……他是如此著作等身，以至于圣彼得堡科学院的期刊在他去世整整 48 年后，还在继续发表他生前积压的论文。”——《Euler: The Master Of Us All》 顺便说一句，去年我读了他的《无穷分析引论》（Introductio in analysin infinitorum，1748年），这是“有史以来最具影响力的数学著作之一”，正是它确立了函数概念在数学中的基础地位。多项式、三角函数、指数函数、对数函数等等……
…prolific was he that the journal of the St. Petersburg Academy was still publishing the backlog of his papers a full 48 years after his death." – Euler: The Master Of Us All p.s. Last year I read his Introductio in analysin infinitorum (1748), "one of the most influential mathematics books of all time", which made the function concept basic in mathematics. Polynomials, trig functions, exponential functions, the logarithm function, etc…
……忽略了许多其他函数也恰好具有完全相同零点的问题。但实际上，欧拉在提出这个论点时并不是一直都这么草率的！例如，在他的《无穷分析引论》（Introductio in Analysin Infinitorum）第一卷第九章中（Ian Bruce 的英译本可在 http://www.17centurymaths.com/contents/introductiontoanalysi... 查阅），我们可以看到欧拉在论证乘积公式时指出（用现代符号表示就是）……
…ignoring the problem of the fact that many other functions have precisely the same zeros. But Euler was not, in fact, always so glib in presenting this argument! For example, in Volume 1, Chapter 9 of his Introductio in Analysin Infinitorum (translation by Ian Bruce available at http://www.17centurymaths.com/contents/introductiontoanalysi...), we see that Euler argues for the product formula by noting (what would in modern notation be) that…
我最近才了解到：> 有人声称欧拉恒等式出现在他 1748 年出版的数学分析巨著《无穷分析引论》（Introductio in analysin infinitorum）中。然而，这个特定概念是否能归功于欧拉本人是存疑的，因为他可能从未这样表述过。https://en.m.wikipedia.org/wiki/Euler's_identity 但不管怎么说这依然很酷。……
I recently learned: > It has been claimed that Euler's identity appears in his monumental work of mathematical analysis published in 1748, Introductio in analysin infinitorum. However, it is questionable whether this particular concept can be attributed to Euler himself, as he may never have expressed it. https://en.m.wikipedia.org/wiki/Euler's_identity But it is still cool.…
…said it would "create forgetfulness in the learners' souls, because they will not use their memories" (274e-275b) 2. Leonard Euler criticized the use of logarithm tables in calculating: in his 1748 "Introductio in analysin infinitorum" he insisted on deriving logarithms from first principles 3. William Thomson (Lord Kelvin) initially dismissed mechanical calculators, stating in an 1878 lecture at Glasgow University that they would…
……他是如此著作等身，以至于圣彼得堡科学院的期刊在他去世整整 48 年后，还在继续发表他生前积压的论文。”——《Euler: The Master Of Us All》 顺便说一句，去年我读了他的《无穷分析引论》（Introductio in analysin infinitorum，1748年），这是“有史以来最具影响力的数学著作之一”，正是它确立了函数概念在数学中的基础地位。多项式、三角函数、指数函数、对数函数等等……
…prolific was he that the journal of the St. Petersburg Academy was still publishing the backlog of his papers a full 48 years after his death." – Euler: The Master Of Us All p.s. Last year I read his Introductio in analysin infinitorum (1748), "one of the most influential mathematics books of all time", which made the function concept basic in mathematics. Polynomials, trig functions, exponential functions, the logarithm function, etc…
莱昂哈德·欧拉（Leonhard Euler）：出生：1707年；获得哲学硕士学位：1723年；右眼失明：1735年；解决柯尼斯堡七桥问题：1736年；出版《无穷分析引论》第一卷（Introductio in analysin infinitorum, volume 1）：1748年[2]；提出欧拉-伯努利梁理论（Euler-Bernoulli Beam Theory）：1750年；欧拉公式（几何学）：1750年[1]；出版《微分学原理》（Institutiones calculi differentialis）：1755年[2]；近乎全盲：1766年；出版《刚体运动理论》（Theoria motuum…）
Leonhard Euler: Born: 1707 completes masters in philosophy: 1723 lost vision in right eye: 1735 Solved 7 bridges problem: 1736 publish Introductio in analysin infinitorum, volume 1: 1748 [2] Euler-Bernoulli Beam Theory: 1750 Euler's Formula (geometry): 1750 [1] publish Institutiones calculi differentialis: 1755 [2] near total blindness: 1766 publish Theoria motuum…
……忽略了许多其他函数也恰好具有完全相同零点的问题。但实际上，欧拉在提出这个论点时并不是一直都这么草率的！例如，在他的《无穷分析引论》（Introductio in Analysin Infinitorum）第一卷第九章中（Ian Bruce 的英译本可在 http://www.17centurymaths.com/contents/introductiontoanalysi... 查阅），我们可以看到欧拉在论证乘积公式时指出（用现代符号表示就是）……
…ignoring the problem of the fact that many other functions have precisely the same zeros. But Euler was not, in fact, always so glib in presenting this argument! For example, in Volume 1, Chapter 9 of his Introductio in Analysin Infinitorum (translation by Ian Bruce available at http://www.17centurymaths.com/contents/introductiontoanalysi...), we see that Euler argues for the product formula by noting (what would in modern notation be) that…
我最近才了解到：> 有人声称欧拉恒等式出现在他 1748 年出版的数学分析巨著《无穷分析引论》（Introductio in analysin infinitorum）中。然而，这个特定概念是否能归功于欧拉本人是存疑的，因为他可能从未这样表述过。https://en.m.wikipedia.org/wiki/Euler's_identity 但不管怎么说这依然很酷。……
I recently learned: > It has been claimed that Euler's identity appears in his monumental work of mathematical analysis published in 1748, Introductio in analysin infinitorum. However, it is questionable whether this particular concept can be attributed to Euler himself, as he may never have expressed it. https://en.m.wikipedia.org/wiki/Euler's_identity But it is still cool.…
……说它会“在学习者的灵魂中造成遗忘，因为他们将不再使用记忆”（274e-275b） 2. 莱昂哈德·欧拉批评了在计算中使用对数表的做法：在他 1748 年的《无穷分析引论》（Introductio in analysin infinitorum）中，他坚持要从第一性原理（first principles）推导对数 3. 威廉·汤姆森（开尔文勋爵）最初对机械计算器不屑一顾，他在 1878 年格拉斯哥大学的演讲中表示，它们会……
…said it would "create forgetfulness in the learners' souls, because they will not use their memories" (274e-275b) 2. Leonard Euler criticized the use of logarithm tables in calculating: in his 1748 "Introductio in analysin infinitorum" he insisted on deriving logarithms from first principles 3. William Thomson (Lord Kelvin) initially dismissed mechanical calculators, stating in an 1878 lecture at Glasgow University that they would…