出版社: Dover Publications
副标题: Fourth Revised Edition
出版年: 19870801
页数: 256
定价: USD 9.95
装帧: Paperback
ISBN: 9780486602554
内容简介 · · · · · ·
Revised 4th edition covers major mathematical ideas and techniques from ancient Near East to 20thcentury computer theory. Work of Archimedes, Pascal, Gauss, Hilbert, etc.
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读书笔记 · · · · · ·
我来写笔记
好养活 (Till then I walk along.)
It is difficult to date new discoveries in the East. The static character of its social structure had tended to preserve scientific lore throughout centuries or even millennia. Discoveries made within the seclusion of a township may never have spread to other localities. Storages of scientific and technical knowledge have been destroyed by dynastic changes, wars, or floods. There is a story that i...20150927 14:52
其实焚书焚的主要是humanities，science方面的相对损失较少。因为一统后数年，有官员建议重新实施分封制和之前的礼乐制度。为了彻底否定这一提案，秦始皇就把那些人文礼乐的书全毁了。。。（以上基本是钱穆先生的分析~）Egyptian, 3000 B.C. and earlier years: The Papyrus ( 85 problems, also the root of “paper”) and the socalled Moscow Papyrus (perhaps two centuries older and 25 problems); To reduce all multiplication to repeated additions (e.g. 13*11=1*11+4*11+8*11); 2/n=1/a+1/b+1/c+…; Ahacalculus;.Mesopotamian, c.2100 B.C.:Sexagesimal system; 60^(n).Babylonian, c.1750 B.C.:A wellestablished algebra; Linear and quadratic equations in two variables, or even higher dimension; 1000 is written as (16,40) and 900 as (15,0)… (WHY?!!!); Babylonian astronomy (seventeen sexagesimal places…); x^3+x^2=a, which calls for the solution of xyz+xy=1+1/6, y=2/3*x, z=12*x);P31It is difficult to date new discoveries in the East. The static character of its social structure had tended to preserve scientific lore throughout centuries or even millennia. Discoveries made within the seclusion of a township may never have spread to other localities. Storages of scientific and technical knowledge have been destroyed by dynastic changes, wars, or floods. There is a story that in 221 B.C., when China was united under one absolute despot, Shi Huangdi, he ordered all books of learning to be destroyed. Later many of them were rewritten partly from memory, but such events make the dating of discoveries very difficult.
To most of the people, they’ve no need to know the deduction and demonstration (+,,*,/ and some rules are enough for their daily life). Therefore, the demonstrations are only showed to the professional staff engaged in research, such as the priest, the scholar and mathmajor guys…（农耕社会）P33Nowhere in all ancient Oriental mathematics do we find any attempt at what we call a demonstration. No argumentation was presented, but only the prescription o certain rules:“Do such, do so.”We are ignorant of the way in which the theorems were found: for instance, how did the Babylonians become acquainted with the theorem of Pythagoras? Several attempts exist to explain the way in which Egyptians and Babylonians obtained their results, but they are all of a hypothetical nature. To those who have been educated in Euclid’s strict argumentation, the entire Oriental way of reasoning seems at first strange and highly unsatisfactory. But the strangeness wears off when we realize that most of the mathematics we teach out presentday engineers and technicians is still of the “do such, do so”type, without much attempt at rigorous demonstration. Algebra os still being taught in many high school as a set of rules rather than a science of deduction. Oriental mathematics, in this respect, never seems to have been emancipated from the millennial influence of the problems in technology and administration, for the use of which it had been invented.
唐代过后，五代十国动乱，宋朝贫弱（冗兵冗吏，重文轻武，科举自宋始成为唯一的入仕途径），元清异族统治，明朝理学盛兴（why？经历元朝之后对儒学的矫枉过正？），民间温饱都成问题，自然难以有数学新发现…………然后唐代中前期人民生活过于富足，沉溺于享乐无心学术，安史之乱后则是无力学术。所以古代中国的数学发展主要还是集中于贵族制度未衰的春秋秦汉？？？（吃饱了撑着才能有心学术——之类的。。。）Chinese mathematics is in the exceptional position that its traditional has remained practically unbroken until recent years, so that we can study its position in the community somewhat better than that of Egyptian and Babylonian mathematics, which belonged to vanished civilizations. We know, for instance, that candidates for examination had to display a precisely circumscribes knowledge of the classics, and that this examination was based mainly on the ability to cite texts correctly from memory. The traditional lore was thus transmitted from generation to generation with painful conscientiousness. In such a stagnant cultural atmosphere new discoveries became extraordinary exception. Such a traditional might be transmitted over millennia, only occasionally shaken by great historical catastrophes.
回应 20150927 14:52 
好养活 (Till then I walk along.)
Our first conceptions of numbers and form date back to times as far removed as the Old State Age, the Paleolithic. Throughout the hundreds or more millennia of the period men lived in small groups, under conditions differing little from those of animals, and their main energies were directly toward the elementary process of collecting food wherever they could get it. They made weapons for huntin...20150924 12:38
Mathematically speaking……就是喜欢这样话锋一转的一句话总结233（才没有十指交叉眼镜反光的MADAO什么的呢LOL）P10Our first conceptions of numbers and form date back to times as far removed as the Old State Age, the Paleolithic. Throughout the hundreds or more millennia of the period men lived in small groups, under conditions differing little from those of animals, and their main energies were directly toward the elementary process of collecting food wherever they could get it. They made weapons for hunting and fishing, developed a language to communicate with each other, and in later paleolithic times enriched their lives with creative art forms, including statuettes and paintings. The painting in caves of France and Spain (over 15,000 years old) may have had some ritual significance; certainly they reveal a remarkable understanding of form; mathematically speaking, they reveal understanding of twodimensional mapping of object in space.
窝草这是要兼修人类史和语言学的节奏吗哈哈哈……PS. 不知道这里qualitative和quantitative有没有写反……PSS. 为什么5不是1+4？？P11Numerical terms — expressing some of “the most abstract ideas which the human mind is capable of forming,” as Adam Smith has said — came only slowly into use. Their first occurrence was qualitative rather than quantitative, making a distinction only between one (or better “a” — “a man,” rather than “one man”) and two and many. In the old Fiji Island language ten boats are called bola, ten coconuts koro, and a thousand coconuts saloro. The ancient qualitative origin of numerical conceptions can still be detected in the special dual terms existing in certain languages such as Greek and Celtic. When the number concept was extended, higher numbers were first formed by addition: 3 by adding 2 and 1, 4 by adding 2 and 2, 5 by adding 2 and 3. Here is an example from some Australian peoples: Murray River: 1 = enea, 2 = petcheval, 3 = petchevalenea, 4 = petcheval petcheval Kamilaroi: 1 = mal, 2 = bulan, 3 = guliba, 4 = bulan bulan, 5 = bulan guliba, 6 = guliba guliba.
Really an interesting phenomenon worth thinking (⊙o⊙)PS. 最后一句莫名喜感……LOLPPS. I love small prime numbers…………End of 1.2P11A curious phenomenon was the love of very large numbers, a love perhaps stimulated by the alltoohuman desire to exaggerate the extent of herds of enemies slain; remnants of this tendency appear in the Bible and in other scared and notsoscared writings.
如果能这样记单词的话绝对事半功倍。。（所以straight, stretch和rope是肿么联系起来的？？QUQP14It also became necessary to measure the length and contents of objects. The standards were rough and often taken from parts of the human body, and in this way units such as fingers, feet, or hands originated. The names “ell,” “fathom,” and “cubit” remind us also of this custom. When house were built, as among the agriculture Indians or the polehouse dwellers of Central Europe, rules were laid down for building along straight line and at right angles. The word “straight” is related to “stretch,” indicating operations with a rope; the word “line” to “linen,” showing the connection between the craft of weaving and the beginning of geometry. This was one way in which interest in mensuration evolved.
End of 1.3.P15“Modern” numerology is a leftover from magical rites dating back to neolithic, and perhaps even to paleolithic, times.
So cute…… LOLThese few illustrations of the beginnings of mathematics show that the historical growth of a science does not necessarily pass through the stages in which we now develop it in our instruction. Some of the oldest geometrical forms known to mankind, such as knots and patterns, only received full scientific attention in recent years. On the other hand, some of our more elementary branches of mathematics, such as the graphical representation or elementary statistics, date back to comparatively modern time. As A. Speiser has remarked with some asperity (and some exaggeration): Already the pronounced tendency toward tediousness, which seems to be inherent in elementary mathematics, might plead for its late origin, since the creative mathematics would prefer to pay his attention to the interesting and beautiful problems.[13] [13] This is a witty remark, but “elementary mathematics,” taught by a good instructor, need not be tedious at all. And do not the regular polyhedra and the golden section, which have excited people from Plato to the present, belong to “elementary mathematics”?
回应 20150924 12:38 
好养活 (Till then I walk along.)
The selection of the material was, of course, not based exclusively on objective factors, but was influenced by the authorâ€™s likes and dislikes, his knowledge and ignorance. As to his ignorance, it was not always possible to consult all sources firsthand; toooften, second or even thirdhand sources had to be used. It is therefore good advise, not only with respect to this book, but with respec...20150924 12:03
The selection of the material was, of course, not based exclusively on objective factors, but was influenced by the author’s likes and dislikes, his knowledge and ignorance. As to his ignorance, it was not always possible to consult all sources firsthand; toooften, second or even thirdhand sources had to be used. It is therefore good advise, not only with respect to this book, but with respect to all such histories, to check the statements as much as possible with the original sources. This is a good principle for more than one reason. Our knowledge of authors such as Euclid, Diophantus, Descartes, Laplace, Gauss, or Riemann should not be obtained exclusively from quotations or histories describing their works. There is the same invigorating power in the original Euclid or Gauss as there is in the original Shakespeare, and there are places in Archimedes, in Fermat, or in Jacobi which are as beautiful as Horace or Emerson.
回应 20150924 12:03

好养活 (Till then I walk along.)
The selection of the material was, of course, not based exclusively on objective factors, but was influenced by the authorâ€™s likes and dislikes, his knowledge and ignorance. As to his ignorance, it was not always possible to consult all sources firsthand; toooften, second or even thirdhand sources had to be used. It is therefore good advise, not only with respect to this book, but with respec...20150924 12:03
The selection of the material was, of course, not based exclusively on objective factors, but was influenced by the author’s likes and dislikes, his knowledge and ignorance. As to his ignorance, it was not always possible to consult all sources firsthand; toooften, second or even thirdhand sources had to be used. It is therefore good advise, not only with respect to this book, but with respect to all such histories, to check the statements as much as possible with the original sources. This is a good principle for more than one reason. Our knowledge of authors such as Euclid, Diophantus, Descartes, Laplace, Gauss, or Riemann should not be obtained exclusively from quotations or histories describing their works. There is the same invigorating power in the original Euclid or Gauss as there is in the original Shakespeare, and there are places in Archimedes, in Fermat, or in Jacobi which are as beautiful as Horace or Emerson.
回应 20150924 12:03 
好养活 (Till then I walk along.)
Our first conceptions of numbers and form date back to times as far removed as the Old State Age, the Paleolithic. Throughout the hundreds or more millennia of the period men lived in small groups, under conditions differing little from those of animals, and their main energies were directly toward the elementary process of collecting food wherever they could get it. They made weapons for huntin...20150924 12:38
Mathematically speaking……就是喜欢这样话锋一转的一句话总结233（才没有十指交叉眼镜反光的MADAO什么的呢LOL）P10Our first conceptions of numbers and form date back to times as far removed as the Old State Age, the Paleolithic. Throughout the hundreds or more millennia of the period men lived in small groups, under conditions differing little from those of animals, and their main energies were directly toward the elementary process of collecting food wherever they could get it. They made weapons for hunting and fishing, developed a language to communicate with each other, and in later paleolithic times enriched their lives with creative art forms, including statuettes and paintings. The painting in caves of France and Spain (over 15,000 years old) may have had some ritual significance; certainly they reveal a remarkable understanding of form; mathematically speaking, they reveal understanding of twodimensional mapping of object in space.
窝草这是要兼修人类史和语言学的节奏吗哈哈哈……PS. 不知道这里qualitative和quantitative有没有写反……PSS. 为什么5不是1+4？？P11Numerical terms — expressing some of “the most abstract ideas which the human mind is capable of forming,” as Adam Smith has said — came only slowly into use. Their first occurrence was qualitative rather than quantitative, making a distinction only between one (or better “a” — “a man,” rather than “one man”) and two and many. In the old Fiji Island language ten boats are called bola, ten coconuts koro, and a thousand coconuts saloro. The ancient qualitative origin of numerical conceptions can still be detected in the special dual terms existing in certain languages such as Greek and Celtic. When the number concept was extended, higher numbers were first formed by addition: 3 by adding 2 and 1, 4 by adding 2 and 2, 5 by adding 2 and 3. Here is an example from some Australian peoples: Murray River: 1 = enea, 2 = petcheval, 3 = petchevalenea, 4 = petcheval petcheval Kamilaroi: 1 = mal, 2 = bulan, 3 = guliba, 4 = bulan bulan, 5 = bulan guliba, 6 = guliba guliba.
Really an interesting phenomenon worth thinking (⊙o⊙)PS. 最后一句莫名喜感……LOLPPS. I love small prime numbers…………End of 1.2P11A curious phenomenon was the love of very large numbers, a love perhaps stimulated by the alltoohuman desire to exaggerate the extent of herds of enemies slain; remnants of this tendency appear in the Bible and in other scared and notsoscared writings.
如果能这样记单词的话绝对事半功倍。。（所以straight, stretch和rope是肿么联系起来的？？QUQP14It also became necessary to measure the length and contents of objects. The standards were rough and often taken from parts of the human body, and in this way units such as fingers, feet, or hands originated. The names “ell,” “fathom,” and “cubit” remind us also of this custom. When house were built, as among the agriculture Indians or the polehouse dwellers of Central Europe, rules were laid down for building along straight line and at right angles. The word “straight” is related to “stretch,” indicating operations with a rope; the word “line” to “linen,” showing the connection between the craft of weaving and the beginning of geometry. This was one way in which interest in mensuration evolved.
End of 1.3.P15“Modern” numerology is a leftover from magical rites dating back to neolithic, and perhaps even to paleolithic, times.
So cute…… LOLThese few illustrations of the beginnings of mathematics show that the historical growth of a science does not necessarily pass through the stages in which we now develop it in our instruction. Some of the oldest geometrical forms known to mankind, such as knots and patterns, only received full scientific attention in recent years. On the other hand, some of our more elementary branches of mathematics, such as the graphical representation or elementary statistics, date back to comparatively modern time. As A. Speiser has remarked with some asperity (and some exaggeration): Already the pronounced tendency toward tediousness, which seems to be inherent in elementary mathematics, might plead for its late origin, since the creative mathematics would prefer to pay his attention to the interesting and beautiful problems.[13] [13] This is a witty remark, but “elementary mathematics,” taught by a good instructor, need not be tedious at all. And do not the regular polyhedra and the golden section, which have excited people from Plato to the present, belong to “elementary mathematics”?
回应 20150924 12:38 
好养活 (Till then I walk along.)
It is difficult to date new discoveries in the East. The static character of its social structure had tended to preserve scientific lore throughout centuries or even millennia. Discoveries made within the seclusion of a township may never have spread to other localities. Storages of scientific and technical knowledge have been destroyed by dynastic changes, wars, or floods. There is a story that i...20150927 14:52
其实焚书焚的主要是humanities，science方面的相对损失较少。因为一统后数年，有官员建议重新实施分封制和之前的礼乐制度。为了彻底否定这一提案，秦始皇就把那些人文礼乐的书全毁了。。。（以上基本是钱穆先生的分析~）Egyptian, 3000 B.C. and earlier years: The Papyrus ( 85 problems, also the root of “paper”) and the socalled Moscow Papyrus (perhaps two centuries older and 25 problems); To reduce all multiplication to repeated additions (e.g. 13*11=1*11+4*11+8*11); 2/n=1/a+1/b+1/c+…; Ahacalculus;.Mesopotamian, c.2100 B.C.:Sexagesimal system; 60^(n).Babylonian, c.1750 B.C.:A wellestablished algebra; Linear and quadratic equations in two variables, or even higher dimension; 1000 is written as (16,40) and 900 as (15,0)… (WHY?!!!); Babylonian astronomy (seventeen sexagesimal places…); x^3+x^2=a, which calls for the solution of xyz+xy=1+1/6, y=2/3*x, z=12*x);P31It is difficult to date new discoveries in the East. The static character of its social structure had tended to preserve scientific lore throughout centuries or even millennia. Discoveries made within the seclusion of a township may never have spread to other localities. Storages of scientific and technical knowledge have been destroyed by dynastic changes, wars, or floods. There is a story that in 221 B.C., when China was united under one absolute despot, Shi Huangdi, he ordered all books of learning to be destroyed. Later many of them were rewritten partly from memory, but such events make the dating of discoveries very difficult.
To most of the people, they’ve no need to know the deduction and demonstration (+,,*,/ and some rules are enough for their daily life). Therefore, the demonstrations are only showed to the professional staff engaged in research, such as the priest, the scholar and mathmajor guys…（农耕社会）P33Nowhere in all ancient Oriental mathematics do we find any attempt at what we call a demonstration. No argumentation was presented, but only the prescription o certain rules:“Do such, do so.”We are ignorant of the way in which the theorems were found: for instance, how did the Babylonians become acquainted with the theorem of Pythagoras? Several attempts exist to explain the way in which Egyptians and Babylonians obtained their results, but they are all of a hypothetical nature. To those who have been educated in Euclid’s strict argumentation, the entire Oriental way of reasoning seems at first strange and highly unsatisfactory. But the strangeness wears off when we realize that most of the mathematics we teach out presentday engineers and technicians is still of the “do such, do so”type, without much attempt at rigorous demonstration. Algebra os still being taught in many high school as a set of rules rather than a science of deduction. Oriental mathematics, in this respect, never seems to have been emancipated from the millennial influence of the problems in technology and administration, for the use of which it had been invented.
唐代过后，五代十国动乱，宋朝贫弱（冗兵冗吏，重文轻武，科举自宋始成为唯一的入仕途径），元清异族统治，明朝理学盛兴（why？经历元朝之后对儒学的矫枉过正？），民间温饱都成问题，自然难以有数学新发现…………然后唐代中前期人民生活过于富足，沉溺于享乐无心学术，安史之乱后则是无力学术。所以古代中国的数学发展主要还是集中于贵族制度未衰的春秋秦汉？？？（吃饱了撑着才能有心学术——之类的。。。）Chinese mathematics is in the exceptional position that its traditional has remained practically unbroken until recent years, so that we can study its position in the community somewhat better than that of Egyptian and Babylonian mathematics, which belonged to vanished civilizations. We know, for instance, that candidates for examination had to display a precisely circumscribes knowledge of the classics, and that this examination was based mainly on the ability to cite texts correctly from memory. The traditional lore was thus transmitted from generation to generation with painful conscientiousness. In such a stagnant cultural atmosphere new discoveries became extraordinary exception. Such a traditional might be transmitted over millennia, only occasionally shaken by great historical catastrophes.
回应 20150927 14:52

好养活 (Till then I walk along.)
It is difficult to date new discoveries in the East. The static character of its social structure had tended to preserve scientific lore throughout centuries or even millennia. Discoveries made within the seclusion of a township may never have spread to other localities. Storages of scientific and technical knowledge have been destroyed by dynastic changes, wars, or floods. There is a story that i...20150927 14:52
其实焚书焚的主要是humanities，science方面的相对损失较少。因为一统后数年，有官员建议重新实施分封制和之前的礼乐制度。为了彻底否定这一提案，秦始皇就把那些人文礼乐的书全毁了。。。（以上基本是钱穆先生的分析~）Egyptian, 3000 B.C. and earlier years: The Papyrus ( 85 problems, also the root of “paper”) and the socalled Moscow Papyrus (perhaps two centuries older and 25 problems); To reduce all multiplication to repeated additions (e.g. 13*11=1*11+4*11+8*11); 2/n=1/a+1/b+1/c+…; Ahacalculus;.Mesopotamian, c.2100 B.C.:Sexagesimal system; 60^(n).Babylonian, c.1750 B.C.:A wellestablished algebra; Linear and quadratic equations in two variables, or even higher dimension; 1000 is written as (16,40) and 900 as (15,0)… (WHY?!!!); Babylonian astronomy (seventeen sexagesimal places…); x^3+x^2=a, which calls for the solution of xyz+xy=1+1/6, y=2/3*x, z=12*x);P31It is difficult to date new discoveries in the East. The static character of its social structure had tended to preserve scientific lore throughout centuries or even millennia. Discoveries made within the seclusion of a township may never have spread to other localities. Storages of scientific and technical knowledge have been destroyed by dynastic changes, wars, or floods. There is a story that in 221 B.C., when China was united under one absolute despot, Shi Huangdi, he ordered all books of learning to be destroyed. Later many of them were rewritten partly from memory, but such events make the dating of discoveries very difficult.
To most of the people, they’ve no need to know the deduction and demonstration (+,,*,/ and some rules are enough for their daily life). Therefore, the demonstrations are only showed to the professional staff engaged in research, such as the priest, the scholar and mathmajor guys…（农耕社会）P33Nowhere in all ancient Oriental mathematics do we find any attempt at what we call a demonstration. No argumentation was presented, but only the prescription o certain rules:“Do such, do so.”We are ignorant of the way in which the theorems were found: for instance, how did the Babylonians become acquainted with the theorem of Pythagoras? Several attempts exist to explain the way in which Egyptians and Babylonians obtained their results, but they are all of a hypothetical nature. To those who have been educated in Euclid’s strict argumentation, the entire Oriental way of reasoning seems at first strange and highly unsatisfactory. But the strangeness wears off when we realize that most of the mathematics we teach out presentday engineers and technicians is still of the “do such, do so”type, without much attempt at rigorous demonstration. Algebra os still being taught in many high school as a set of rules rather than a science of deduction. Oriental mathematics, in this respect, never seems to have been emancipated from the millennial influence of the problems in technology and administration, for the use of which it had been invented.
唐代过后，五代十国动乱，宋朝贫弱（冗兵冗吏，重文轻武，科举自宋始成为唯一的入仕途径），元清异族统治，明朝理学盛兴（why？经历元朝之后对儒学的矫枉过正？），民间温饱都成问题，自然难以有数学新发现…………然后唐代中前期人民生活过于富足，沉溺于享乐无心学术，安史之乱后则是无力学术。所以古代中国的数学发展主要还是集中于贵族制度未衰的春秋秦汉？？？（吃饱了撑着才能有心学术——之类的。。。）Chinese mathematics is in the exceptional position that its traditional has remained practically unbroken until recent years, so that we can study its position in the community somewhat better than that of Egyptian and Babylonian mathematics, which belonged to vanished civilizations. We know, for instance, that candidates for examination had to display a precisely circumscribes knowledge of the classics, and that this examination was based mainly on the ability to cite texts correctly from memory. The traditional lore was thus transmitted from generation to generation with painful conscientiousness. In such a stagnant cultural atmosphere new discoveries became extraordinary exception. Such a traditional might be transmitted over millennia, only occasionally shaken by great historical catastrophes.
回应 20150927 14:52 
好养活 (Till then I walk along.)
Our first conceptions of numbers and form date back to times as far removed as the Old State Age, the Paleolithic. Throughout the hundreds or more millennia of the period men lived in small groups, under conditions differing little from those of animals, and their main energies were directly toward the elementary process of collecting food wherever they could get it. They made weapons for huntin...20150924 12:38
Mathematically speaking……就是喜欢这样话锋一转的一句话总结233（才没有十指交叉眼镜反光的MADAO什么的呢LOL）P10Our first conceptions of numbers and form date back to times as far removed as the Old State Age, the Paleolithic. Throughout the hundreds or more millennia of the period men lived in small groups, under conditions differing little from those of animals, and their main energies were directly toward the elementary process of collecting food wherever they could get it. They made weapons for hunting and fishing, developed a language to communicate with each other, and in later paleolithic times enriched their lives with creative art forms, including statuettes and paintings. The painting in caves of France and Spain (over 15,000 years old) may have had some ritual significance; certainly they reveal a remarkable understanding of form; mathematically speaking, they reveal understanding of twodimensional mapping of object in space.
窝草这是要兼修人类史和语言学的节奏吗哈哈哈……PS. 不知道这里qualitative和quantitative有没有写反……PSS. 为什么5不是1+4？？P11Numerical terms — expressing some of “the most abstract ideas which the human mind is capable of forming,” as Adam Smith has said — came only slowly into use. Their first occurrence was qualitative rather than quantitative, making a distinction only between one (or better “a” — “a man,” rather than “one man”) and two and many. In the old Fiji Island language ten boats are called bola, ten coconuts koro, and a thousand coconuts saloro. The ancient qualitative origin of numerical conceptions can still be detected in the special dual terms existing in certain languages such as Greek and Celtic. When the number concept was extended, higher numbers were first formed by addition: 3 by adding 2 and 1, 4 by adding 2 and 2, 5 by adding 2 and 3. Here is an example from some Australian peoples: Murray River: 1 = enea, 2 = petcheval, 3 = petchevalenea, 4 = petcheval petcheval Kamilaroi: 1 = mal, 2 = bulan, 3 = guliba, 4 = bulan bulan, 5 = bulan guliba, 6 = guliba guliba.
Really an interesting phenomenon worth thinking (⊙o⊙)PS. 最后一句莫名喜感……LOLPPS. I love small prime numbers…………End of 1.2P11A curious phenomenon was the love of very large numbers, a love perhaps stimulated by the alltoohuman desire to exaggerate the extent of herds of enemies slain; remnants of this tendency appear in the Bible and in other scared and notsoscared writings.
如果能这样记单词的话绝对事半功倍。。（所以straight, stretch和rope是肿么联系起来的？？QUQP14It also became necessary to measure the length and contents of objects. The standards were rough and often taken from parts of the human body, and in this way units such as fingers, feet, or hands originated. The names “ell,” “fathom,” and “cubit” remind us also of this custom. When house were built, as among the agriculture Indians or the polehouse dwellers of Central Europe, rules were laid down for building along straight line and at right angles. The word “straight” is related to “stretch,” indicating operations with a rope; the word “line” to “linen,” showing the connection between the craft of weaving and the beginning of geometry. This was one way in which interest in mensuration evolved.
End of 1.3.P15“Modern” numerology is a leftover from magical rites dating back to neolithic, and perhaps even to paleolithic, times.
So cute…… LOLThese few illustrations of the beginnings of mathematics show that the historical growth of a science does not necessarily pass through the stages in which we now develop it in our instruction. Some of the oldest geometrical forms known to mankind, such as knots and patterns, only received full scientific attention in recent years. On the other hand, some of our more elementary branches of mathematics, such as the graphical representation or elementary statistics, date back to comparatively modern time. As A. Speiser has remarked with some asperity (and some exaggeration): Already the pronounced tendency toward tediousness, which seems to be inherent in elementary mathematics, might plead for its late origin, since the creative mathematics would prefer to pay his attention to the interesting and beautiful problems.[13] [13] This is a witty remark, but “elementary mathematics,” taught by a good instructor, need not be tedious at all. And do not the regular polyhedra and the golden section, which have excited people from Plato to the present, belong to “elementary mathematics”?
回应 20150924 12:38 
好养活 (Till then I walk along.)
The selection of the material was, of course, not based exclusively on objective factors, but was influenced by the authorâ€™s likes and dislikes, his knowledge and ignorance. As to his ignorance, it was not always possible to consult all sources firsthand; toooften, second or even thirdhand sources had to be used. It is therefore good advise, not only with respect to this book, but with respec...20150924 12:03
The selection of the material was, of course, not based exclusively on objective factors, but was influenced by the author’s likes and dislikes, his knowledge and ignorance. As to his ignorance, it was not always possible to consult all sources firsthand; toooften, second or even thirdhand sources had to be used. It is therefore good advise, not only with respect to this book, but with respect to all such histories, to check the statements as much as possible with the original sources. This is a good principle for more than one reason. Our knowledge of authors such as Euclid, Diophantus, Descartes, Laplace, Gauss, or Riemann should not be obtained exclusively from quotations or histories describing their works. There is the same invigorating power in the original Euclid or Gauss as there is in the original Shakespeare, and there are places in Archimedes, in Fermat, or in Jacobi which are as beautiful as Horace or Emerson.
回应 20150924 12:03
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