PREFACE |
TABLE OF CONTENTS |
CHAPTER I. EGYPTIAN AND PHOENICIAN MATHEMATICS. |
The history of mathematics begins with that of the Ionian Greeks |
Greek indebtedness to Egyptians and Phoenicians |
Knowledge of the science of numbers possessed by the Phoenicians |
Knowledge of the science of numbers possessed by the Egyptians |
Knowledge of the science of geometry possessed by Egyptians |
Note on ignorance of mathematics shewn by the Chinese |
First Period. Mathematics under Greek Influence. |
CHAPTER II. THE IONIAN AND PYTHAGOREAN SCHOOLS. |
Authorities |
The Ionian School |
"THALES, 640-550 B.C." |
His geometrical discoveries |
His astronomical teaching |
Anaximander. Anaximenes. Mamercus. Mandryatus |
The Pythagorean School |
"PYTHAGORAS, 569-500 B.C." |
The Pythagorean teaching |
The Pythagorean geometry |
The Pythagorean theory of numbers |
Epicharmus. Hippasus. Phiololaus. Archippus. Lysis |
"ARCHYTAS, circ. 400 B.C." |
His solution of the duplication of a cube |
Theodorus. Timaeus. Bryso |
Other Greek Mathematical Schools in the Fifth Century B.C. |
Oenopides of Chios |
Zeno of Elea. Democritus of Abdera |
CHAPTER III. THE SCHOOLS OF ATHENS AND CYZICUS. |
Authorities |
Mathematical teachers at Athens prior to 420 B.C. |
Anaxogoras. The Sophists. Hippias (The quadratrix) |
Antipho |
Three problems in which these schools were specially interested |
"HIPPOCRATES of Chios, circ. 420 B.C." |
Letters used to describe geometrical diagrams |
Introduction in geometry of the method of reduction |
The quadrature of certain lunes |
The problem of the duplication of the cube |
"Plato, 429-348 B.C." |
Introduction in geometry of the method of analysis |
Theorem on the duplication of the cube |
"EUDOXUS, 408-355 B.C." |
Theorems on the golden section |
Introduction of the method of exhaustions |
Pupils of Plato and Eudoxus |
"MENAECHMUS, circ. 340 B.C." |
Discussion of the conic selections |
His two solutions of the duplication of the cube |
Aristaeus. Theaetetus |
"Aristotle, 384-322 B.C." |
Questions on mechanics. Letters used to indicate magnitudes |
CHAPTER IV. THE FIRST ALEXANDRIAN SCHOOL |
Authorities |
Foundation of Alexandria |
The Third Century before Christ |
"EUCLID, circ. 330-275 B.C." |
Euclid's Elements |
The Elements as a text-book of geo |
The Elements as a text-book of the theory of numbers |
Euclid's other works |
"Aristarchus, circ. 310-250 B.C." |
Method of determining the distance of the sun |
Conon. Dositheus. Zeuxippus. Nicoteles |
"ARCHIMEDES, 287-212 B.C." |
His works on plane geometry |
His works on geometry of three dimensions |
"His two papers on arithmetic, and the "cattle problem" |
His works on the statistics of solids and fluids |
His astronomy |
The principles of geometry and that of Archimedes |
"APOLLONIUS, circ. 260-200 B.C." |
His conic sections |
His other works |
His solution of the duplication of a cube |
Contrast between his geometry and that of Archimedes |
"Erathosthenes, 275-194 B.C." |
The Sieve of Eratosthenes |
The Second Century before Christ |
"Hypsicles (Euclid, book XIV). Nicomedes. Diocles" |
Perseus. Zejodorus |
"HIPPARCHUS, circ. 130 B.C." |
Foundation of scientific astronomy |
Foundation of trigonometry |
"HERO of Alexandria, circ. 125 B.C." |
Foundation of scientific engineering and of land-surveying |
Area of a triangle determined in terms of its sides |
Features of Hero's works |
The First Century before Christ |
Theodosius |
Dionysodorus |
End of the First Alexandrian School |
Egypt constituted a Roman province |
CHAPTER V. THE SECOND ALEXANDRIAN SCHOOL |
Authorities |
The First Century after Christ |
Serenus. Menelaus |
Nicomachus |
Introduction of the arithmetic current in medieval Europe |
The Second Century after Christ |
Theon of Smyran. Thymaridas |
"PTOLEMY, died in 168" |
The Almagest |
Ptolemy's astronomy |
Ptolemy's geometry |
The Third Century after Christ |
"Pappus, circ. 280" |
"The Suagwg?, a synopsis of Greek mathematics" |
The Fourth Century after Christ |
Metrodorus. Elementary problems in arithmetic and algebra |
Three stages in the development of algebra |
"DIOPHANTUS, circ. 320 (?)" |
Introduction of syncopated algebra in his Arithmetic |
"The notation, methods, and subject-matter of the work" |
His Porisms |
Subsequent neglect of his discoveries |
Iamblichus |
Theon of Alexandria. Hypatia |
Hostility of the Eastern Church to Greek science |
The Athenian School (in the Fifth Century) |
"Proclus, 412-485. Damascius. Euto |
Roman Mathematics |
Nature and extent of the mathematics read at Rome |
Contrast between the conditions at Rome and at Alexandria |
End of the Second Alexandrian School |
"The capture of Alexandria, and end of the Alexandrian Schools" |
CHAPTER VI. THE BYZANTINE SCHOOL. |
Preservation of works of the great Greek Mathematicians |
Hero of Constantinople. Psellus. Planudes. Barlaam. Argyrus |
Nicholas Rhabdas. Pachymeres. Moschopulus (Magic Squares) |
"Capture of Constantinople, and dispersal of Greek Mathematicians" |
CHAPTER VII. SYSTEMS OF NUMERATION AND PRIMITIVE ARITHMETIC. |
Authorities |
Methods of counting and indicating numbers amoung primitive races |
Use of the abacus or swan-pan for practical calculation |
Methods of representing nu |
The Lilavati or arithmetic ; decimal numeration used |
The Bija Ganita or algebra |
Development of Mathematics in Arabia |
"ALKARISMI or AL-KHWARIZMI, circ. 830" |
His Al-gebr we 'l mukabala |
His solution of a quadratic equation |
Introduction of Arabic or Indian system of numeration |
"TABIT IBN KORRA, 836-901 ; solution of a cubic equation" |
Alkayami. Alkarki. Development of algebra |
Albategni. Albuzjani. Development of trigonometry |
Alhazen. Abd-al-gehl. Development of geometry |
Characteristics of the Arabian School |
CHAPTER X. INTRODUCTION OF ARABIAN WORKS INTO EUROPE. |
The Eleventh Century |
Moorish Teachers. Geber ibn Aphla. Arzachel |
The Twelfth Century |
Adelhard of Bath |
Ben-Ezra. Gerad. John Hispalensis |
The Thirteenth Century |
"LEONARDO OF PISA, circ. 1175-1230" |
"The Liber Abaci, 1202" |
The introduction of the Arabic numerals into commerceThe introduction of the Arabic numerals into science |
The mathematic tournament |
"Frederick II., 1194-1250" |
"JORDANUS, circ. 1220" |
His De Numeris Datis ; syncopated algebra |
Holywood |
"ROGER BACON, 1214-1294" |
Campanus |
The Fourteenth Century |
Bradwardine |
Oresmus |
The reform of the university curriculum |
The Fifteenth Century |
Beldomandi |
CHAPTER XI. THE DEVELOPMENT OF ARITHMETIC. |
Authorities |
The Boethian arithmetic |
Algorism or modern arithmetic |
The Arabic (or Indian) symbols : history of |
"Introduction into Europe by science, commerce, and calendars" |
Improvements introduced in algoristic arithmetic |
(I) Simplification of the fundemental processe |
(ii) Introduction of signs for addition and subtra |
(iii) "Invention of logarithms, 1614" |
(iv) "Use of decimals, 1619" |
CHAPTER XII. THE MATHEMATICS OF THE RENAISSANCE. |
Authorities |
Effect of invention of printing. The renaissance |
Development of Syncopated Algebra and Trigonometry |
"REGIOMONTANUS, 1436-1476" |
His De Triangulis (printed in 1496) |
"Purbach, 1423-1461. Cusa, 1401-1464. Chuquet, circ. 1484" |
Introduction and origin of symbols + and - |
"Pacioli or Lucas di Burgo, circ. 1500" |
"His arithmetic and geometry, 1494" |
"Leonardo da Vinci, 1452-1519" |
"Dürer, 1471-1528. Copernicus, 1473-1543" |
"Record, 1510-1588 ; introduction of symbol for equality" |
"Rudolff, circ. 1525. Riese, 1489-1559" |
"STIFEL, 1486-1567" |
"His Arithmetica Integra, 1544" |
"TARTAGLIA, 1500-1559" |
"His solution of a cubic equation, 1535" |
"His arithmetic, 1556-1560" |
"CARDAN, 1501-1576" |
"Hid Ars Magna, 1545 ; the third work printed on algebra" |
His solution of a cubic equation |
"Ferrari, 1522-1565 ; solution of a biquadratic equation" |
"Rheticus, 1514-1576. Maurolycus. Borrel. Xylander" |
"Commandino. Peletier. Romanus. Pitiscus. Ramus, 1515-1572" |
"Bombelli, circ. 1570" |
Development of Symbolic Algebra |
"VIETA, 1540-1603" |
"The In Artem ; introduction of symbolic algebra, 1591" |
Vieta's other works |
"Girard, 1590-1633 ; development of trigonometry and algebra" |
"NAPIER, 1550-1617 ; development of trigonometry and algebra" |
"Briggs, 1556-1631 ; calculations of tables of logarithms" |
"HARRIOT, 1560-1621 ; development of analysis in algebra" |
"Oughtred, 1574-1660" |
The Origin of the more Common Symbols in Algebra |
CHAPTER XIII. THE CLOSE OF THE RENAISSANCE. |
Authorities |
Development of Mechanics and Experimental Methods |
"STEVINUS, 1548-1620" |
"Commencement of the modern treatment of statistics, 1586" |
"GALILEO, 1564-1642" |
Commencement of the science of dynamics |
Galileo's astronomy |
"Francis Bacon, 1561-1626" |
Revival of Interest in Pure Geometry |
"KEPLER, 1571-1630" |
"His Paralipomena, 1604 ; principle of continuity" |
"His Stereometria, 1615 ; use of infinitesimals" |
"Kepler's laws of planetary motion, 1609 and 1619" |
"Desargues, 1593-1662" |
His Brouillon project ; use of projective geometry |
Mathematical Knowledge at the Close of the Renaissance |
Third Period. Modern Mathematics |
CHAPTER XIV. THE HISTORY OF MODERN MATHEMATICS. |
Treatment of the subject |
Invention of analytical geometry and the method of indivis |
Invention of the calculus |
Development of mechanics |
Application of mathematics to physics |
Recent development of pure mathematics |
CHAPTER XV. HISTORY OF MATHEMATICS FROM DESCARTES TO HUYGENS. |
Authorities |
"DESCARTES, 1596-1650" |
His views on philosophy |
"His invention of analytical geometry, 1637" |
"His algebra, optics, and theory of vortices" |
"CAVALIERI, 1598-1647" |
The method of indivisibles |
"PASCAL, 1623-1662" |
His geometrical conics |
The arthmetical triangle |
"Foundation of the theory of probabilities, 1654" |
His discussion of the cycloid |
"WALLIS, 1616-1703" |
"The Arithmetica Infinitorum, 1656" |
Law of indices in algebra |
Use of series in quadratures |
"Earliest rectification of curves, 1657" |
Wallis's algebra |
"FERMAT, 1601-1665" |
His investigation on the theory of numbers |
His use in geometry of analysis and of infinitesimals |
"Foundation of the theory of probabilities, 1654" |
"HUYGENS, 1629-1695" |
"The Horologium Oscillatorium, 1673" |
The undulatory theory of light |
Other Mathematicians of this Time |
Bachet |
Marsenne ; theorem on primes and perfect numbers |
Roberval. Van Schooten. Saint-Vincent |
Torricelli. Hudde. Frénicle |
De Laloubère. Mercator. Barrow ; the differential triangle |
Brouncker ; continued fractions |
James Gregory ; distinction between convergent and divergent series |
Sir Christopher Wren |
Hooke. Collins |
Pell. Sluze. Viviani |
Tschirnhausen. De la Hire. Roemer. Rolle. |
CHAPTER XVI. THE LIFE AND WORKS OF NEWTON. |
Authorities |
Newton's school and undergraduate life |
"Investigations in 1665-1666 on fluxions, optics, and gravitation" |
"His views on gravitation, 1666" |
Researches in 1667-1669 |
"Elected Lucasian professor, 1669" |
"Optical lectures and discoveries, 1669-1671" |
"Emission theory of light, 1675" |
"The Leibnitz Letters, 1676" |
"Discoveries and lectures on algebra, 1673-1683" |
"Discoveries and lectures on gravitation, 1684" |
"The Principia, 1685-1686" |
The subject-matter of the Principia |
Publication of the Principia |
Investigations and work from 1686 to 1696 |
"Appointment at the Mint, and removal to London, 1696" |
"Publication of the Optics, 1704" |
Appendix on classification of cubic curves |
Appendix on quadrature by |
The controversy as t |