#### Article Title

### Tangent Lines

#### Abstract

In [1] Leibniz published the first treatment of the subject of calculus. An English translation can be found in [2]; he says that

to find a *tangent* is to draw a right line, which joins two points of the curve having an infinitely small difference, or the side of an infinite angled polygon produced, which is equivalent to the *curve* for us.

Today, according to [3],

a straight line is said to be a tangent line of a curve *y = f(x)* at a point *x = c* on the curve if the line passes through the point (*c, f* (*c*)) on the curve and has slope *f'*(*c*) where *f'* is the derivative of *f*.

At first glance, it would appear that this second definition is simply a more precise version of the first; indeed, the cited Wikipedia article states this sentiment explicitly. In this paper we examine cases where Wikipedia's definition is more strict than Leibniz's original one, and present two attempts at formulating a more general, but still precise, definition.

#### Recommended Citations

MLA:

Estep, Samuel
"Tangent Lines,"
*The Kabod*
5.
1
(2018)
Article 1.

*Liberty University Digital Commons.*
Web. [xx Month xxxx].

APA:

Estep, Samuel
(2018)
"Tangent Lines"
*The Kabod*
5(
1
(2018)), Article 1. Retrieved from https://digitalcommons.liberty.edu/kabod/vol5/iss1/1

Turabian:

Estep, Samuel
"Tangent Lines"
*The Kabod*
5
, no.
1
2018
(2018)
Accessed [Month x, xxxx]. Liberty University Digital Commons.