Skip to main content
Арабские красавицы на фестивале в Дубаи. ТОП-10Арабские красавицы на фестивале в Дубаи. ТОП-10 14 самых удивительных вертикальных садов мира14 самых удивительных вертикальных садов мира Крупнейшие радиационные аварии и катастрофы современностиКрупнейшие радиационные аварии и катастрофы современности
Leonhard Euler

Since the fabric of the unive...

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 ... there is absolutely no doubt that every affect in the universe can be explained satisfactorily from final causes, by the aid of the method of maxima and minima, as it can be from the effective causes themselves ... Of course, when the effective causes are too obscure, but the final causes are readily ascertained, the problem is commonly solved by the indirect method.

Leonhard Euler 23 quotes
Leonhard Euler

Mathematicians have tried in ...

Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.

Leonhard Euler 23 quotes
Leonhard Euler

For since the fabric of the u...

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.

Leonhard Euler 23 quotes
Leonhard Euler

After exponential quantities ...

After exponential quantities the circular functions, sine and cosine, should be considered because they arise when imaginary quantities are involved in the exponential.

Leonhard Euler 23 quotes
Leonhard Euler

A function of a variable quan...

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 23 quotes
Leonhard Euler

Thus you see, most noble Sir,...

Thus you see, most noble Sir, how this type of solution to the K?nigsberg bridge problem bears little relationship to mathematics, and I do not understand why you expect a mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle.

Leonhard Euler 23 quotes
Leonhard Euler

Notable enough, however, are ...

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.

Leonhard Euler 23 quotes
Leonhard Euler

If a nonnegative quantity was...

If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything but zero. 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. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages, where we shall explain this calculus.

Leonhard Euler 23 quotes
Leonhard Euler

Although to penetrate into th...

Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena.

Leonhard Euler 23 quotes
Leonhard Euler

The kind of knowledge which i...

The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such a discovery as an opportunity to investigate more exactly the properties discovered and to prove or disprove them; in both cases we may learn something useful.

Leonhard Euler 23 quotes
Leonhard Euler

I soon found an opportunity t...

I soon found an opportunity to be introduced to a famous professor Johann Bernoulli. ... True, he was very busy and so refused flatly to give me private lessons; but he gave me much more valuable advice to start reading more difficult mathematical books on my own and to study them as diligently as I could; if I came across some obstacle or difficulty, I was given permission to visit him freely every Sunday afternoon and he kindly explained to me everything I could not understand.

Leonhard Euler 23 quotes
Leonhard Euler

Notable enough, however, are t...

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.

Leonhard Euler 23 quotes
Leonhard Euler

Transcendental [numbers], They...

Transcendental [numbers], They transcend the power of algebraic methods.

Leonhard Euler 23 quotes
Leonhard Euler

If a nonnegative quantity was ...

If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything but zero. 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. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages, where we s

Leonhard Euler 23 quotes
Leonhard Euler

In the meantime, most noble Si...

In the meantime, most noble Sir, you have assigned this question to the geometry of position, but I am ignorant as to what this new discipline involves, and as to which types of problem Leibniz and Wolff expected to see expressed in this way.

Leonhard Euler 23 quotes
Leonhard Euler

Thus you see, most noble Sir, ...

Thus you see, most noble Sir, how this type of solution to the Königsberg bridge problem bears little relationship to mathematics, and I do not understand why you expect a mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle...

Leonhard Euler 23 quotes
Leonhard Euler

The kind of knowledge which is...

The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such a discovery as an opportunity to investigate more exactly the properties discovered

Leonhard Euler 23 quotes
Leonhard Euler

... I soon found an opportunit...

... I soon found an opportunity to be introduced to a famous professor Johann Bernoulli. ... True, he was very busy and so refused flatly to give me private lessons; but he gave me much more valuable advice to start reading more difficult mathematical books on my own and to study them as diligently as I could; if I came across some obstacle or difficulty, I was given permission to visit him freely every Sunday afternoon and he kindly explained to me everything I could not understand ...

Leonhard Euler 23 quotes
Leonhard Euler

Mathematicians have tried in v...

Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.

Leonhard Euler 23 quotes
Leonhard Euler

For since the fabric of the un...

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.

Leonhard Euler 23 quotes

Last interesting articles

Добрые, щедрые, великодушные: 6 советских актеров, которые были всеобщими любимчиками Holiday

Добрые, щедрые, великодушные: 6 советских актеров, которые были всеобщими любимчиками

23

Советских актёров часто ставят в пример как образец духовной силы, национальной гордости и внутренней красоты. Они стали символами эпохи, носителями культуры и нравственности. Но, как известно, за кул...

Десять кинозвезд, которые отлично поют Holiday

Десять кинозвезд, которые отлично поют

83

Актеры — люди творческие, но кто бы мог подумать, что некоторые из них скрывают прекрасный голос. В эпоху раннего Голливуда актеров с музыкальными способностями было немало — это считалось скорее норм...

Мэрилин Монро, Ким Кардашьян и другие Holiday

Мэрилин Монро, Ким Кардашьян и другие

115

Неузнаваемая Ким Кардашьян в объективе фотографа Маркуса Клинко, 2009 год. Памела Андерсон в самой первой съёмке для журнала «Playboy», 1990. На фото голливудская актриса Dorothy Lamour и шимпанзе Джи...

Что стало с детьми-звездами: Рэдклифф и компания спустя годы Holiday

Что стало с детьми-звездами: Рэдклифф и компания спустя годы

219

Расскажем, как сложилась судьба актеров, которые начинали сниматься еще в детстве.
Остаться на вершине в Голливуде удаётся не каждому, особенно если путь начался в детстве. Одни актёры теряются из-за...

Жизнь за границей: как изменились судьбы 7 уехавших телеведущих Holiday

Жизнь за границей: как изменились судьбы 7 уехавших телеведущих

541

Два года назад отечественное телевидение столкнулось с беспрецедентной кадровой тектоникой — целая группа ярких и узнаваемых ведущих стремительно исчезла с экранов федеральных каналов. Эти лица долгие...

Кира Найтли, Деми Мур и другие Holiday

Кира Найтли, Деми Мур и другие

165

Кира Найтли на страницах журнала к выходу фильма «Пиджак», 2005. Следы динозавра, раскопанные в русле реки Палакси. Техас. США. 1952г. Самая большая женщина рядом с самым маленьким мужчиной, 1922 год....