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11.6.14  A point on a geometric object in the plane: element

The element command is most useful in a two-dimensional geometry screen; it creates objects that are restricted to a geometric figure.

element takes different types of arguments:

If a point A (corresponding to the complex number a) is defined as an element of a curve C and B is a point (corresponding to the complex number b), then A + B will be a point on C; it will be the projection onto C of the point corresponding to a + b.

Note that in this case, if B′ is another point, then A + (BB′) isn’t the same as A + BB′. The expression A + (BB′) is interpreted as adding the point A, defined as a point on C, to the point BB′, and so the sum will be on C. The expression A + BB′ is interpreted as (A + B) − B′, and so the point B′ is not being added to a point defined as an element of the curve C, and so this sum may not be on C.

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