 |
 |
Because of his results in the infinitesimal calculus, our math class started to study on Leibniz` theories this year and we decided to work with those theories in detail. Leibniz solved the problem of the tangent at the same time as Newton, a problem which at that time had been solved for special graphs only.
Leibniz` thoughts were the following:
The subnormal QR, the normal PR and also the ordinate PQ form a rectangular
triangle. This triangle is similar to all other rectangular triangles which
consist of the tangent and the parts on the parallels to the ordinate
and to the abscissa. The relation of the "Katheten" of both triangles is
the same and remains identical even when dx gets very small in the smaller
triangle. The closer dx approaches 0, the closer the gradient of
ds approaches the gradient of the curve in P.
Hereby Leibniz proved that one can find the gradient of a special point
within every continuous curve. This was the beginning of the infinitesimal
calculus.
(Claudia Ruch, Elisabeth Schallhart, Jennifer Galambos)
 |
 |
|
|