Questions tagged [leibniz]

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1 answer
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Are there any direct comments by Isaac Newton on Leibniz's living force / vis-viva?

The living force or the vis-viva is a quantity usually attributed to Leibniz (although there were a few other people who identified it as a conserved quantity in certain collisions earlier). Many ...
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1 vote
1 answer
153 views

How to understand Poincaré's interpretation of Newton's anagram "aaaaabbbeeeeii"

In Science and Method, page 37, Poincaré (as translated by Francis Maitland) states, The story goes that Newton once communicated to Leibnitz an anagram somewhat like the following: aaaaabbbeeeeii, ...
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2 votes
1 answer
94 views

How did the idea of a formal derivation emerge?

Infinitesimal calculus and the introduction of derivatives is often linked to Newton and Leibniz. I was wondering, when and why the idea of studying formal derivatives (e.g., of a formal polynomial) ...
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0 answers
69 views

Did Leibniz ever express any opinion about Aristotle, Plato or Archimedes?

Since Leibniz is known to have expressed opinions about Descartes' and Newton's abilities maybe he did the same for the prominent thinkers of antiquity. Did Leibniz ever express any opinion about ...
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8 votes
2 answers
1k views

Where did Leibniz explore the product rule of differential calculus?

In what book/letter did Gottfried Wilhelm Leibniz explore the product rule as part of differential calculus?
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5 votes
2 answers
643 views

Why do we use Leibniz's “version” of calculus instead of Newton's?

I understand that they invented calculus independently at roughly the same time, but why do we use Leibniz's terminology/notation rather than Newton's? For example, why don't we use "fluxion"...
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  • 53
3 votes
1 answer
393 views

Source of claim that Leibniz discovered separation of variables for ODEs in 1691?

Claims I'm evaluating I've read in multiple sources that Leibniz formulated separation of variables for ODEs in 1691. A couple example sources are below. Mathematical Thought from Ancient to Modern ...
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17 votes
3 answers
3k views

What does it mean by "d-ism of Leibniz" and "dotage of Newton" in simple English?

I am reading this article by Donald E. Knuth and get stuck by this sentence: Our mathematical language continues to improve, just as “the d-ism of Leibniz overtook the dotage of Newton” in past ...
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10 votes
1 answer
1k views

Why is differentiation under the integral sign named the Leibniz rule?

The question here asked why differentiation under the integral sign is named "Feynman's trick". That is a comparatively recent name for the method. Aside from the name "differentiation under the ...
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  • 4,084
13 votes
3 answers
1k views

Was English mathematics behind Europe by many years because of Newton's notation?

Below are several quotes suggesting that Newton's notation had the effect of retarding English mathematics by 50 years, 100 years, or even centuries. Here is my simplistic two-sentence historical ...
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1 vote
1 answer
163 views

What was the mechanical principle of Leibniz's "integraph"?

For a very long time I've searched in the internet what was the actual integrating device which Leibniz designed in 1693. Yesterday I found the answer - the instrument which Leibniz devised is the ...
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1 vote
1 answer
132 views

Did Leibniz also design analog computers?

My question is based on the information that appears in several websites, according to which I found three examples of a kind of instrument that was probably an analog computer. The first one ...
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  • 3,969
2 votes
2 answers
144 views

What navigation instrument did Leibniz develop?

My question refers to Gottfried Leibniz's "instrumentum longuitidimum" mentioned in some sites — a device that could record the course of a ship in sea and display its recent position directly on a ...
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  • 3,969
3 votes
0 answers
227 views

How did Leibniz's prototypes of a yaw system and a braking mechanism (for windmills) work?

My question is concerned with two hardly mentioned yet very ingenious inventions of Leibniz. These two inventions represent technological inventiveness and visionary insight (about wind energy ...
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  • 3,969
4 votes
1 answer
266 views

Did Leibniz sketch a design for a machine capable of solving a system of linear equations?

My question is based on the information on pages 108-109 of the book The Tangled Origins of the Leibnizian Calculus. I know that Leibniz invented the stepped drum and used it to build the stepped ...
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  • 3,969
15 votes
1 answer
385 views

What kind of mathematical education did Leibniz have?

It doesn't seem that he began his life in mathematics. Does anyone know how it came to be ? What did he read ?
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  • 927
6 votes
2 answers
282 views

Did Leibniz use infinite numbers?

Arthur's recent article Arthur, Richard T. W. Leibniz's actual infinite in relation to his analysis of matter. G. W. Leibniz, interrelations between mathematics and philosophy, 137–156, Archimedes,...
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  • 3,649
13 votes
2 answers
767 views

Why is Leibniz less well regarded?

A well-known and specific example is that Leibniz is less well regarded than Newton for his calculus, the reason being notation, Leibniz notation lets you incorrectly work with derivatives as ...
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38 votes
6 answers
14k views

What is the difference between Calculus of Newton and that of Leibniz?

Are there any differences between the study of Calculus done by Newton as compared to that done by Leibniz? If yes, please mention point by point.
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