Leibniz's idea of infinity

[Numerarius]

Leibniz said that the circunference of an infinite circle would be for us like a rect line. I would want some information about these ideas of Leibniz, and oher ideas that would be on the origins of calculus.

[matt grime]

That is more than just a mere idea of leibnitz, we commonly refer to a circle of infinite radius as being a straight line, especially in the plane (ie in C), it is the limiting case as the radius tends to infinity of a circle. Eg consider a circle of radius y and centre (y,0), then letting y tend to infinity the resulting shapes tend to the x axis.

 

I would want world peace and a million pounds, not necessarily in that order.

[insane_alien]

Newton also done a lot on calculus. AFAIK Newton and Leibniz developed calculus simultaneously without any correspondance, hence we have Newtonian and Leibniz notaion.

[Sisyphus]

Actually, I believe the first person to speak of a straight line as the circumference of an infinite circle was Galileo. He spoke at great length of that sort of infinity, the kind that comes from increasing the finite indefinitely, through a kind of motion (infinitely divisible, but not divided, thus sidestepping Zeno's paradoxes). This was most definitely a precursor to calculus and the work of Newton and Leibniz.

[cosine]

Actually, I believe the first person to speak of a straight line as the circumference of an infinite circle was Galileo. He spoke at great length of that sort of infinity, the kind that comes from increasing the finite indefinitely, through a kind of motion (infinitely divisible, but not divided, thus sidestepping Zeno's paradoxes). This was most definitely a precursor to calculus and the work of Newton and Leibniz.

 

Even more directly, it was definitely a precursor to Mobius Geometry, a generalized geometry that includes a point at infinity, and holds that lines are circles that go through the point at infinity.