INDEX

Bold-faced numbers refer to authors

Abbreviations:— m. = mathematics, math. = mathematical, math’n. = mathematician.

Abbott, [1001].
Abstract method, Development of, [729].
Abstract nature of m., Reason for, [638].
Abstractness, math., Compared with logical, [1304].
Abstract reasoning, Objection to, [1941].
Adams, Henry,
M. and history, [1599].
Math’ns practice freedom, [208], [805].
Adams, John, Method in m., [226].
Aeneid, Euler’s knowledge of, [859].
Aeschylus. On number, [1606].
Aim in teaching m., [501-508], [517], [844].
Airy, Pythagorean theorem, [2126].
Akenside, [1532].
Alexander, [901], [902].
Algebra,
Chapter [XVII].
Definitions of, [110], [1714], [1715].
Problems in, [320], [530], [1738].
Of use to grown men, [425].
And geometry, [525-527], [1610], [1707].
Advantages of, [1701], [1703], [1705].
Laws of, [1708-1710].
As an art, [1711].
Review of, [1713].
Designations of, [1717].
Origin of, [1736].
Burlesque on modern, [1741].
Hume on, [1863].
Algebraic notation, value of, [1213], [1214].
Algebraic treatises, How to read, [601].
Amusements in m., [904], [905].
Anagrams,
On De Morgan, [947].
On Domus Lescinia, [2155].
On Flamsteed, [968].
On Macaulay, [996].
On Nelson, [2153].
On Newton, [1028].
On Voltaire, [2154].
Analysis,
Invigorates the faculty of resolution, [416].
Relation of geometry to, [1931].
Analytical geometry, [1889], [1890], [1893].
Method of, [310].
Importance of, [949].
Burlesque on, [2040].
Ancient geometry,
Characteristics of, [712], [714].
Compared with modern, [1711-1716].
Method of, [1425], [1873-1875].
Ancients, M. among the, [321].
Anecdotes, Chapters, [IX], [X].
Anger, M. destroys predisposition to, [458].
Angling like m., [739].
Anglo-Danes, Aptitude for m., [836].
Anglo-Saxons,
Aptitude for m., [837].
Newton as representative of, [1014].
Anonymous, Song of the screw, [1894].
[Appolonius], [712], [714].
Approximate m., Why not sufficient, [1518].
Aptitude for m., [509], [510], [520], [836-838], [976], [1617].
Arabic notation, [1614].
Arago,
M. the enemy of scientific romances, [267].
Euler, “analysis incarnate,” [961].
Euler as a computer, [962].
On Kepler’s discovery, [982].
Newton’s efforts superhuman, [1006].
On probabilities, [1591].
Geometry as an instrument, [1868].
Arbuthnot,
M. frees from prejudice, credulity and superstition, [449].
M. the friend of religion, [458].
M. compared to music, [1112].
On math, reasoning, [1503].
Archimedes,
His machines, [903], [904].
Estimate of math, appliances, [904-906], [908].
Wordsworth on, [906].
Schiller on, [907].
And engineering, [908].
Death of, [909].
His tomb, [910].
Compared with Newton, [911].
Character of his work, [912], [913].
Applied m., [1312].
Architecture and m., [276].
Archytas, [904].
And Plato, [1427].
Aristippus the Cyrenaic, [845].
Aristotle, [914].
On relation of m. to esthetics, [318].
Arithmetic,
Chapter [XVI].
Definitions of, [106], [110], [1611], [1612], [1714].
Emerson on advantage of study of, [408].
Problems in, [528].
A master-key, [1571].
Based on concept of time, [1613].
Method of teaching, [1618].
Purpose of teaching, [454], [1624].
As logic, [1624], [1625].
The queen of m.,[1642].
Higher, [1755].
Hume on, [1863].
Arithmetical theorems, [1639].
Art, M. as a fine, Chapter [XI].
Arts, M. and the, [1568-1570], [1573].
Astronomy and m., [1554], [1559], [1562-1567].
“Auge et impera.,” [631].
Authority in science, [1528].
Axioms, [518], [2015].
In geometry, [1812], [2004], [2006].
Def. in disguise, [2005].
Euclid’s, [2007-2010], [2014].
Nature of, [2012].
Proofs of, [2013].
And the idea of space, [2004].
Babbage, [923].
Bacon, Lord,
Classification of m., [106].
M. makes men subtile, [248].
View of m., [316], [915], [916].
M. held in high esteem by ancients, [321].
On the generalizing power of m., [327].
On the value of math, studies, [410].
M. develops concentration of mind, [411].
M. cures distraction of mind, [412].
M. essential to study of nature, [436].
His view of m., [915], [916].
His knowledge of m., [917], [918].
M. and logic, [1310].
Growth of m., [1511].
Bacon, Roger,
Neglect of m. works injury to all science, [310].
On the value of m., [1547].
Bain,
Importance of m. in education, [442].
On the charm of the study of m., [453].
M. and science teaching, [522].
Teaching of arithmetic, [1618].
Ball, R. S., [2010].
Ball, W. W. R.,
On Babbage, [923].
On Demoivre’s death, [944].
De Morgan and the actuary, [945].
Gauss as astronomer, [971].
Laplace’s “It is easy to see” [986].
Lagrange, Laplace and Gauss contrasted, [993].
Newton’s interest in chemistry and theology, [1015].
On Newton’s method of work, [1026].
On Newton’s discovery of the calculus, [1027].
Gauss’s estimate of Newton, [1029].
M. and philosophy, [1417].
Advance in physics, [1530].
Plato on geometry, [1804].
Notation of the calculus, [1904].
Barnett, M. the type of perfect reasoning, [307].
Barrow,
On the method of m., [213], [227].
Eulogy of m., [330].
M. as a discipline of the mind, [402].
M. and eloquence, [830].
Philosophy and m., [1430].
Uses of m., [1572].
On surd numbers, [1728].
Euclid’s definition of proportion, [1835].
Beattie, [1431].
Beauty of m., [453], [824], [1208].
Consists in simplicity, [242], [315].
Sylvester on, [1101].
Russell on, [1104].
Young on, [1110].
Kummer on, [1111].
White on, [1119].
And truth, [1114].
Boltzmann on, [1116].
Beltrami, On reading of the masters, [614].
Berkeley,
On geometry as logic, [428].
On math. symbols, [1214].
On fluxions, [1915], [1942-1944].
On infinite divisibility, [1945].
Bernoulli, Daniel, [919].
Bernoulli, James,
Legend for his tomb, [920], [922].
Computation of sum of tenth powers of numbers, [921].
Discussion of logarithmic spiral, [922].
Berthelot, M. inspires respect for truth, [438].
Bija Ganita, Solution of problems, [1739].
Billingsley, M. beautifies the mind, [319].
Binary arithmetic, [991].
Biology and m., [1579-1581].
Biot, Laplace’s “It is easy to see,” [986].
[Bôcher],
M. likened to painting, [1103].
Interrelation of m. and logic, [1313].
Geometry as a natural science, [1866].
Boerne, On Pythagoras, [1855].
Bois-Reymond,
On the analytic method, [1893].
Natural selection and the calculus, [1921].
Boltzmann, On beauty in m., [1116].
Bolyai, Janos,
Duel with officers, [924].
Universal language, [925].
Science absolute of space, [926].
Bolyai, Wolfgang, [927].
On Gauss, [972].
Bolzano, [928].
Cured by Euclid, [929].
Parallel axiom, [2110].
Book-keeping, Importance of the art of, [1571].
Boole, M. E. [719].
Boole’s Laws of Thought, [1318].
Borda-Demoulins, Philosophy and m., [1405].
Boswell, [981].
Bowditch, On Laplace’s “Thus it plainly appears,” [985].
Boyle,
Usefulness of m. to physics, [437].
M. and science, [1513], [1533].
Ignorance of m., [1577].
M. and physiology, [1582].
Wings of m., [1626].
Advantages of algebra, [1703].
Brahmagupta, Estimate of m., [320].
Brewster,
On Euler’s knowledge of the Aeneid, [959].
On Euler as a computer, [963].
On Newton’s fame, [1002].
Brougham, [1202].
Buckle, On geometry, [1810], [1837].
Burke, On the value of m., [447].
Burkhardt,
On discovery in m., [618].
On universal symbolism, [1221].
Butler, N. M.,
M. demonstrates the supremacy of the human reason, [309].
M. the most astounding intellectual creation, [707].
Geometry before algebra, [1871].
Butler, Samuel, [2118].
Byerly, On hyperbolic functions, [1929].
Cajori,
On the value of the history of m., [615].
On Bolyai, [927].
Cayley’s view of Euclid, [936].
On the extent of Euler’s work, [960].
On Euler’s math. power, [964].
On the Darmstaetter prize, [967].
On Sylvester’s first class at Johns Hopkins, [1031].
On music and m. among the Pythagoreans, [1130].
On the greatest achievement of the Hindoos, [1615].
On modern calculation, [1614].
On review in arithmetic, [1713].
On Indian m., [1737].
On the characteristics of ancient geometry, [1873].
On Napier’s rule, [1888].
Calculating machines, [1641].
Calculation,
Importance of, [602].
Not the sole object of m., [268].
Calculus,
Chapter [XIX].
Foundation of [253].
As a method, [309].
May be taught at an early age,[519], [1917], [1918].
Cambridge m., [836], [1210].
Cantor,
On freedom in m., [205], [207].
On the character of Gauss’s writing, [975].
Zeno’s problem, [1938].
On the infinite, [1952].
Carlisle life tables, [946].
Carnot,
On limiting ratios, [1908].
On the infinitesimal method, [1907].
Carson, Value of geometrical training, [1841].
Cartesian method, [1889], [1890].
Carus,
Estimate of m., [326].
M. reveals supernatural God, [460].
Number and nature, [1603].
Zero and infinity, [1948].
Non-euclidean geometry, [2016].
Cathedral, “Petrified mathematics,” [1110].
Causation in m., [251], [254].
Cayley,
Advantage of modern geometry over ancient, [711].
On the imaginary, [722].
Sylvester on, [930].
Noether on, [931].
His style, [932].
Forsyth on, [932-934].
His method, [933].
Compared with Euler, [934].
Hermite on, [935].
His view of Euclid, [936].
His estimate of quaternions, [937].
M. and philosophy, [1420].
Certainty of m., [222], [1440-1442], [1628], [1863].
Chamisso, Pythagorean theorem, [1856].
Chancellor, M. develops observation, imagination and reason, [433].
Chapman, Different aspects of m., [265].
Characteristics of m., [225], [229], [247], [263].
Characteristics of modern m., [720], [724-729].
Charm in m., [1115], [1640], [1848].
Chasles, Advantage of modern geometry over ancient, [712].
Checks in m., [230].
Chemistry and m., [1520], [1560], [1561], [1750].
Chess, M. like, [840].
Chrystal,
Definition of m., [113].
Definition of quantity, [115].
On problem solving, [531].
On modern text-books, [533].
How to read m., [607].
His algebra, [635].
On Bernoulli’s numbers, [921].
On math. versus logical abstractness, [1304].
Rules of algebra, [1710].
On universal arithmetic, [1717].
On Horner’s method, [1744].
On probabilities, [1967].
Cicero, Decadence of geometry among Romans, [1807].
Circle, Properties of, [1852], [1857].
Circle-squarers, [2108], [2109].
Clarke, Descriptive geometry, [1882].
Classic problems, Hilbert on, [627].
Clebsch, On math. research, [644].
Clifford,
On direct usefulness of math. results, [652].
Correspondence the central idea of modern m., [726].
His vision, [938].
His method, [939].
His knowledge of languages, [940].
His physical strength, [941].
On Helmholtz, [979].
On m. and mineralogy, [1558].
On algebra and good English, [1712].
Euclid the encouragement and guide of scientific thought, [1820].
Euclid the inspiration and aspiration of scientific thought, [1821].
On geometry for girls, [1842].
On Euclid’s axioms, [2015].
On non-Euclidean geometry, [2022]
Colburn, [967].
Coleridge,
On problems in m., [534].
Proposition, gentle maid, [1419].
M. the quintessence of truth, [2019].
Colton, On the effect of math. training, [417].
Commensurable numbers, [1966].
Commerce and m., [1571].
Committee of Ten,
On figures in geometry, [524].
On projective geometry, [1876].
Common sense, M. the etherealization of, [312].
Computation,
Not m., [515].
And m., [810].
Not concerned with significance of numbers, [1641].
Comte,
On the object of m., [103].
On the business of concrete m., [104].
M. the indispensable basis of all education, [334].
Mill on, [942].
Hamilton on, [943].
M. and logic, [1308], [1314], [1325].
On Kant’s view of m., [1437].
Estimate of m., [1504].
M. essential to scientific education, [1505].
M. and natural philosophy, [1506].
M. and physics, [1535], [1551].
M. and science, [1536].
M. and biology, [1578], [1580], [1581].
M. and social science, [1587].
Every inquiry reducible to a question of number, [1602].
Definition of algebra and arithmetic, [1714].
Geometry a natural science, [1813].
Ancient and modern methods, [1875].
On the graphic method, [1881].
On descriptive geometry, [1883].
Mill’s estimate of, [1903].
Congreve, [2143].
Congruence, Symbol of, [1646].
Conic sections, [658], [660], [1541], [1542].
Conjecture, M. free from, [234].
Contingent truths, [1966].
Controversies in m., [215], [243], [1859].
Correlation in m., [525-527], [1707], [1710].
Correspondence, Concept of, [725], [726].
Coulomb, [1516].
Counting, Every problem can be solved by, [1601].
Cournot,
On the object of m., [268].
On algebraic notation, [1213].
Advantage of math, notation, [1220].
Craig, On the origin of a new science, [646].
Credulity, M. frees mind from, [450].
Cremona, On English text-books, [609].
Crofton,
On value of probabilities, [1590].
On probabilities, [1952], [1970], [1972].
Cromwell, On m. and public service, [328].
Curiosities, Chapter [XXI].
Curtius, M. and philosophy, [1409].
Curve, Definition of, [1927].
Cyclometers, Notions of, [2108].
Cyclotomy depends on number theory, [1647].
D’Alembert,
On rigor in m., [536].
Geometry as logic, [1311].
Algebra is generous, [1702].
Geometrical versus physical truths, [1809].
Standards in m., [1851].
Dante, [1858], [2117].
Darmstaetter prize, [2129].
Davis,
On Sylvester’s method, [1035].
M. and science, [1510].
On probability, [1968].
Decimal fractions, [1217], [1614].
Decker, [2142].
Dedekind, Zeno’s Problem, [1938].
Deduction,
Why necessary, [219].
M. based on, [224].
And Intuition, [1413].
Dee, On the nature of m., [261].
Definitions of m., Chapter [I].
Also [2005].
Democritus, [321].
Demoivre, His death, [944].
Demonstrations,
Locke on, [236].
Outside of m., [1312].
In m., [1423].
De Morgan,
Imagination in m., [258].
M. as an exercise in reasoning, [430].
On difficulties in m., [521].
On correlation in m., [525].
On extempore lectures, [540].
On reading algebraic works, [601].
On numerical calculations, [602].
On practice problems, [603].
On the value of the history of m., [615], [616].
On math’ns., [812].
On Bacon’s knowledge of m., [918].
And the actuary, [945].
On life tables, [946].
Anagrams’ on his name, [947].
On translations of Euclid, [953].
Euclid’s elements compared with Newton’s Principia, [954].
Euler and Diderot, [966].
Lagrange and the parallel axiom, [984].
Anagram on Macaulay’s name, [996].
Anagrams on Newton’s name, [1028].
On math, notation, [1216].
Antagonism of m. and logic, [1315].
On German metaphysics, [1416].
On m. and science, [1537].
On m. and physics, [1538].
On the advantages of algebra, [1701].
On algebra as an art, [1711].
On double algebra and quaternions, [1720].
On assumptions in geometry, [1812].
On Euclid in schools, [1819].
Euclid not faultless, [1823].
On Euclid’s rigor, [1831].
Geometry before algebra, [1872].
On trigonometry, [1885].
On the calculus in elementary instruction, [1916].
On integration, [1919].
On divergent series, [1935], [1936].
Ad infinitum, [1949].
On the fourth dimension, [2032].
Pseudomath and graphomath, [2101].
On proof, [2102].
On paradoxers, [2105].
Budget of paradoxes, [2106].
On D’Israeli’s six follies of science, [2107].
On notions of cyclometers, [2108].
On St. Vincent, [2109].
Where Euclid failed, [2114].
On the number of the beast, [2151].
Descartes,
On the use of the term m., [102].
On intuition and deduction, [219], [1413].
Math’ns alone arrive at proofs, [817].
The most completely math. type of mind, [948].
Hankel on, [949].
Mill on, [950].
Hankel on, [1404].
On m. and philosophy, [1425], [1434].
Estimate of m., [1426].
Unpopularity of, [1501].
On the certainty of m., [1628].
On the method of the ancients, [1874].
On probable truth, [1964].
Descriptive geometry, [1882], [1883].
Dessoir, M. and medicine, [1585].
Determinants, [1740], [1741].
Diderot and Euler, [966].
Differential calculus,
Chapter [XIX].
And scientific physics, [1549].
Differential equations, [1549-1552], [1924], [1926].
Difficulties in m., [240], [521], [605-607], [634], [734], [735].
Dillmann,
M. a royal science, [204].
On m. as a high school subject, [401].
Ancient and modern geometry compared, [715].
On ignorance of, [807].
On m. as a language, [1204].
Number regulates all things, [1505].
Dirichlet,
On math, discovery, [625].
As a student of Gauss, [977].
Discovery in m., [617-622], [625].
D-ism versus dot-age, [923].
Disquisitiones Arithmeticae, [975], [977], [1637], [1638].
D’Israeli, [2007].
Divergent series, [1935-1937].
“Divide et impera,” [631].
Divine character of m., [325], [329].
“Divinez avant de demontrer,” [630].
Division of labor in m., [631], [632].
Dodgson,
On the charm of, [302].
Pythagorean theorem, [1854].
Ignes fatui in m., [2103].
Dolbear, On experiment in math. research, [613].
Domus Lescinia, Anagram on, [2155].
Donne, [1816].
Dot-age versus d-ism, [923].
Durfee, On Sylvester’s forgetfulness, [1038].
Dutton, On the ethical value of m., [446].
“Eadem mutata resurgo.” [920], [922].
Echols, On the ethical value of m., [455].
Economics and m., [1593], [1594].
Edinburgh Review, M. and astronomy, [1565], [1566].
Education,
Place of m. in, [334], [408].
Study of arithmetic better than rhetoric, [408].
M. as an instrument in, [413], [414].
M. in primary, [431].
M. as a common school subject, [432].
Bain on m. in, [442].
Calculus in elementary, [1916], [1917].
Electricity, M. and the theory of, [1554].
Elegance in m., [640], [728].
Ellis,
On precocity in m., [835].
On aptitude of Anglo-Danes for m., [836].
On Newton’s genius, [1014].
Emerson,
On Newton and Laplace, [1003].
On poetry and m., [1124].
Endowment of math’ns, [818].
Enthusiasm, [801].
Equality, Grassmann’s definition of, [105].
Equations, [104], [526], [1891], [1892].
Errors, Theory of, [1973], [1974].
Esthetic element in m., [453-455], [640], [1102], [1105], [1852], [1853].
Esthetic tact, [622].
Esthetic value of m., [1848], [1850].
Esthetics, Relation of m. to, [318], [319], [439].
Estimates of m., Chapter [III].
See also [1317], [1324], [1325], [1427], [1504], [1508].
Ethical value of m., [402], [438], [446], [449], [455-457].
Euclid,
Bolzano cured by, [929].
And Ptolemy, [951], [1878].
And the student, [952].
Euclid’s Elements,
Translations of, [953].
Compared with the Principia, [954].
Greatness of, [955].
Greatest of human productions, [1817].
Performance in, [1818].
In English schools, [1819].
Encouragement and guide, [1820].
Inspiration and aspiration, [1821].
The only perfect model, [1822].
Not altogether faultless, [1823].
Only a small part of m., [1824].
Not fitted for boys, [1825].
Early study of, [1826].
Newton and, [1827].
Its place, [1828].
Unexceptional in rigor, [1829].
Origin of, [1831].
Doctrine of proportion, [1834].
Definition of proportion, [1835].
Steps in demonstration, [1839].
Parallel axiom, [2007].
Euclidean geometry, [711], [713], [715].
Eudoxus, [904].
Euler,
the myriad-minded, [255].
Pencil outruns intelligence, [626].
On theoretical investigations, [657].
Merit of his work, [956].
The creator of modern math. thought, [957].
His general knowledge, [958].
His knowledge of the Aeneid, [959].
Extent of his work, [960].
“Analysis incarnate,” [961].
As a computer, [962], [963].
His math. power, [964].
His Tentamen novae theorae musicae, [965].
And Diderot, [966].
Error in Fermat’s law of prime numbers, [967].
Eureka, [911], [917].
Euripedes, [1568].
Everett,
Estimate of m., [325].
Value of math. training, [443].
Theoretical investigations, [656].
Arithmetic a master-key, [1571].
On m. and law, [1598].
Exactness, See precision.
Examinations, [407].
Examples, [422].
Experiment in m., [612], [613], [1530], [1531].
Extent of m., [737], [738].
Fairbairn, [528].
Fallacies, [610].
Faraday, M. and physics, [1554].
Fermat, [255], [967], [1902].
Fermat’s theorem, [2129].
Figures,
Committee of Ten on, [524].
Democritus view of, [321].
Battalions of, [1631].
Fine,
Definition of number, [1610].
On the imaginary, [1732].
Fine Art, M. as a, Chapter [XI].
Fisher, M. and economics, [1594].
Fiske,
Imagination in m., [256].
Advantage of m. as logic, [1324].
Fitch,
Definition of m., [125].
M. in education, [429].
Purpose of teaching arithmetic, [1624], [1625].
Fizi, Origin of the Liliwati, [995].
Flamsteed, Anagram on, [968].
Fluxions, [1911], [1915], [1942-1944].
Fontenelle, Bernoulli’s tomb, [920].
Formulas, Compared to focus of a lens, [1515].
Forsyth,
On direct usefulness of math. results, [654].
On theoretical investigations, [664].
Progress of m. [704].
On Cayley, [932-934].
On m. and physics, [1539].
On m. and applications, [1540].
On invariants, [1747].
On function theory, [1754], [1755].
Foster,
On m. and physics, [1516], [1522].
On experiment in m., [1531].
Foundations of m., [717].
Four, The number, [2147], [2148].
Fourier, Math, analysis co-extensive with nature, [218].
On math. research, [612].
Hamilton on, [969].
On m. and physics, [1552], [1553].
On the advantage of the Cartesian method, [1889].
Fourier’s theorem, [1928].
Fourth dimension, [2032], [2039].
Frankland, A., M. and chemistry, [1560].
Frankland, W. B., Motto of Pythagorean brotherhood, [1833].
The most beautiful truth in geometry, [1857].
Franklin, B.,
Estimate of m., [322].
On the value of the study of m., [323].
On the excellence of m., [324].
On m. as a logical exercise, [1303].
Franklin, F., On Sylvester’s weakness, [1033].
Frederick the Great, On geometry, [1860].
Freedom in m., [205-208], [805].
French m., [1210].
Fresnel, [662].
Frischlinus, [1801].
Froebel, M. a mediator between man and nature, [262].
Function theory, [709], [1732], [1754], [1755].
Functional exponent, [1210].
Functionality,
The central idea of modern m., [254].
Correlated to life, [272].
Functions, [1932], [1933].
Concept not used by Sylvester, [1034].
Fundamental concepts, Chapter [XX].
Fuss, On Euler’s Tentamen novae theorae musicae, [965].
Galileo, On authority in science, [1528].
Galton, [838].
Gauss,
His motto, [649].
Mere math’ns, [820].
And Newton compared, [827].
His power, [964].
His favorite pursuits, [970].
The first of theoretical astronomers, [971].
The greatest of arithmeticians, [971].
The math. giant, [972].
Greatness of, [973].
Lectures to three students, [974].
His style and method, [983].
His estimate of Newton, [1029].
On the advantage of new calculi, [1215].
M. and experiment, [1531].
His Disquisitiones Arithmeticae, [1639], [1640].
M. the queen of the sciences, [1642].
On number theory, [1644].
On imaginaries, [1730].
On the notation sin₂φ, [1886].
On infinite magnitude, [1950].
On non-euclidean geometry, [2023-2028].
On the nature of space, [2034].
Generalization in m., [245], [246], [252], [253], [327], [728].
Genius, [819].
Geometrical investigations, [642], [643].
Geometrical training, Value of, [1841], [1842], [1844-1846].
Geometry,
Chapter [XVIII].
Bacon’s definition of, [106].
Sylvester’s definition of, [110].
Value to mankind, [332], [449].
And patriotism, [332].
An excellent logic, [428].
Plato’s view of, [429].
The fountain of all thought, [451].
And algebra, [525-527].
Lack of concreteness, [710].
Advantage of modern over ancient, [711], [712].
And music, [965].
And arithmetic, [1604].
Is figured algebra, [1706].
Name inapt, [1801].
And experience, [1814].
Halsted’s definition of, [1815].
And observation, [1830].
Controversy in, [1859].
A mechanical science, [1865].
A natural science, [1866].
Not an experimental science, [1867].
Should come before algebra, 1767, [1871], [1872].
And analysis, [1931].
Germain, Algebra is written geometry, [1706].
Gilman, Enlist a great math’n, [808].
Glaisher,
On the importance of broad training, [623].
On the importance of a well-chosen notation, [634].
On the expansion of the field of m., [634].
On the need of text-books on higher m., [635].
On the perfection of math. productions, [649].
On the invention of logarithms, [1616].
On the theory of numbers, [1640].
Goethe,
On the exactness of m., [228].
M. an organ of the higher sense, [273].
Estimate of m., [311].
M. opens the fountain of all thought, [451].
Math’ns must perceive beauty of truth, [803].
Math’ns bear semblance of divinity, [804].
Math’ns like Frenchmen, [813].
His aptitude for m., [976].
M. like dialectics, [1307].
On the infinite, [1957].
Golden age of m., [701], [702].
Of art and m. coincident, [1134].
Gordan, When a math. subject is complete, [636].
Gow, Origin of Euclid, [1832].
Gower, [1808].
Grammar and m. compared, [441].
Grandeur of m., [325].
Grassmann,
Definition of m., [105].
Definition of magnitude, [105].
Definition of equality, [105].
On rigor in m., [538].
On the value of m., [1512].
Greek view of science, [1429].
Graphic method, [1881].
Graphomath, [2101].
Group, Notion of, [1751].
Growth of m., [209], [211], [703].
Hall, G. S., M. the ideal and norm of all careful thinking, [304].
Hall and Stevens, On the parallel axiom, [2008].
Haller, On the infinite, [1958].
Halley, On Cartesian geometry, [716].
[Halsted],
On Bolyai, [924-926].
On Sylvester, [1030], [1039].
And [Sylvester], [1031], [1032].
On m. as logic, [1305].
Definition of geometry, [1815].
Hamilton, Sir William, His ignorance of m., [978].
Hamilton, W. R.,
Importance of his quaternions, [333].
Estimate of Comte’s ability, [943].
To the memory of Fourier, [969].
Discovery in light, [1558].
On algebra as the science of time, [1715], [1716].
On quaternions, [1718].
On trisection of an angle, [2112].
Hankel,
Definition of m., [114].
On freedom in m., [206].
On the permanency of math. knowledge, [216].
On aim in m., [508].
On isolated theorems, [621].
On tact in m., [622].
On geometry, [714].
Ancient and modern m. compared, [718], [720].
Variability the central idea in modern m., [720].
Characteristics of modern m., [728].
On Descartes, [949].
On Euler’s work, [956].
On philosophy and m., [1404].
On the origin of m., [1412].
On irrationals and imaginaries, [1729].
On the origin of algebra, [1736].
Euclid the only perfect model, [1822].
Modern geometry a royal road, [1878].
Harmony, [326], [1208].
Harris, M. gives command over nature, [434].
Hathaway, On Sylvester, [1036].
Heat, M. and the theory of, [1552], [1553].
Heath, Character of Archimedes’ work, [913].
Heaviside, The place of Euclid, [1828].
Hebrew and Latin races, Aptitude for m., [838].
Hegel, [1417].
Heiss,
Famous anagrams, [2055].
Reversible verses, [2056].
Helmholtz,
M. the purest form of logical activity, [231].
M. requires perseverance and great caution, [240].
M. should take more important place in education, [441].
Clifford on, [979].
M. the purest logic, [1302].
M. and applications, [1445].
On geometry, [1836].
On the importance of the calculus, [1939].
A non-euclidean world, [2029].
Herbart,
Definition of m., [117].
M. the predominant science, [209].
On the method of m., [212], [1576].
M. the priestess of definiteness and clearness, [217].
On the importance of checks, [230].
On imagination in m, [257].
M. and invention, [406].
M. the chief subject for common schools, [432].
On aptitude for m., [509].
On the teaching of m., [516].
M. the greatest blessing, [1401].
M. and philosophy, [1408].
If philosophers understood m., [1415].
M. indispensable to science, [1502].
M. and psychology, [1583], [1584].
On trigonometry, [1884].
Hermite, On Cayley, [935].
Herschel,
M. and astronomy, [1564].
On probabilities, [1592].
Hiero, [903], [904].
Higher m., Mellor’s definition of, [108].
Hilbert,
On the nature of m., [266].
On rigor in m., [537].
On the importance of problems, [624], [628].
On the solvability of problems, [627].
Problems should be difficult, [629].
On the abstract character of m., [638].
On arithmetical symbols, [1627].
On non-euclidean geometry, [2019].
Hill, Aaron, On Newton, [1009].
Hill, Thomas,
On the spirit of mathesis, [274].
M. expresses thoughts of God, [275].
Value of m., [332].
Estimate of Newton’s work, [333].
Math’ns difficult to judge, [841].
Math’ns indifferent to ordinary interests of life, [842].
A geometer must be tried by his peers, [843].
On Bernoulli’s spiral, [922].
On mathesis and poetry, [1125].
On poesy and m., [1126].
On m. as a language, [1209].
Math, language untranslatable, [1210].
On quaternions, [1719].
On the imaginary, [1734].
On geometry and literature, [1847].
M. and miracles, [2157], [2158].
Hindoos, Grandest achievement of, [1615].
History and m., [1599].
History of m., [615], [616], [625], [635].
Hobson,
Definition of m., [118].
On the nature of m., [252].
Functionality the central idea of m., [264].
On theoretical investigations, [663].
On the growth of m., [703].
A great math’n a great artist, [1109].
On m. and science, [1508].
Hoffman, Science and poetry not antagonistic, [1122].
Holzmüller, On the teaching of m., [518].
Hooker, [1432].
Hopkinson, M. a mill, [239].
Horner’s method, [1744].
Howison,
Definition of m., [134], [135].
Definition of arithmetic, [1612].
Hudson, On the teaching of m., [512].
Hughes, On science for its own sake, [1546].
Humboldt, M. and astronomy, [1567].
Hume,
On the advantage of math, science, [1438].
On geometry, [1862].
On certainty in m., [1863].
Objection to abstract reasoning, [1941].
Humor in m., [539].
Hutton,
On Bernoulli, [919].
On Euler’s knowledge, [958].
On the method of fluxions, [1911].
Huxley, Negative qualities of m., [250].
Hyper-space, [2030], [2031], [2033], [2036-2038].
Hyperbolic functions, [1929], [1930].
Ignes fatui in m., [2103].
Ignorabimus, None in m., [627].
Ignorance of m., [310], [331], [807], [1537], [1577].
Imaginaries, [722], [1729-1735].
Imagination in m., [246], [251], [253], [256-258], [433], [1883].
Improvement of elementary m., [617].
Incommensurable numbers, contingent truths like, [1966].
Indian m., [1736], [1737].
Induction in m., [220-223], [244].
And analogy, [724].
Infinite collection, Definition of, [1959], [1960].
Infinite divisibility, [1945].
Infinitesimal analysis, [1914].
Infinitesimals, [1905-1907], [1940], [1946], [1954].
Infinitum, Ad, [1949].
Infinity and infinite magnitude, [723], [928], [1947], [1948], [1950-1958].
Integers, Kronecker on, [1634], [1635].
Integral numbers, Minkowsky on, [1636].
Integrals, Invention of, [1922].
Integration, [1919-1921], [1923], [1925].
International Commission on m., [501], [502], [938].
Intuition and deduction, [1413].
Invariance,
Correlated to life, [272].
MacMahon on, [1746].
Keyser on, [1749].
Invariants,
Changeless in the midst of change, [276].
Importance of concept of, [727].
Sylvester on, [1742].
Forsyth on, [1747].
Keyser on, [1748].
Lie on, [1752].
Invention in m., [251], [260].
Inverse process, [1207].
Investigations, See research.
Irrationals, [1729].
Isolated theorems in m., [620], [621].
“It is easy to see,” [985], [986], [1045].
Jacobi,
His talent for philology, [980].
Aphorism, [1635].
Die “Ewige Zahl,” [1643].
[Jefferson], [On] m. and law, [1597].
Johnson,
His recourse to m., [981].
Aptitude for numbers, [1617].
On round numbers, [2137].
Journals and transactions, [635].
Jowett, M. as an instrument in education, [413].
Judgment, M. requires, [823].
Jupiter’s eclipses, [1544].
Justitia, The goddess, [824].
Juvenal, Nemo mathematicus etc., [831].
Kant,
On the a priori nature of m., [130].
M. follows the safe way of science, [201].
On the origin of scientific m., [201].
On m. in primary education, [431].
M. the embarrassment of metaphysics, [1402].
His view of m., [1436], [1437].
On the difference between m. and philosophy, [1436].
On m. and science, [1508].
Esthetic elements in m., [1852], [1853].
Doctrine of time, [2001].
Doctrine of space, [2003].
Karpinsky, M. and efficiency, [1573].
Kasner,
“Divinez avant de demontrer," [630].
On modern geometry, [710].
Kelland, On Euclid’s elements, [1817].
Kelvin, Lord, See William Thomson.
Kepler,
His method, [982].
Planetary orbits and the regular solids, [2134].
Keyser,
Definition of m., [132].
Three characteristics of m., [225].
On the method of m., [244].
On ratiocination, [246].
M. not detached from life, [273].
On the spirit of mathesis, [276].
Computation not m., [515].
Math, output of present day, [702].
Modern theory of functions, [709].
M. and journalism, [731].
Difficulty of m., [735].
M. appeals to whole mind, [815].
Endowment of math’ns, [818].
Math’ns in public service, [823].
The aim of the math’n, [844].
On Bolzano, [929].
On Lie, [992].
On symbolic logic, [1321].
On the emancipation of logic, [1322].
On the Principia Mathematica, [1326].
On invariants, [1728].
On invariance, [1729].
On the notion of group, [1751].
On the elements of Euclid, [1824].
On protective geometry, [1880].
Definition of infinite assemblage, [1960].
On the infinite, [1961].
On non-euclidean geometry, [2035].
On hyper-space, [2037], [2038].
Khulasat-al-Hisab, Problems, [1738].
Kipling, [1633].
Kirchhoff, Artistic nature of his works, [1116].
Klein,
Definition of m., [123].
M. a versatile science, [264].
Aim in teaching, [507], [517].
Analysts versus synthesists, [651].
On theory and practice, [661].
Math, aptitudes of various races, [838].
Lie’s final aim, [993].
Lie’s genius, [994].
On m. and science, [1520].
Famous aphorisms, [1635].
Calculating machines, [1641].
Calculus for high schools, [1918].
On differential equations, [1926].
Definition of a curve, [1927].
On axioms of geometry, [2006].
On the parallel axiom, [2009].
On non-euclidean geometry, [2017], [2021].
On hyper-space, [2030].
Kronecker,
On the greatness of Gauss, [973].
God made integers etc., [1634].
Kummer,
On Dirichlet, [977].
On beauty in m., [1111].
LaFaille, Mathesis few know, [1870].
Lagrange, On correlation of algebra and geometry, [527].
His style and method, [983].
And the parallel axiom, [984].
On Newton, [1011].
Wings of m., [1604].
Union of algebra and geometry, [1707].
On the infinitesimal method, [1906].
Lalande, M. in French army, [314].
Langley, M. in Prussia, [513].
Lampe,
On division of labor in m., [632].
On Weierstrass, [1049].
Weierstrass and Sylvester, [1050].
Qualities common to math’ns and artists, [1113].
Charm of m., [1115].
Golden age of art and m. coincident, [1134].
Language,
Chapter [XII].
See also [311], [419], [443], [1523], [1804], [1889].
Laplace,
On instruction in m., [220].
His style and method, [983].
“Thus it plainly appears,” [985], [986].
Emerson on, [1003].
On Leibnitz, [991].
On the language of analysis, [1222].
On m. and nature, [1525].
On the origin of the calculus, [1902].
On the exactitude of the differential calculus, [1910].
The universe in a single formula, [1920].
On probability, [1963], [1969], [1971].
Laputa,
Math’ns of, [2120-2122],
Math. school of, [2123].
Lasswitz,
On modern algebra, [1741].
On function theory, [1934].
On non-euclidean geometry, [2040].
Latin squares, [252].
Latta, On Leibnitz’s logical calculus, [1317].
Law and m., [1597], [1598].
Laws of thought, [719], [1318].
Leadership, M. as training for, [317].
Lecture, Preparation of, [540].
Lefevre,
M. hateful to weak minds, [733].
Logic and m., [1309].
Leibnitz,
On difficulties in m., [241].
His greatness, [987].
His influence, [988].
The nature of his work, [989].
His math. tendencies, [990].
His binary arithmetic, [991].
On Newton, [1010].
On demonstrations outside of m., [1312].
Ars characteristica, [1316].
His logical calculus, [1317].
Union of philosophical and m. productivity, [1404].
M. and philosophy, [1435].
On the certainty of math. knowledge, [1442].
On controversy in geometry, [1859].
His differential calculus, [1902].
His notation of the calculus, [1904].
On necessary and contingent truth, [1966].
Leverrier, Discovery of Neptune, [1559].
Lewes, On the infinite, [1953].
Lie,
On central conceptions in modern m., [727].
Endowment of math’ns, [818].
The comparative anatomist, [992].
Aim of his work, [993].
His genius, [994].
On groups, [1752].
On the origin of the calculus, [1901].
On differential equations, [1924].
Liliwati, Origin of, [995].
Limitations of math. science, [1437].
Limits, Method of, [1905], [1908], [1909], [1940].
Lindeman, On m. and science, [1523].
Liouville, [822].
Lobatchewsky, [2022].
Locke,
On the method of m., [214], [235].
On proofs and demonstrations, [236].
On the unpopularity of m., [271].
On m. as a logical exercise, [423], [424].
M. cures presumption, [425].
Math, reasoning of universal application, [426].
On reading of classic authors, [604].
On Aristotle, [914].
On m. and philosophy, [1433].
On m. and moral science, [1439], [1440].
On the certainty of math. knowledge, [1440], [1441].
On unity, [1607].
On number, [1608].
On demonstrations in numbers, [1630].
On the advantages of algebra, [1705].
On infinity, [1955], [1957].
On probability, [1965].
Logarithmic spiral, [922].
Logarithmic tables, [602].
Logarithms, [1526], [1614], [1616].
Logic and m., Chapter [XIII].
See also [423-430], [442].
Logical calculus, [1316], [1317].
Longevity of math’ns, [839].
Lovelace, Why are wise few etc., [1629].
Lover, [2140].
Macaulay,
Plato and Bacon, [316].
On Archimedes, [905].
Bacon’s view of m., [915], [916].
Anagram on his name, [996].
Plato and Archytas, [1427].
On the power of m., [1527].
Macfarlane,
On Tait, Maxwell, Thomson, [1042].
On Tait and Hamilton’s quaternions, [1044].
Mach,
On thought-economy in m., [203].
M. seems possessed of intelligence, [626].
On aim of research, [647].
On m. and counting, [1601].
On the space of experience, [2011].
MacMahon,
Latin squares, [252].
On Sylvester’s bend of mind, [645].
On Sylvester’s style, [1040].
On the idea of invariance, [1746].
Magnitude, Grassmann’s definition, [105].
Magnus, On the aim in teaching m., [505].
Manhattan Island, Cost of, [2130].
Marcellus, Estimate of Archimedes, [909].
Maschke, Man above method, [650].
Masters, On the reading of the, [614].
Mathematic,
Sylvester on use of term, [101].
Bacon’s use of term, [106].
Mathematical faculty, Frequency of, [832].
Mathematical mill, The, [239], [1891].
Mathematical productions, [648], [649].
Mathematical theory, When complete, [636], [637].
Mathematical training, [443], [444].
Maxims of math’ns, [630], [631], [649].
Not a computer, [1211].
Intellectual habits of math’ns, [1428].
The place of the, [1529].
Characteristics of the mind of a, [1534].
Mathematician, The, Chapter [VIII].
Mathematics,
Definitions of, Chapter [I].
Objects of, Chapter [I].
Nature of, Chapter [II].
Estimates of, Chapter [III].
Value of, Chapter [IV].
Teaching of, Chapter [V].
Study of, Chapter [VI].
Research in, Chapter [VI].
Modern, Chapter [VII].
As a fine art, Chapter [XI].
As a language, Chapter [XII].
Also [445], [1814].
And logic, Chapter [XIII].
And philosophy, Chapter [XIV].
And science, Chapter [XV].
And applications, Chapter [XV].
Knowledge most in, [214].
Suppl. brevity of life, [218].
The range of, [269].
Compared to French language, [311].
The care of great men, [322].
And professional education, [429].
And science teaching, [522].
The queen of the sciences, [975].
Advantage over philosophy, [1436], [1438].
As an instrument, [1506].
For its own sake, [1540], [1541], [1545], [1546].
The wings of, [1604].
Mathesis, [274], [276], [1870], [2015].
Mathews,
On Disqu. Arith. [1638].
On number theory, [1639].
The symbol ≡, [1646].
On Cyclotomy, [1647].
Laws of algebra, [1709].
On infinite, zero, infinitesimal, [1954].
Maxims of great math’ns, [630], [631], [649].
Maxwell, [1043], [1116].
McCormack,
On the unpopularity of m., [270].
On function, [1933].
Méchanique céleste, [985], [986].
Medicine, M. and the study of, [1585], [1918].
Mellor,
Definition of higher m., [108].
Conclusions involved in premises, [238].
On m. and science, [1561].
On the calculus, [1912].
On integration, [1923], [1925].
Memory in m., [253].
Menæchmus, [901].
Mere math’ns, [820], [821].
Merz,
On the transforming power of m., [303].
On the dominant ideas in m., [725].
On extreme views in m., [827].
On Leibnitz’s work, [989].
On the math. tendency of Leibnitz, [990].
On m. as a lens, [1515].
M. extends knowledge, [1524].
Disquisitiones Arithmeticae, [1637].
On functions, [1932].
On hyper-space, [2036].
Metaphysics, M. the only true, [305].
Meteorology and m., [1557].
Method of m. [212-215], [226], [227], [230], [235], [244], [806], [1576].
Metric system, [1725].
Military training, M. in, [314], [418], [1574].
Mill,
On induction in m., [221], [222].
On generalization in m., [245].
On math. studies, [409].
On m. in a scientific education, [444].
Math’ns hard to convince, [811].
Math’ns require genius, [819].
On Comte, [942].
On Descartes, [942], [948].
On Sir William Hamilton’s ignorance of m., [978].
On Leibnitz, [987].
On m. and philosophy, [1421].
On m. as training for philosophers, [1422].
M. indispensable to science, [1519].
M. and social science, [1595].
On the nature of geometry, [1838].
On geometrical method, [1861].
On the calculus, [1903].
Miller, On the Darmstaetter prize, [2129].
Milner, Geometry and poetry, [1118].
Minchin, On English text-books, [539].
Mineralogy and m., [1558].
Minkowski, On integral numbers, [1636].
Miracles and m., [2157], [2158], [2160].
Mixed m.,
Bacon’s definition of, [106].
Whewell’s definition of, [107].
Modern algebra, [1031], [1032], [1638], [1741].
Modern geometry, [1710-1713], [715], [716], [1878].
Modern m., Chapter [VII].
Moebius,
Math’ns constitute a favorite class, [809].
M. a fine art, [1107].
Moral science and m., [1438-1440].
Moral value of m., See ethical value.
Mottoes,
Of math’ns, [630], [631], [649].
Of Pythagoreans, [1833].
Murray, Definition of m., [116].
Music and m., [101], [276], [965], [1107], [1112], [1116], [1127], [1128], [1130-1133], [1135], [1136].
Myers,
On m. as a school subject, [403].
On pleasure in m., [454].
On the ethical value of m., [457].
On the value of arithmetic, [1622].
Mysticism and numbers, [2136-2141], [2143].
Napier’s rule, [1888].
Napoleon,
M. and the welfare of the state, [313].
His interest in m., [314], [1001].
Natural science and m.,
Chapter [XV].
Also [244], [444], [445], [501].
Natural selection, [1921].
Nature of m.,
Chapter [II].
See also [815], [1215], [1308], [1426],[1525], [1628].
Nature, Study of, [433-436], [514], [516], [612].
Navigation and m., [1543], [1544].
Nelson, Anagram on, [2153].
Neptune, Discovery of, [1554], [1559].
Newcomb, On geometrical paradoxers, [2113].
Newton,
Importance of his work,[333].
On correlation in m., [526].
On problems in algebra, [530].
And Gauss compared, [827].
His fame, [1002].
Emerson on, [1003].
Whewell on, [1004],[1005].
Arago on, [1006].
Pope on, [1007].
Southey on, [1008].
Hill on, [1009].
Leibnitz on, [1010].
Lagrange on, [1011].
No monument to, [1012].
Wilson on, [1012], [1013].
His genius, [1014].
His interest in chemistry and theology, [1015].
And alchemy, [1016], [1017].
His first experiment, [1018].
As a lecturer, [1019].
As an accountant, [1020].
His memorandum-book, [1021].
His absent-mindedness, [1022].
Estimate of himself, [1023-1025].
His method of work, [1026].
Discovery of the calculus, [1027].
Anagrams on, [1028].
Gauss’s estimate of, [1029].
On geometry, [1811].
Compared with Euclid, [1827].
Geometry a mechanical science, [1865].
Test of simplicity, [1892].
Method of fluxions, [1902].
Newton’s rule, [1743].
Nile, Origin of name, [2150].
Noether,
On Cayley, [931].
On Sylvester, [1034], [1041].
Non-euclidean geometry, [1322], [2016-2029], [2033], [2035], [2040].
Nonnus, On the mystic four, [2148].
Northrup, On Lord Kelvin, [1048].
Notation,
Importance of, [634], [1222], [1646].
Value of algebraic, [1213], [1214].
Criterion of good, [1216].
On Arabic, [1217], [1614].
Advantage of math., [1220].
See also symbolism.
Notions,
Cardinal of m., [110].
Indefinable, [1219].
Novalis, Definition of pure m., [112].
M. the life supreme, [329].
Without enthusiasm no m., [801].
Method is the essence of m., [806].
Math’ns not good computers, [810].
Music and algebra, [1128].
Philosophy and m., [1406].
M. and science, [1507], [1526].
M. and historic science, [1599].
M. and magic, [2159].
M. and miracles, [2160].
Number,
Every inquiry reducible to a question of, [1602].
And nature, [1603].
Regulates all things, [1605].
Aeschylus on, [1606].
Definition of, [1609], [1610].
And superstition, [1632].
Distinctness of, [1707].
Of the beast, [2151], [2152].
Number-theory,
The queen of m., [975].
Nature of, [1639].
Gauss on, [1644].
Smith on, [1645].
Notation in, [1646].
Aid to geometry, [1647].
Mystery in, [1648].
Number-work, Purpose of, [1623].
Numbers,
Pythagoras’ view of, [321].
Mighty are, [1568].
Aptitude for, [1617].
Demonstrations in, [1630].
Prime, [1648].
Necessary truths like, [1966].
Round, [2137].
Odd, [2138-2141].
Golden, [2142].
Magic, [2143].
Obscurity in m. and philosophy, [1407].
Observation in m., [251-253], [255], [433], [1830].
Obviousness in m., [985], [986], [1045].
Olney, On the nature of m., [253].
Oratory and m., [829], [830].
Order and arrangement, [725].
Origin of m., [1412].
Orr, Memory verse for π, [2127].
Osgood, On the calculus, [1913].
Ostwald, On four-dimensional space, [2039].
π.
In actuarial formula, [945].
Memory verse for, [2127].
Pacioli, On the number three, [2145].
Painting and m., [1103], [1107].
Papperitz, On the object of pure m., [111].
Paradoxes, Chapter [XXI].
Parallel axiom,
Proof of, [984], [2110], [2111].
See also non-euclidean geometry.
Parker,
Definition of arithmetic, [1611].
Number born in superstition, [1632].
On geometry, [1805].
Parton, On Newton, [1917-1919], [1021], [1022], [1827].
Pascal, Logic and m., [1306].
[Peacock],
On the mysticism of Greek [philosophers], [2136].
The Yankos word for three, [2144].
The number of the beast, [2152].
Pearson, M. and natural selection, [834].
Peirce, Benjamin,
Definition of m., [120].
M. as an arbiter, [210].
Logic dependent on m., [1301].
On the symbol √-1, [1733].
Peirce, C. S.
Definition of m., [133].
On accidental relations, [2128].
Perry, On the teaching of m., [510], [511], [519], [837].
Persons and anecdotes, Chapters [IX]. and [X].
Philosophy and m.,
Chapter [XIV].
Also [332], [401], [414], [444], [445], [452].
Physics and m., [129], [437], [1516], [1530], [1535], [1538], [1539], [1548], [1549], [1550], [1555], [1556].
Physiology and m., [1578], [1581], [1582].
Picard, On the use of equations, [1891].
Pierce, On infinitesimals, [1940].
Pierpont,
Golden age of m., [701].
On the progress of m., [708].
Characteristics of modern m., [717].
On variability, [721].
On divergent series, [1937].
Plato,
His view of m., [316], [429].
M. a study suitable for freemen, [317].
His conic sections, [332].
And Archimedes, [904].
Union of math. and philosophical productivity, [1404].
Diagonal of square, [1411].
And Archytas, [1427].
M. and the arts, [1567].
On the value of m., [1574].
On arithmetic, [1620], [1621].
God geometrizes, [1635], [1636]. [1702].
On geometry, [429], [1803], [1804], [1806], [1844], [1845].
Pleasure, Element of in m., [1622], [1629], [1848], [1850], [1851].
Pliny, [2039].
Plus and minus signs, [1727].
Plutarch,
On Archimedes, [903], [904], [908-910], [912].
God geometrizes, [1802].
Poe, [417].
Poetry and m.,
Weierstrass on, [802].
Pringsheim on, [1108].
Wordsworth on, [1117].
Milner on, [1118].
Workman on, [1120].
Pollock on, [1121].
Hoffman on, [1122].
Thoreau on, [1123].
Emerson on, [1124].
Hill on, [1125], [1126].
Shakespeare on, [1127].
Poincaré,
On elegance in m., [640].
M. has a triple end, [1102].
M. as a language, [1208].
Geometry not an experimental science, [1867].
On geometrical axioms, [2005].
Point, [1816].
Political science, M. and, [1201], [1324].
Politics, Math’ns and, [814].
Pollock, On Clifford, [938-941], [1121].
Pope, [907], [2015], [2031], [2046].
Precision in m., [228], [639], [728].
Precocity in m., [835].
Predicabilia a priori, [2003].
Press, M. ignored by daily, [731], [732].
Price,
Characteristics of m., [247].
On m. and physics, [1550].
Prime numbers, Sylvester on, [1648].
Principia Mathematica, [1326].
Pringsheim,
M. the science of the self-evident, [232].
M. should be studied for its own sake, [439].
On the indirect value of m., [448].
On rigor in m., [535].
On m. and journalism, [732].
On math’ns in public service, [824].
Math’n somewhat of a poet, [1108].
On music and m., [1132].
On the language of m., [1211].
On m. and physics, [1548].
Probabilities, [442], [823], [1589], [1590-1592], [1962-1972], [1975].
Problem solving, [531], [532].
Problems,
In m., [523], [534].
In arithmetic, [528].
In algebra, [530].
Should be simple, [603].
In Cambridge texts, [608].
On solution of, [611].
On importance of, [624], [628].
What constitutes good, [629].
Aid to research, [644].
Of modern m., [1926].
Proclus,
Ptolemy and Euclid, [951].
On characteristics of geometry, [1869].
Progress in m., [209], [211], [212], [216], [218], [702-705], [708].
Projective geometry, [1876], [1877], [1879], [1880].
Proportion,
Euclid’s doctrine of, [1834].
Euclid’s definition of, [1835].
Proposition, [1219], [1419].
Prussia, M. in, [513].
Pseudomath, Defined, [2101].
Psychology and m., [1576], [1583], [1584].
Ptolemy and Euclid, [951].
Public service, M. and, [823], [824], [1303], [1574].
Public speaking, M. and, [420], [829], [830].
Publications, Math. of present day, [702], [703].
Pure M.,
Bacon’s definition of, [106].
Whewell’s definition of, [107].
On the object of, [111], [129].
Novalis’ conception of, [112].
Hobson’s definition of, [118].
Russell’s definition of, [127], [128].
Pursuit of m., [842].
Pythagoras,
Number the nature of things, [321].
Union of math, and philosophical productivity, [1404].
The number four, [2147].
Pythagorean brotherhood, Motto of, [1833].
Pythagorean theorem, [1854-1856], [2026].
Pythagoreans, Music and M., [1130].
Quadrature, See Squaring of the circle.
Quantity, Chrystal’s definition of, [115].
Quarles, On quadrature, [2116].
Quaternions, [333], [841], [937], [1044], [1210], [1718-1726].
Quetelet, Growth of m., [1514].
Railway-making, [1570].
Reading of m., [601], [604-606].
Reason,
M. most solid fabric of human, [308].
M. demonstrates supremacy of human, [309].
Reasoning,
M. a type of perfect, [307].
M. as an exercise in, [423-427], [429], [430], [1503].
Recorde, Value of arithmetic, [1619].
Regiomontanus, [1543].
Regular solids, [2132-2135].
Reid,
M. frees from sophistry, [215].
Conjecture has no place in m., [234].
M. the most solid fabric, [308].
On Euclid’s elements, [955].
M. manifests what is impossible [1414].
On m. and philosophy, [1423].
Probability and Christianity, [1975].
On Pythagoras and the regular solids, [2132].
Reidt,
M, as an exercise in language, [419].
On the ethical value of m., [456].
On aim in math. instruction, [506].
Religion and m., [274-276], [459], [460], [1013].
Research in m., Chapter [VI].
Reversible verses, [2156].
Reye, Advantages of modern over ancient geometry, [714].
Rhetoric and m., [1599].
Riemann, On m. and physics, [1549].
Rigor in m., [535-538].
Rosanes, On the unpopularity of m., [730].
Royal road, [201], [901], [951], [1774].
Royal science, M. a, [204].
Rudio,
On Euler, [957].
M. and great artists, [1105].
On m. and navigation, [1543].
Rush, M. cures predisposition to anger, [458].
Russell,
Definition of m., [127], [128].
On nineteenth century m., [705].
Chief triumph of modern m., [706].
On the infinite, [723].
On beauty in m., [1104].
On the value of symbols, [1219].
On Boole’s Laws of Thought, [1318].
Principia Mathematica, [1326].
On geometry and philosophy, [1410].
Definition of number, [1609].
Fruitful uses of imaginaries, [1735].
Geometrical reasoning circular, [1864].
On projective geometry, [1879].
Zeno’s problems, [1938].
Definition of infinite collection, [1959].
On proofs of axioms, [2013].
On non-euclidean geometry, [2018].
Safford,
On aptitude for m., [520].
On m. and science, [1509].
Sage, Battalions of figures, [1631].
Sartorius, Gauss on the nature of space, [2034].
Scepticism, [452], [811].
Schellbach,
Estimate of m., [306].
On truth, [1114].
Schiller, Archimedes and the youth, [907].
Schopenhauer,
Arithmetic rests on the concept of time, [1613].
Predicabilia a priori, [2003].
Schröder, M. as a branch of logic, [1323].
Schubert,
Three characteristics of m., [229].
On controversies in m., [243].
Characteristics of m., [263].
M. an exclusive science, [734].
Science and m.,
Chapter [XV].
M. an indispensible tool of, [309].
Neglect of m. works injury to, [310].
Craig on origin of new, [646].
Greek view of, [1429].
Six follies of, [2107].
See also [433], [436], [437], [461], [725].
Scientific education, Math. training indispensable basis of, [444].
Screw,
The song of the, [1894].
As an instrument in geometry, [2114].
Sedgwick, Quaternion of maladies, [1723].
Segre,
On research in m., [619].
What kind of investigations are important, [641].
On the worthlessness of certain investigations, [642], [643].
On hyper-space, [2031].
Seneca, Alexander and geometry, [902].
Seventy-seven, The number, [2149].
Shakespeare, [1127], [1129], [2141].
Shaw, J. B., M. like game of chess, [840].
Shaw, W. H., M. and professional life, [1596].
Sherman, M. and rhetoric, [1599].
Smith, Adam, [1324].
Smith, D. E.,
On problem solving, [532].
Value of geometrical training, [1846].
Reason for studying geometry, [1850].
Smith, H. J. S.,
When a math. theory is completed, [637].
On the growth of m., [1521].
On m. and science, [1542].
On m. and physics, [1556].
On m. and meteorology, [1557].
On number theory, [1645].
Rigor in Euclid, [1829].
On Euclid’s doctrine of proportion, [1834].
Smith, W. B.,
Definition of m., [121].
On infinitesimal analysis, [1914].
On non-euclidean and hyperspaces, [2033].
Simon, On beauty and truth, [1114].
Simplicity in m., [315], [526].
Sin₂φ, On the notation of, [1886].
Six hundred sixty-six, The number, [2151], [2152].
Social science and m., [1201], [1586], [1587].
Social service, M. as an aid to, [313], [314], [328].
Social value of m., [456], [1588].
Solitude and m., [1849], [1851].
Sophistry, M. free from, [215].
Sound, M. and the theory of, [1551].
Southey, On Newton, [1008].
Space,
Of experience, [2011].
Kant’s doctrine of, [2003].
Schopenhauer’s predicabilia, [2004].
Whewell, On the idea of, [2004].
Non-euclidean, [2015], [2016], [2018].
Hyper-, [2030], [2031], [2033], [2036-2038].
Spedding, On Bacon’s knowledge of m., [917].
Speer, On m. and nature-study, [514].
Spence, On Newton, [1016], [1020].
Spencer, On m. in the arts, [1570].
Spherical trigonometry, [1887].
Spira mirabilis, [922].
Spottiswoode, On the kingdom of m., [269].
Squaring the circle, [1537], [1858], [1934], [1948], [2115-2117].
St. Augustine, The number seventy seven, [2149].
St. Vincent, As a circle-squarer, [2109].
Steiner, On projective geometry, [1877].
Stewart,
M. and facts, [237].
On beauty in m., [242].
What we most admire in m., [315].
M. for its own sake, [440].
M. the noblest instance of force of the human mind, [452].
Math’ns and applause, [816].
Mere math’ns, [821].
Shortcomings of math’ns, [828].
On the influence of Leibnitz, [988].
Reason supreme, [1424].
M. and philosophy compared, [1428].
M. and natural philosophy, [1555].
Stifel, The number of the beast, [2152].
Stobæus,
Alexander and Menæchmus, [901].
Euclid and the student, [952].
Study of m., Chapter [VI].
Substitution, Concept of, [727].
Superstition,
M. frees mind from, [450].
Number was born in, [1632].
Surd numbers, [1728].
Surprises, M. rich in, [202].
Swift,
On m. and politics, [814].
The math’ns of Laputa, [2120-2122].
The math. school of Laputa, [2123].
His ignorance of m., [2124], [2125].
Sylvester,
On the use of the terms mathematic and mathematics, [101].
Order and arrangement the basic ideas of m., [109], [110].
Definition of algebra, [110].
Definition of arithmetic, [110].
Definition of geometry, [110].
On the object of pure m., [129].
M. requires harmonious action of all the faculties, [202].
Answer to Huxley, [251].
On the nature of m., [251].
On observation in m., [255].
Invention in m., [260].
M. entitled to human regard, [301].
On the ethical value of m., [449].
On isolated theorems, [620].
“Auge et impera.” [631].
His bent of mind, [645].
Apology for imperfections, [648].
On theoretical investigations, [658].
Characteristics of modern m., [724].
Invested m. with halo of glory, [740].
M. and eloquence, [829].
On longevity of math’ns, [839].
On Cayley, [930].
His view of Euclid, [936].
Jacobi’s talent for philology, [980].
His eloquence, [1030].
Researches in quantics, [1032].
His weakness, [1033], [1036], [1037].
One-sided character of his work, [1034].
His method, [1035], [1036], [1041].
His forgetfulness, [1037], [1038].
Relations with students, [1039].
His style, [1040], [1041].
His characteristics, [1041].
His enthusiasm, [1041].
The math. Adam, [1042].
And Weierstrass, [1050].
On divine beauty and order in m., [1101].
M. among the fine arts, [1106].
On music and m., [1131].
M. the quintessence of language, [1205].
M. the language of the universe, [1206].
On prime numbers, [1648].
On determinants, [1740].
On invariants, [1742].
Contribution to theory of equations, [1743].
To a missing member etc., [1745].
Invariants and isomerism, [1750].
His dislike for Euclid, [1826].
On the invention of integrals, [1922].
On geometry and analysis, [1931].
On paradoxes, [2104].
Symbolic language,
M. as a, [1207], [1212].
Use of, [1573].
Symbolic logic, [1316-1321].
Symbolism,
On the nature of math., [1210].
Difficulty of math., [1218].
Universal impossible, [1221].
See also notation.
Symbols, Burlesque on, [1741].
Symbols,
M. leads to mastery of, [421].
Value of math., [1209], [1212],[1219].
Essential to demonstration, [1316].
Arithmetical, [1627].
Tact in m., [622], [623].
Tait,
On the unpopularity of m., [740].
And Thomson, [1043].
And Hamilton, [1044].
On quaternions, [1724-1726].
On spherical trigonometry, [1887].
Talent, Math’ns men of, [825].
Teaching of m., Chapter [V].
Tennyson, [1843].
Teutonic race, Aptitude for m., [838].
Text-books,
Chrystal on, [533].
Minchin on, [539].
Cremona on English, [609].
Glaisher on need of, [635].
Thales, [201].
Theoretical investigations, [652-664].
Theory and practice, [661].
Thompson, Sylvanus,
Lord Kelvin’s definition of a math’n, [822].
Cayley’s estimate of quaternions, [937].
Thomson’s “It is obvious that,” [1045].
Anecdote of Lord Kelvin, [1046], [1047].
On the calculus for beginners, [1917].
Thomson, Sir William,
M. the only true metaphysics, [305].
M. not repulsive to common sense, [312].
What is a math’n? [822].
And Tait, [1043].
“It is obvious that,” [1045].
Anecdotes concerning, [1046], [1047], [1048].
On m. and astronomy, [1562].
On quaternions, [1721], [1722].
Thomson and Tait, [1043].
On Fourier’s theorem, [1928].
Thoreau, On poetry and m., [1123].
Thought-economy in m., [203], [1209], [1704].
Three,
The Yankos word for, [2144].
Pacioli on the number, [2145].
Time,
Arithmetic rests on notion of [1613].
As a concept in algebra, [1715], [1716], [1717].
Kant’s doctrine of, [2001].
Schopenhauer’s predicabilia, [2003].
Todhunter,
On m. as a university subject, [405].
On m. as a test of performance, [408].
On m. as an instrument in education, [414].
M. requires voluntary exertion, [415].
On exercises, [422].
On problems, [523], [608].
How to read m., [605], [606].
On discovery in elementary m., [617].
On Sylvester’s theorem, [1743].
On performance in Euclid, [1818].
Transformation, Concept of, [727].
Trigonometry, [1881], [1884-1889].
Trilinear co-ordinates, [611].
Trisection of angle, [2112].
Truth,
and m., [306].
Math’ns must perceive beauty of, [803].
And beauty, [1114].
Tzetzes, Plato on geom., [1803].
Unity, Locke on the idea of, [1607].
Universal algebra, [1753].
Universal arithmetic, [1717].
Universal language, [925].
Unpopularity of m., [270], [271], [730-736], [738], [740], [1501], [1628].
Usefulness, As a principle in research, [652-655], [659], [664].
Uses of m., See value of m.
Value of m.,
Chapter [IV].
See also [330], [333], [1414], [1422], [1505], [1506], [1512], [1523], [1526], [1527], [1533], [1541], [1542], [1543], [1547-1576], [1619-1626], [1841], [1844-1851].
Variability, The central idea of modern m., [720], [721].
Venn,
On m. as a symbolic language, [1207].
M. the only gate, [1517].
Viola, On the use of fallacies, [610].
Virgil, [2138].
Voltaire,
Archimedes more imaginative than Homer, [259].
M. the staff of the blind, [461].
On direct usefulness of results, [653].
On infinite magnitudes, [1947].
On the symbol, [1950].
Anagram on, [2154].
Walcott, On hyperbolic functions, [1930].
Walker,
On problems in arithmetic, [528].
On the teaching of geometry, [529].
Wallace, On the frequency of the math. faculty, [832].
On m. and natural selection, [833], [834].
Parallel growth of m. and music, [1135].
Walton, Angling like m., [739].
Weber, On m. and physics, [1549].
Webster, Estimate of m., [331].
Weierstrass,
Math’ns are poets, [802].
Anecdote concerning, [1049].
And Sylvester, [1050].
Problem of infinitesimals, [1938].
Weismann, On the origin of the math. faculty, [1136].
Wells, On m. as a world language, [1201].
Whately,
On m. as an exercise, [427].
On m. and navigation, [1544].
On geometrical demonstrations, [1839].
On Swift’s ignorance of m., [2124].
Whetham, On symbolic logic, [1319].
Whewell,
On mixed and pure math., [107].
M. not an inductive science, [223].
Nature of m., [224].
Value of geometry, [445].
On theoretical investigations, [660], [662].
Math’ns men of talent, [825].
Fame of math’ns, [826].
On Newton’s greatness, [1004].
On Newton’s theory, [1005].
On Newton’s humility, [1025].
On symbols, [1212].
On philosophy and m., [1429].
On m. and science, [1534].
Quotation from R. Bacon, [1547].
On m. and applications, [1541].
Geometry and experience, [1814].
Geometry not an inductive science, [1830].
On limits, [1909].
On the idea of space, [2004].
On Plato and the regular solids, [2133], [2135].
White, H. S., On the growth of m., [211].
White, W. F.,
Definition of m., [131], [1203].
M. as a prerequisite for public speaking, [420].
On beauty in m., [1119].
The place of the math’n, [1529].
On m. and social science, [1586].
The cost of Manhattan island, [2130].
Whitehead, On the ideal of m., [119].
Definition of m., [122].
On the scope of m., [126].
On the nature of m., [233].
Precision necessary in m., [639].
On practical applications, [655].
On theoretical investigations, [659].
Characteristics of ancient geometry, [713].
On the extent of m., [737].
Archimedes compared with Newton, [911].
On the Arabic notation, [1217].
Difficulty of math. notation, [1218].
On symbolic logic, [1320].
Principia Mathematica, [1326].
On philosophy and m., [1403].
On obscurity in m. and philosophy, [1407].
On the laws of algebra, [1708].
On + and − signs, [1727].
On universal algebra, [1753].
On the Cartesian method, [1890].
On Swift’s ignorance of m., [2125].
Whitworth, On the solution of problems, [611].
Williamson,
On the value of m., [1575].
Infinitesimals and limits, [1905].
On infinitesimals, [1946].
Wilson, E. B.,
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