After exponential quantities the circular functions, sine and cosine, should be considered because they arise when imaginary quantities are involved in the… — Leonhard Euler Copy Share Image
For the sake of brevity, we will always represent this number 2.718281828459... by the letter e. — Leonhard Euler Copy Share Image
A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or… — Leonhard Euler Copy Share Image
Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to… — Leonhard Euler Copy Share Image
In the meantime, most noble Sir, you have assigned this question to the geometry of position, but I am ignorant as to… — Leonhard Euler Copy Share Image
Thus you see, most noble Sir, how this type of solution to the Königsberg bridge problem bears little relationship to mathematics, and… — Leonhard Euler Copy Share Image
Notable enough, however, are the controversies over the series 1 - 1 + 1 - 1 + 1 - ... whose sum… — Leonhard Euler Copy Share Image
If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything… — Leonhard Euler Copy Share Image
... I soon found an opportunity to be introduced to a famous professor Johann Bernoulli. ... True, he was very busy and… — Leonhard Euler Copy Share Image
Since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place… — Leonhard Euler Copy Share Image
The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth;… — Leonhard Euler Copy Share Image
Nothing takes place in the world whose meaning is not that of some maximum or minimum. — Leonhard Euler Copy Share
Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless… — Leonhard Euler Copy Share
A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities. — Leonhard Euler Copy Share
Thus you see, most noble Sir, how this type of solution to the Königsberg bridge problem bears little relationship to mathematics, and I do… — Leonhard Euler Copy Share
The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is… — Leonhard Euler Copy Share
Since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the… — Leonhard Euler Copy Share
If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything but zero.… — Leonhard Euler Copy Share
Logic is the foundation of the certainty of all the knowledge we acquire. — Leonhard Euler Copy Share
For the sake of brevity, we will always represent this number 2.718281828459... by the letter e. — Leonhard Euler Copy Share
In the meantime, most noble Sir, you have assigned this question to the geometry of position, but I am ignorant as to what this… — Leonhard Euler Copy Share
For since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in… — Leonhard Euler Copy Share
Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe… — Leonhard Euler Copy Share
To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so… — Leonhard Euler Copy Share
