous posts go to http://lyris.collegeboard.com/read/?forum=ap-calculus To unsubscribe click here: http://lyris.collegeboard.com/read/my_forums/ To change your subscription address or other settings click here: http://lyris.collegeboard.com/read/my_account/edit