Book Description

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

Book Description
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. The proof-shoots o f this chapter have also been submitted to Dr. J. E. Davies and Professor C. A. Van Velzer, both of the University of Wisconsin to Dr. G-. B. Halsted, of the University of Texas Professor L. M. HosMns, of the Leland Stanford Jr. University and Professor Gr. D. Olds, of Amherst College, all of whom have afforded valuable assistance. 1 am specially indebted to Professor 3T. H. Loud, of Colorado College, who has read the proof-sheets throughout. To all the gentlemen above named, as well as to Dr. Carlo Veneziani v vi PKEFACE. of Salt Lake City, who read the first part of my work in. manuscript, I desire to express my hearty thanks. But in acknowledging their kindness, I trust that I shall not seem to lay upon them any share in the responsibility for errors which I may have introduced in subsequent revision of the FLORIAN CAJOBL COLORADO COLLEGE, December, 1893. TABLE OF CONTENTS. 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 NBWTGN TO EULBK 199 vii Viii TABLE OF CONTENTS. PAGE EULER, LAGRANGE, AND LAPLACE 246 The Origin of Modern Geometry 285 KECENT 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. HANKBL, HERMANN... ... Read more

Book 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

Book Description
Written as a teaching aid for graduate and undergraduate math students, Florian Cajori's comprehensive 1896 survey of mathematics from Babylonian to modern times makes for a fascinating read. (Did you know that the decimal system is based on our having ten fingers and toes?) Beginning with the number systems of antiquity, continuing through the Hindu and Arabic influence on medieval thought, and concluding with an overview of trends in modern mathematical teaching, this is an invaluable work not only for students and educators but for readers of the history of human thought as well. 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 Mathematical Notations, and The Chequered Career of Ferdinand Rudolph Hassler. ... Read more

Customer Reviews (1)

long out of print
Dover has done historians and students of mathematics a favour by publishing this long out of print text, from 1917. It was a seminal study of how mathematics developed in the ancient world. Cajori focused on the classical realm of the Mediterranean world. But then also in more recent times, when Europe was in its Dark Ages. He explains how the Arabs and Indians gave their contributions. Especially the role of the Arabs in, albeit inadvertantly, nurturing the maths knowledge painfully accrued in past millenia.

Unlike recent texts, there are no snazzy diagrams or whatnot to enliven the narrative. Figures in books were very expensive to arrange in the 1910s. But the writing itself remains lucid. ... Read more

Book Description
A HISTORY OF MATHEMATICAL NOTATIONS BY FLORIAN CAJORJ H. D. Professor of the History of Mathematics University of California VOLUME 1 NOTATIONS IN ELEMENTARY MATHEMATICSPREFACE The study of the history of mathematical notations was sug gested to me by Professor E. H. Moore, of the University of Chicago. To him and to Professor M. W. Haskell, of the University of California, I am indebted for encouragement in the pursuit of this research. As completed in August, 1925, the present history was intended to be brought out in one volume. To Professor H. E. Slaught, of the Uni versity of Chicago, I owe the suggestion that the work be divided into two volumes, of which the first should limit itself to the history of symbols in elementary mathematics, since such a volume would ap peal to a wider constituency of readers than would be the case with the part on symbols in higher mathematics. To Professor Slaught I also owe generous and vital assistance in many other ways. He exam ined the entire manuscript of this work in detail, and brought it to the sympathetic attention of the Open Court Publishing Company. I desire to record my gratitude to Mrs. Mary Hegeler Carus, president of the Open Court Publishing Company, for undertaking this expen sive publication from which no financial profits can be expected to accrue. I gratefully acknowledge the assistance in the reading of the proofs of part of this history rendered by Professor Haskell, of the Uni versity of California Professor R. C. Archibald, of Brown University and Professor L. C. Karpinski, of the University of Michigan. FLORIAN CAJORI UNIVERSITY OF CALIFORNIA . TABLE OF CONTENTS I. INTRODUCTION PARAGRAPHS II. NUMERAL SYMBOLS AND COMBINATIONS OF SYMBOLS . . . 1-99 Babylonians 1-15 Egyptians 16-26 Phoenicians and Syrians 27-28 Hebrews 29-31 Greeks 32-44 Early Arabs 45 Romans 46-61 Peruvian and North American Knot Records .... 62-65 Aztecs 66-67 Maya 68 Chinese and Japanese 69-73 Hindu-Arabic Numerals 74-99 Introduction 74-77 Principle of Local Value 78-80 Forms of Numerals 81-88 Freak Forms 89 Negative Numerals 90 Grouping of Digits in Numeration 91 The Spanish Calderon 92-93 The Portuguese Cifrao 94 Relative Size of Numerals in Tables 95 Fanciful Hypotheses on the Origin of Numeral Forms . 96 A Sporadic Artificial System 97 General Remarks 98 Opinion of Laplace 99 III. SYMBOLS IN ARITHMETIC AND ALGEBRA ELEMENTARY PART 100 A. Groups of Symbols Used by Individual Writers ... 101 Greeks Diophantus, Third Century A. D 101-5 Hindu Brahmagupta, Seventh Century .... 106-8 Hindu The Bakhshal Manuscript 109 Hindu Bhaskara, Twelfth Century 110-14 Arabic al-Khow rizmi, Ninth Century .... 115 Arabic al-Karkhf, Eleventh Century 116 Byzantine Michael Psellus, Eleventh Century . . 117 Arabic Ibn Albanna, Thirteenth Century ... 118 Chinese Chu Shih-Chieh, Fourteenth Century . .119, 120 vii viii TABLE OF CONTENTS PARAGRAPHS Byzantine Maximus Planudes, Fourteenth Century 121 Italian Leonardo of Pisa, Thirteenth Century . . 122 French Nicole Oresme, Fourteenth Century . . . 123 Arabic al-Qalasadi, Fifteenth Century .... 124 German Regiomontanus, Fifteenth Century . . . 125-27 ItalianEarliest Printed Arithmetic, 1478 . . . . 128 French Nicolas Chuquet, 1484 129-31 French Estienne de la Roche, 1520 132 Italian Pietro Borgi, 1484, 1488 133 Italian Luca Pacioli, 1494, 1523 134-38 Italian F. Ghaligai, 1521, 1548, 1552 139 Italian H. Cardan, 1532, 1545, 1570 140, 141 Italian Nicolo Tartaglia, 1506-60 142, 143 Italian Rafaele Bombelli, 1572 144, 145 German Johann Widman, 1489, 1526 146 Austrian Grarnrnateus, 1518, 1535 147 German Christoff Rudolff, 1525 148, 149 Dutch Gielis van der Hoecke, 1537 150 German Michael Stifel, 1544, 1545, 1553 ...... ... Read more

Book Description
PREFACE TO THE FIRST EDITION THE education of the child must accord both in mode and arrangement with the education of mankind as consid ered historically or, in other words, the genesis of knowledge in the individual must follow the same course as the genesis of knowledge in the race. To M. Comte we believe society owes the enunciation of this doctrine a doctrine which we may accept without committing ourselves to his theory of the genesis of knowledge, either in its causes or its order. 1 If this principle, held also by Pestalozzi and Proebel, be correct, then it would seem as if the knowledge of the history of a science must be an effectual aid in teaching that science. Be this doctrine true or false, certainly the experience of many instructors establishes the importance of mathematical history in teaching. 2 With the hope of being of some assistance to niy fellow-teachers, I have pre pared this book and have interlined my narrative with occasional remarks and suggestions on methods of teaching. No doubt, the thoughtful reader will draw many useful 1 HJBRBEHT SFBNCEK, Education Intellectual, Moral, and Physical New York, 1894, p. 122. See also B. H. QUICK, Educational Beformers, 1879, p. 191. 2 See G. HEFFEL, The Use of History in Teaching Mathematics, Nature, Vol. 48, 18S08, J 1175497 M 21 946 lessons from f the . study of matliematical history which, are not directly pctiitfed out in the text. In the preparation of this history, I have made extensive use of the works of Cantor, Hankel, linger, De Morgan, Pea cock, Gow, Allman, Loria, and of other prominent writers on the history of mathematics. Original sources have been consulted, whenever opportunity has presented itself. It gives me much pleasure to acknowledge the assistance ren dered by the United States Bureau of Education, in for warding for examination a number of old text-books which otherwise would have been inaccessible to me. It should also be said that a large number of passages in this book are taken, with only slight alteration, from my History of Mathematics, Macmillan Co., 1895. . . . ELOBIAN CAJORI. COLORADO COLLEGE, COLORADO SPRINGS, July, 1896. PREFACE TO THE SECOND EDITION IN the endeavor to bring this history down to date, nume ous alterations and additions have been made. FLORIAN CAJOBI. COLORADO COLLEGE, December, 1916. CONTENTS PA S ANTIQUITY 1 NUMBER-SYSTEMS AND NUMERALS 1 ARITHMETIC AND ALGEBRA 19 Egypt ,19 Greece 26 Some .37 GEOMETRY AND TRIGONOMETRY 43 Egypt and Babylonia 43 Greece . 46 Home 89 MIDDLE AGES .93 ARITHMETIC AND ALGEBRA 93 Hindus 93 Arabs 103 Europe during the Middle Ages Ill Introduction of Roman Arithmetic Ill Translation of Arabic Manuscripts ..... 118 The First Awakening 119 GEOMETRY AND TRIGONOMETRY 122 Hindus 122 Arabs , 12 Europe during the Middle Ages 131 Introduction of Roman Geometry ..... 131 Translation of Arabic Manuscripts 132 The First Awakening 134 ttt Till CONTENTS MODERN TIMES ARITHMETIC ....... ... 139 Its Development as a Science and Art ..... 139 English Weights and Measures ...... 157 Rise of the Commercial School in England . . . .179 Causes which Checked the Growth of Demonstrative Arith metic in England . . ...... 204 Reforms in Arithmetical Teaching ..... 211 Arithmetic in the United States ...... 215 Pleasant and Diverting Questions ....... ... Read more

Product Description
This volume is produced from digital images created through the University of Michigan University Library's preservation reformatting program. ... Read more