Meetkunde

Ik zou voor een praktische opdracht graag de definities van kegels die Grieken hanteerden willen weten.

Alvast Bedankt

Frans
Leerling bovenbouw havo-vwo - maandag 4 februari 2002

Antwoord

Apollonius van Perga schrijft in Boek I van zijn Conica (in Engelse vertaling van R. Catesby Taliaferro vanuit het Grieks):

1.
If from a point a straight line is joined to the circumference of a circle which is not in the same plane with the point, and the line is produced in both directions, and if, with the point remaining fixed, the straight line being rotated about the circumference of the circle returns from the same place from which it began, then the generated surface composed of the two surfaces lying vertically opposite one another, each of which increases indefinitely as the generating straight line is produced indefinitely, I call a conic surface, and I call the fixed point the vertex, and the straight line drawn from the vertex to the center of the circle I call the axis.
2.
And the figure contained by the circle and by the conic surface between the vertex en the circumference of the circle I call a cone, and the point which is also the vertex of the surface I call the vertex of the cone, and the straight line drawn from the vertex to the center of the circle I call the axis and the circle I call the base of the cone.

maandag 4 februari 2002

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