Product Description
Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free.This is an OCR edition with typos.Excerpt from book:THE GREEKS Greek Geometry About the seventh century B. c. an active commercial intercourse sprang up between Greece and Egypt. Naturally there arose an interchange of ideas as well as of merchandise. Greeks, thirsting for knowledge, sought the Egyptian priests for instruction. Thales, Pythagoras, CEnopides, Plato, Democritus, Eudoxus, all visited the land of the pyramids. Egyptian ideas were thus transplanted across the sea and there stimulated Greek thought, directed it into new lines, and gave to it a basis to work upon. Greek culture, therefore, is not primitive. Not only in mathematics, but also in mythology and art, Hellas owes a debt to older countries. To Egypt Greece is indebted, among other things, for its elementary geometry. But this does not lessen our admiration for the Greek mind. From the moment that Hellenic philosophers applied themselves to the study of Egyptian geometry, this science assumed a radically different aspect. "Whatever we Greeks receive, we improve and perfect," says Plato. The Egyptians carried geometry no further than was absolutely necessary for their practical wants. The Greeks, on the other hand, had within them a strong speculative tendency. They felt a craving to discover the reasons for things. They found pleasure in the contemplation of ideal relations, and loved science as science.Our sources of information on the history of Greek geometry before Euclid consist merely of scattered notices in ancient writeis. The early mathematicians, Thales and Pythagoras, left behind no written records of their discoveries. A full history of Greek geometry and astronomy during this period, written by Eudemus, a pupil of Aristotle, has been lost. It was well known to Proclus, who, in his commentaries on Euclid, gives a brief account of it. This abst... ... Read more

Customer Reviews (2)

A History of Mathematics

The Encyclopædia Britannica entry on Florian Cajori says, in part:

Cajori, Florian
born Feb. 28, 1859, St. Aignan, Switz.
died Aug. 14, 1930, Berkeley, Calif., U.S

"Cajori emigrated to the United States in 1875 and taught at Tulane University in New Orleans (1885-88) and at Colorado College (1889-1918), where he also served as dean of the department of engineering (1903-18). In 1918 he became professor of the history of mathematics at the University of California, Berkeley."

Reference: "Cajori, Florian." Encyclopædia Britannica from Encyclopædia Britannica 2006 Ultimate Reference Suite DVD.

The first edition of this History of Mathematics occurred in 1893. Subsequent editions were in 1919, 1980, 1985, and this 5th edition in 1991. Apart from stylistic changes and minor corrections, the main revisions in the 3rd and later editions are said by the editor to be concerned with the eight page chapter on Babylonian mathematics, which was rewritten for the 4th edition and partly rewritten for the 5th. A book of similar title by Cajori, A History of Elementary Mathematics, although based upon this book under review, is a different work.

This is a densely written book, and especially in its later chapters assumes a mathematical background consonant with the period in which it was originally published. This is not a textbook. It is a scholarly discussion on the history of its subject. The historical limit of Cajori's discussion, mentioned in the preface to the 3rd edition and operative still in the current edition, is "the close of World War I." His viewpoint is not that of a modern reader. He is writing during the first blooms of 20th century abstract mathematics. The 1st edition of Whitehead and Russell's Principia Mathematica, which he mentions, occurred over the course of the years 1910 to 1913. The 1st edition of Felix Hausdorff's Grundzüge der Mengenlehre, which he doesn't mention, occurred in 1914. Emmy Noether (1882-1935) didn't arrive at Göttingen until 1915. Bourbaki's first book wasn't published until 1939.

Although Cajori lived until 1930, in revising his book for the 2nd edition (later editions occurred after his death), he could not know where mathematics was going in its methods of abstraction or how educational reforms and popular culture would affect the intellectual background and concerns of future readers, and so he could not write his history to speak to the viewpoint and expectations of a reader in the 21st century. But if you enjoy this sort of thing, this book is worth your attention, regardless of how well you understand everything in it.

The editor of the 3rd edition remarks: "With so vast and complex a subject to set forth within so small a compass, the author of a one-volume history of Mathematics must decide what facts to select, what interrelations to point out, whom to name, how much to explain, and the like. There is no optimum, no one way of doing this. Every one-volume history of mathematics is therefore necessarily very different. Indeed, each of the few that exist are, as the reader can easily verify, strikingly different." (p. iii)

Content may be good but Kindle version is useless
This isn't a proper e-book. It obviously is just a raw OCR scan without any human 'cleaning up'. I feel I should be given a proper copy for my Kindle when it's appropriately formatted. Riddled with misspellings and 'junk'. Especially when dealing with mathematics formatting is key, otherwise the book is unreadable.

Because of this, I am unable to review the actual content of the book. ... Read more

Product Description
Described even today as "unsurpassed," this history of mathematical notation stretching back to the Babylonians and Egyptians is one of the most comprehensive written. In two impressive volumes--first published in 1928-9--distinguished mathematician Florian Cajori shows the origin, evolution, and dissemination of each symbol and the competition it faced in its rise to popularity or fall into obscurity.

Illustrated with more than a hundred diagrams and figures, this "mirror of past and present conditions in mathematics" will give students and historians a whole new appreciation for "1 + 1 = 2."

Swiss-American author, educator, and mathematician FLORIAN CAJORI (1859-1930) was one of the world's most distinguished mathematical historians. Appointed to a specially created chair in the history of mathematics at the University of California, Berkeley, he also wrote An Introduction to the Theory of Equations, A History of Elementary Mathematics, and The Chequered Career of Ferdinand Rudolph Hassler. ... Read more

Customer Reviews (3)

Not quite what I expected, but interesting and thorough
I had been looking for a concise reference for reading modern mathematical and engineering texts.This book is too broad to serve that purpose.

It does do a very thorough job looking at ancient mathematical notation.How the Romans counted, how the Greeks counted, how the Hebrews counted, for example.And it doesn't stop there, it talks about how each civilization changed over time, etc.If you like the History Channel, and you like Math, you'll probably love this book.

I'm still in search of a modern, concise reference for math notations.

Thorough, but stodgy and dated
A thorough review of mathematical notations, I know of no other tome thatcovers this material in the depth that this book uses.However, there arethree improvements that come readily to mind.

1) This book is stodgy,written in a high scholarly style of the late 1920's.This is notsurprising since it _was_ written as a scholarly book in the late 1920's.Still, one could hope for a more accessible reading style. 2) The book isdated, written in the late 1920's.Again, not surprising, but one couldhope for a supplement that would cover the mostly minor changes in notationthat have occurred since then. 3) The book arranges the material only bythe area of mathematics used.When a given symbol has been used in anothersense, the book often but not always covers the other uses of the symbol inquestion. It would be nice if coverage by symbol were consistentlyavailable for _all_ symbols.

In summary, a good book if you need theinformation, but one I would not recommend for casual reading in the areaof mathematics.

The Ultimate Resource For Helpful Mathematical Notations
Notation is so important to mathematics because symbols should be easilywritten to facilitate calculations.This book provides a clear, detailedhistory of the development of mathematical notation, allowing the reader tounderstand the conceptual development of mathematics itself.Especiallyinteresting is its treatment of the development of numerical notationbecause the growth of civilizations has changed it since prehistoric times.Because the notation of newly developed, mathematical subjects is mostlikely to be revised, the historical information provided by this book maybe used to change it.Mathematicians, and enthusiasts of mathematics,should enjoy both perusing the development of this subject and utilizingthe techniques of previous mathematicians to develop their own notation. Also, knowledge of the conceptual or notational history of a subject-whichthis book plentifully provides-enriches one's appreciation andunderstanding of that subject.Finally, this book reveals to its readersthat notation is critical to visualizing mathematical concepts, andconsequentially is central to their development, both of which are valuablelessons. ... Read more

Product Description
Originally published in 1899.This volume from the Cornell University Library's print collections was scanned on an APT BookScan and converted to JPG 2000 format by Kirtas Technologies.All titles scanned cover to cover and pages may include marks notations and other marginalia present in the original volume. ... Read more

Product Description
Described even today as "unsurpassed," this history of mathematical notation stretching back to the Babylonians and Egyptians is one of the most comprehensive written. In two impressive volumes-first published in 1928-9-distinguished mathematician Florian Cajori shows the origin, evolution, and dissemination of each symbol and the competition it faced in its rise to popularity or fall into obscurity. Illustrated with more than a hundred diagrams and figures, this "mirror of past and present conditions in mathematics" will give students and historians a whole new appreciation for "1 + 1 = 2."Swiss-American author, educator, and mathematician FLORIAN CAJORI (1859-1930) was one of the world's most distinguished mathematical historians. Appointed to a specially created chair in the history of mathematics at the University of California, Berkeley, he also wrote An Introduction to the Theory of Equations, A History of Elementary Mathematics, and The Chequered Career of Ferdinand Rudolph Hassler. ... Read more

Product Description
This is a reproduction of a book published before 1923.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process.We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide.We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
Originally published in 1893. PREFACE: AN increased interest in the history of the exact sciences manifested in recent years by teachers everywhere, and the attention given to historical inquiry in the mathematical class-rooms and seminaries of our leading universities, cause me to believe that a brief general History of Mathematics will be found acceptable to teachers and students. The pages treating necessarily in a very condensed form of the progress made during the present century, are put forth with great diffidence, although I have spent much time in the effort to render them accurate and reasonably complete. Many valuable suggestions and criti cisms on the chapter on quot B ecent Times quot have been made by , I r. E. W. Davis, of the University of Nebraska. ...FLORIAN CAJOBL COLORADO COLLEGE, December, 1893. Contents include: PAGE INTRODUCTION 1 , ANTIQUITY 5 THE BABYLONIANS 5 THE EGYPTIANS 9 THE GREEKS 16 Greek Geometry 16 The Ionic School 17 The School of Pythagoras 19 The Sophist School 23 The Platonic School 29 The First Alexandrian School 34 The Second Alexandrian School 54 Greek Arithmetic 63 TUB ROMANS 77 MIDDLE AGES 84 THE HINDOOS 84 THE ARABS 100 EtJBOPE DURING THE MIDDLE AOES 117 Introduction of Roman Mathematics 117 Translation of Arabic Manuscripts 124 The First Awakening and its Sequel 128 MODERN EUROPE 138 THE RENAISSANCE . . . . 189 VIETA TO DJCSOARTES DBSGARTES TO NEWTON 183 NEWTON TO EULER 199 EULER, LAGRANGE, AND LAPLACE 246 The Origin of Modern Geometry 285 RECENT TIMES 291 SYNTHETIC GEOMETRY 293 ANALYTIC GEOMETRY 307 ALGEBRA 315 ANALYSIS 331 THEORY OP FUNCTIONS 347 THEORY OF NUMBERS 362 APPLIED MATHEMATICS 373 INDEX 405 BOOKS OF REFEKENCE. The following books, pamphlets, and articles have been used in the preparation of this history. Reference to any of them is made in the text by giving the respective number. Histories marked with a star are the only ones of which extensive use has been made. 1. GUNTHER, S. Ziele tmd Hesultate der neueren Mathematisch-his torischen JForschung. Erlangen, 1876. 2. CAJTOEI, F. The Teaching and History of Mathematics in the U. S. Washington, 1890. 3. CANToit, MORITZ. Vorlesungen uber Gfeschichte der MathematiJc. Leipzig. Bel I., 1880 Bd. II., 1892. 4. EPPING, J. Astronomisches aus Babylon. Unter Mitwirlcung von P. J. K. STUASSMAIER. Freiburg, 1889. 5. BituTHOHNKiDfflR, C. A. Die Qeometrie und die G-eometer vor Eukli des. Leipzig, 1870. 6. Gow, JAMES. A Short History of Greek Mathematics. Cambridge, 1884. 7. HANKBL, HERMANN. Zur Gfeschichte der MathematiJc im Alterthum und Mittelalter. Leipzig, 1874. 8. ALLMAN, G. J. G-reek G-eometr y from Thales to JEuclid. Dublin, 1889. 9. DB MORGAN, A. quot Euclides quot in Smith s Dictionary of Greek and Itoman Biography and Mythology. 10. ... Read more

Customer Reviews (2)

A History of Mathematics

The Encyclopædia Britannica entry on Florian Cajori says, in part:

Cajori, Florian
born Feb. 28, 1859, St. Aignan, Switz.
died Aug. 14, 1930, Berkeley, Calif., U.S

"Cajori emigrated to the United States in 1875 and taught at Tulane University in New Orleans (1885-88) and at Colorado College (1889-1918), where he also served as dean of the department of engineering (1903-18). In 1918 he became professor of the history of mathematics at the University of California, Berkeley."

Reference: "Cajori, Florian." Encyclopædia Britannica from Encyclopædia Britannica 2006 Ultimate Reference Suite DVD.

The first edition of this History of Mathematics occurred in 1893. Subsequent editions were in 1919, 1980, 1985, and this 5th edition in 1991. Apart from stylistic changes and minor corrections, the main revisions in the 3rd and later editions are said by the editor to be concerned with the eight page chapter on Babylonian mathematics, which was rewritten for the 4th edition and partly rewritten for the 5th. A book of similar title by Cajori, A History of Elementary Mathematics, although based upon this book under review, is a different work.

This is a densely written book, and especially in its later chapters assumes a mathematical background consonant with the period in which it was originally published. This is not a textbook. It is a scholarly discussion on the history of its subject. The historical limit of Cajori's discussion, mentioned in the preface to the 3rd edition and operative still in the current edition, is "the close of World War I." His viewpoint is not that of a modern reader. He is writing during the first blooms of 20th century abstract mathematics. The 1st edition of Whitehead and Russell's Principia Mathematica, which he mentions, occurred over the course of the years 1910 to 1913. The 1st edition of Felix Hausdorff's Grundzüge der Mengenlehre, which he doesn't mention, occurred in 1914. Emmy Noether (1882-1935) didn't arrive at Göttingen until 1915. Bourbaki's first book wasn't published until 1939.

Although Cajori lived until 1930, in revising his book for the 2nd edition (later editions occurred after his death), he could not know where mathematics was going in its methods of abstraction or how educational reforms and popular culture would affect the intellectual background and concerns of future readers, and so he could not write his history to speak to the viewpoint and expectations of a reader in the 21st century. But if you enjoy this sort of thing, this book is worth your attention, regardless of how well you understand everything in it.

The editor of the 3rd edition remarks: "With so vast and complex a subject to set forth within so small a compass, the author of a one-volume history of Mathematics must decide what facts to select, what interrelations to point out, whom to name, how much to explain, and the like. There is no optimum, no one way of doing this. Every one-volume history of mathematics is therefore necessarily very different. Indeed, each of the few that exist are, as the reader can easily verify, strikingly different." (p. iii)

Content may be good but Kindle version is useless
This isn't a proper e-book. It obviously is just a raw OCR scan without any human 'cleaning up'. I feel I should be given a proper copy for my Kindle when it's appropriately formatted. Riddled with misspellings and 'junk'. Especially when dealing with mathematics formatting is key, otherwise the book is unreadable.

Because of this, I am unable to review the actual content of the book. ... Read more

Product Description
Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free.This is an OCR edition with typos.Excerpt from book:THE GREEKS Greek Geometry About the seventh century B. c. an active commercial intercourse sprang up between Greece and Egypt. Naturally there arose an interchange of ideas as well as of merchandise. Greeks, thirsting for knowledge, sought the Egyptian priests for instruction. Thales, Pythagoras, CEnopides, Plato, Democritus, Eudoxus, all visited the land of the pyramids. Egyptian ideas were thus transplanted across the sea and there stimulated Greek thought, directed it into new lines, and gave to it a basis to work upon. Greek culture, therefore, is not primitive. Not only in mathematics, but also in mythology and art, Hellas owes a debt to older countries. To Egypt Greece is indebted, among other things, for its elementary geometry. But this does not lessen our admiration for the Greek mind. From the moment that Hellenic philosophers applied themselves to the study of Egyptian geometry, this science assumed a radically different aspect. "Whatever we Greeks receive, we improve and perfect," says Plato. The Egyptians carried geometry no further than was absolutely necessary for their practical wants. The Greeks, on the other hand, had within them a strong speculative tendency. They felt a craving to discover the reasons for things. They found pleasure in the contemplation of ideal relations, and loved science as science.Our sources of information on the history of Greek geometry before Euclid consist merely of scattered notices in ancient writeis. The early mathematicians, Thales and Pythagoras, left behind no written records of their discoveries. A full history of Greek geometry and astronomy during this period, written by Eudemus, a pupil of Aristotle, has been lost. It was well known to Proclus, who, in his commentaries on Euclid, gives a brief account of it. This abst... ... Read more

Customer Reviews (2)

A History of Mathematics

The Encyclopædia Britannica entry on Florian Cajori says, in part:

Cajori, Florian
born Feb. 28, 1859, St. Aignan, Switz.
died Aug. 14, 1930, Berkeley, Calif., U.S

"Cajori emigrated to the United States in 1875 and taught at Tulane University in New Orleans (1885-88) and at Colorado College (1889-1918), where he also served as dean of the department of engineering (1903-18). In 1918 he became professor of the history of mathematics at the University of California, Berkeley."

Reference: "Cajori, Florian." Encyclopædia Britannica from Encyclopædia Britannica 2006 Ultimate Reference Suite DVD.

The first edition of this History of Mathematics occurred in 1893. Subsequent editions were in 1919, 1980, 1985, and this 5th edition in 1991. Apart from stylistic changes and minor corrections, the main revisions in the 3rd and later editions are said by the editor to be concerned with the eight page chapter on Babylonian mathematics, which was rewritten for the 4th edition and partly rewritten for the 5th. A book of similar title by Cajori, A History of Elementary Mathematics, although based upon this book under review, is a different work.

This is a densely written book, and especially in its later chapters assumes a mathematical background consonant with the period in which it was originally published. This is not a textbook. It is a scholarly discussion on the history of its subject. The historical limit of Cajori's discussion, mentioned in the preface to the 3rd edition and operative still in the current edition, is "the close of World War I." His viewpoint is not that of a modern reader. He is writing during the first blooms of 20th century abstract mathematics. The 1st edition of Whitehead and Russell's Principia Mathematica, which he mentions, occurred over the course of the years 1910 to 1913. The 1st edition of Felix Hausdorff's Grundzüge der Mengenlehre, which he doesn't mention, occurred in 1914. Emmy Noether (1882-1935) didn't arrive at Göttingen until 1915. Bourbaki's first book wasn't published until 1939.

Although Cajori lived until 1930, in revising his book for the 2nd edition (later editions occurred after his death), he could not know where mathematics was going in its methods of abstraction or how educational reforms and popular culture would affect the intellectual background and concerns of future readers, and so he could not write his history to speak to the viewpoint and expectations of a reader in the 21st century. But if you enjoy this sort of thing, this book is worth your attention, regardless of how well you understand everything in it.

The editor of the 3rd edition remarks: "With so vast and complex a subject to set forth within so small a compass, the author of a one-volume history of Mathematics must decide what facts to select, what interrelations to point out, whom to name, how much to explain, and the like. There is no optimum, no one way of doing this. Every one-volume history of mathematics is therefore necessarily very different. Indeed, each of the few that exist are, as the reader can easily verify, strikingly different." (p. iii)

Content may be good but Kindle version is useless
This isn't a proper e-book. It obviously is just a raw OCR scan without any human 'cleaning up'. I feel I should be given a proper copy for my Kindle when it's appropriately formatted. Riddled with misspellings and 'junk'. Especially when dealing with mathematics formatting is key, otherwise the book is unreadable.

Because of this, I am unable to review the actual content of the book. ... Read more

Product Description
This scarce antiquarian book is a selection from Kessinger Publishings Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the worlds literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

Product Description
Originally published in 1897.This volume from the Cornell University Library's print collections was scanned on an APT BookScan and converted to JPG 2000 format by Kirtas Technologies.All titles scanned cover to cover and pages may include marks notations and other marginalia present in the original volume. ... Read more

Customer Reviews (1)

Good old book
This is a good old book on the history of elementary mathematics, written by a distinguished scholar. Historians should certainly buy this book on behalf of the author's name, but newcomers shouldn't rely on it alone. Katz is a modern and reliable alternative, based on new research. Nonetheless, it's possible to learn much from this book, and you won't regret of purchasing it. ... Read more

Product Description
Originally published in 1896.This volume from the Cornell University Library's print collections was scanned on an APT BookScan and converted to JPG 2000 format by Kirtas Technologies.All titles scanned cover to cover and pages may include marks notations and other marginalia present in the original volume. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
Publisher: New York, MacmillanPublication date: 1915Subjects: ArithmeticNotes: This is an OCR reprint. There may be typos or missing text. There are no illustrations or indexes.When you buy the General Books edition of this book you get free trial access to Million-Books.com where you can select from more than a million books for free. You can also preview the book there. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is a reproduction of a book published before 1923.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process.We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide.We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more