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.,
- On the social value of m., [1588].
- On m. and economics, [1593].
- On the nature of axioms, [2012].
- Wilson, John,
- On Newton and Shakespeare, [1012].
- Newton and Linnæus, [1013].
- Woodward,
- On probabilities, [1589].
- On the theory of errors, [1973], [1974].
- Wordsworth, W.,
- On Archimedes, [906].
- On poetry and geometric truth, [1117].
- On geometric rules, [1418].
- On geometry, [1840], [1848].
- M. and solitude, [1859].
- Workman, On the poetic nature of m., [1120].
- Young, C. A., On the discovery of Neptune, [1559].
- Young, C. W., Definition of m., [124].
- Young, J. W. A.,
- On m. as type a of thought, [404].
- M. as preparation for science study, [421].
- M. essential to comprehension of nature, [435].
- Development of abstract methods, [729].
- Beauty in m., [1110].
- On Euclid’s axiom, [2014].
- Zeno, His problems, [1938].
- Zero, [1948], [1954].