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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 theline 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
asthe 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 aremovable. However, the green points are fixed to remain on the same horizonal line and the blue points must lie on a line that does not change the intersection point of the two lines. Notice that whereever 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 or Pat's Math Website |
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that is all three of these lines are coincident. The line n neednot
be distinct from m.