Bold-faced numbers refer to authors Abbreviations:— m.=mathematics, math.=mathematical, math’n.=mathematician.
inition 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, 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, 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, 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.<
/li> 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, 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, 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, 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. Sin2?, 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
. 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, 101
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