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The Construction: Observation ThreeLet x
=(X1,X2,X3) and
y=(Y1,Y2,Y3) be
two sets of three collinear points that lie on the line l andm
respectively. Let z=(Z
1,Z2,Z3) be a triple of collinear
points that lie on the linen, where n is a line such that Observation 3 The triple of points
on the line l constructed from the triples of pointsx and
yby the construction described in Observation Two is exactly the same
as the triple of points constructed using the triples of points x and
z. An applet demonstrating Observation Three is shown below: The green and the blue points in the applet above are movable. However, the green points are fixed to remain on the same horizontal line and the blue points must lie on a line that does not change the intersection point of the two lines. Notice that wherever the blue points are moved,the red points that lie on the same line as the green points are not affected. Return to: Pappus' Theorem Main Page
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