Author: John Gabriel
Date: 17 July 2014

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Rotate the green point to see the slope of each line.

Slope

What the Ancient Greeks knew:  

What Newton did:

Slope   

Slope has dimension.

Slope has no dimension.

All straight lines have slope.

Vertical lines no longer have slope.

The Greeks defined slope in terms of angle.

Newton and Leibniz defined slope as 

$ \frac{rise}{run} $

C = Intersect(xAxis, yAxis)
B = (1.8, 1.8)
c = Circle(C, B)
A = Intersect(c, xAxis, 2)
slope = Angle(A, C, B)
a = Segment(C, B)
b = Segment(A, C)
D = Point(yAxis)
E = Point(yAxis)
ang: slope / °
GreekAngle: (ang / 45 * 0.5)
NewtonAngle: y(B) / x(B)
F = Intersect(c, xAxis, 1)
g = Segment(F, C)
G = Intersect(c, yAxis, 2)
H = Intersect(c, yAxis, 1)
d = Segment(G, H)
text7: "$=tan(" + (LaTeX[slope]) + ") =" + (LaTeX[NewtonAngle]) + " $"
num: (GreekAngle * 100)
top = Div((num * 1000), 1000)
text2: "$ =" + (LaTeX[slope]) + "= \frac{" + (LaTeX[top]) + "}{100}(right ∠)  $"