After exponential quantities the circular functions, sine and cosine, should be considered because they arise when imaginary quantities are involved in the exponential.
Leonhard EulerRead
For since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the universe in which some rule of maximum or minimum does not appear.
Interpretation
What this quote means
The universe operates under precise mathematical laws set by a wise Creator, reflecting principles of optimization.
Leonhard Euler emphasizes the idea that the universe is a well-ordered and harmonious creation, governed by rules of optimization. Every event or phenomenon within it adheres to these principles, highlighting the significance of mathematics and logic in understanding the cosmos. This perspective invites deeper contemplation about the relationship between science, mathematics, and the divine ordering of existence.
Themes
UniverseMathematicsCreatorOptimizationLaws
In practice
Example use cases
In a lecture about the significance of mathematics in the natural sciences.
More from Leonhard Euler
All quotes →To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.
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Notable enough, however, are the controversies over the series 1 - 1 + 1 - 1 + 1 - ... whose sum was given by Leibniz as 1/2, although others disagree. ... Understanding of this question is to be sought in the word "sum"; this idea, if thus conceived - namely, the sum of a series is said to be that quantity to which it is brought closer as more terms of the series are taken - has relevance only for convergent series, and we should in general give up the idea of sum for divergent series.
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