more from this thinker | more from this text
Full Idea
We have only to keep in mind that to find a tangent means to draw a line that connects two points of a curve at an infinitely small distance.
Gist of Idea
A tangent is a line connecting two points on a curve that are infinitely close together
Source
Gottfried Leibniz (works [1690]), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.1
Book Ref
Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.234
A Reaction
[The quote can be tracked through Kitcher's footnote]
21382 | Things get smaller without end [Anaxagoras] |
18081 | Nature uses the infinite everywhere [Leibniz] |
18080 | A tangent is a line connecting two points on a curve that are infinitely close together [Leibniz] |
18091 | Infinitesimals are ghosts of departed quantities [Berkeley] |
18085 | Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy] |
18086 | Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher] |
18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
18083 | With infinitesimals, you divide by the time, then set the time to zero [Kitcher] |
18834 | Infinitesimals do not stand in a determinate order relation to zero [Rumfitt] |