Science and m. Chapter XV
Science, M. an indispensible tool of 309
Segre, On hyper-space 2031
Segre, On research in m. 619
Segre, On the worthlessness of certain investigations 612 613
Segre, What kind of investigations are important 641
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 1696
Sherman, M. and rhetoric 1699
Simon, On beauty and truth 1114
Simplicity in m. 315 526
Sinty, On the notation of 1886
Six hundred sixty-six, The number 2151 2152
Smith, Adam 1324
Smith, D. E., On problem solving 632
Smith, D. E., Reason for studying geometry 1860
Smith, D. E., Value of geometrical training 1846
Smith, H. J. S., On Euclid’s doctrine of proportion 1834
Smith, H. J. S., On m. and meteorology 1567
Smith, H. J. S., On m. and physics 1666
Smith, H. J. S., On m. and science 1642
Smith, H. J. S., On number theory 1646
Smith, H. J. S., On the growth of m. 1621
Smith, H. J. S., Rigor in Euclid 1829
Smith, H. J. S., When a math, theory is completed 637
Smith, W. B., Definition of m. 121
Smith, W. B., On infinitesimal analysis 1914
Smith, W. B., On non-euclidean and hyper-spaces 2033
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, Hyper 2030 2031 2033 2036— 2038
Space, Kant’s doctrine of 2003
Space, non-Euclidean 2015 2016 2018
Space, Of experience 2011
Space, Schopenhauer’s predicabilia 2004
Space, Whewell, On the idea of 2004
Spedding, On Bacon’s knowledge of m. 917
Speer, On m. and nature-study 611
Spence, On Newton 1016 1020
Spencer, On m. in the arts 1670
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
Stewart, M. and natural philosophy 1666
Stewart, M. and philosophy compared 1428
Stewart, M. for its own sake 440
Stewart, M. the noblest instance of force of the human mind 462
Stewart, Math’ns and applause 816
Stewart, Mere math’ns 821
Stewart, On beauty in m. 242
Stewart, On the influence of Leibnitz 988
Stewart, Reason supreme 1424
Stewart, Shortcomings of math’ns 828
Stewart, What we most admire in m. 316
Stifel, The number of the beast 2162
Stobseus, Alexander and Menaechmus 901
Stobseus, Euclid and the student 962
Study of m. Chapter VI
Substitution, Concept of 727
Superstition, M. frees mind from 450
Superstition, Number was bom in 1632
Surd numbers 1728
Surprises, M. rich in 202
Swift, His ignorance of m. 2124 2125
Swift, On m. and politics 814
Swift, The math, school of Laputa 2123
Swift, The math’ns of Laputa 2120— 2122
Sylvester, Answer to Huxley 261
Sylvester, Apology for imperfections 648
Sylvester, Characteristics of modem m. 724
Sylvester, Definition of algebra 110
Sylvester, Definition of arithmetic 110
Sylvester, Definition of geometry 110
Sylvester, His bent of mind 646
Sylvester, Invention in m. 260
Sylvester, Invested m. with halo of glory 740
Sylvester, M. and eloquence 829
Sylvester, M. entitled to human regard 301
Sylvester, M. requires harmonious action of all the faculties 202
Sylvester, On isolated theorems 620
Sylvester, On observation in m. 266
Sylvester, On the ethical value of m. 449
Sylvester, On the nature of m. 261
Sylvester, On the object of pure m. 129
Sylvester, On the use of the terms mathematic and mathematics 101
Sylvester, On theoretical investigations 668
Sylvester, Order and arrangement the basic ideas of m. 109 110
Sylvester, “Auge et impera” 631
Symbolic logic 1316—1321
Symbolism, Difficulty of math. 1218
Symbolism, On the nature of math. 1210
Symbolism, Universal impossible 1221 (see also Notation)
Symbols, Arithmetical 1627
Symbols, Burlesque on 1741
Symbols, Essential to demonstration 1316
Symbols, M. leads to mastery of 421
Symbols, Value of math. 1209 1212 1219
Tact in m. 622 623
Tait, And Hamilton 1044
Tait, And Thomson 1043
Tait, On quaternions 1724—1726
Tait, On spherical trigonometry 1887
Tait, On the unpopularity of m. 740
Talent, Math’ns men of 825
Teaching of m. Chapter V
Tennyson 1843
Teutonic race, Aptitude for m. 838
Textr-books, Chrystal on 533
Textr-books, Glaisher onneedof 635
Textr-books, Minchin on 539
Thales 201
Theoretical investigations 652 664
Theory and practice 661
Thompson, Cayley’s estimate of quaternions 937
Thompson, Sylvanus, Lord Kelvin’s definition of a math’n 822
Thomson and Tait 1043
Thomson and Tait On Fourier’s theorem 1928
Thomson, Sir William, And Tait 1043
Thomson, Sir William, M. not repulsive to common sense 312
Thomson, Sir William, M. the only true metaphysics 306
Thomson, Sir William, What is a math'n 822
Thomson, Sir William, “It is obvious that” 1045
Thomson’s “It is obvious that” 1046
Thoreau, On poetry and m. 1123
Thought-economy in m. 203 1209 1704
Three, Pacioli on the number 2145
Three, The Yankos wordfor 2144
Time, Arithmetic rests on notion of 1613
| Time, As a concept in algebra 1715 1716 1717
Time, Kant’s doctrine of 2001
Time, Schopenhauer’s predicabilia 2003
Todhunter, How to read m. 606 606
Todhunter, M. requires voluntary exertion 416
Todhunter, On discovery in elementary m. 617
Todhunter, On exercises 422
Todhunter, On m. as a test of performance 408
Todhunter, On m. as a university subject 406
Todhunter, On m. as an instrument in education 414
Todhunter, On performance in Euclid 1818
Todhunter, On problems 623 608
Todhunter, On Sylvester’s theorem 1743
Transformation, Concept of 727
Trigonometry 1881 1884—1889
Trilinear co-ordinates 611
Trisection of angle 2112
Truth, And beauty 1114
Truth, and m. 306
Truth, Math’ns must perceive beauty of 803
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 modem m. 720 721
Venn, M. the only gate 1617
Venn, On m. as a symbolic language 1207
Viola, On the use of fallacies 610
Virgil 2138
Voltaire, Anagram on 2154
Voltaire, Archimedes more imaginative than Homer 269
Voltaire, M. the staff of the blind 461
Voltaire, On direct usefulness of results 663
Voltaire, On infinite magnitudes 1947
Voltaire, On the symbol 1960
Walcott, On hyperbolic functions 1930
Walker, On problems in arithmetic 628
Walker, On the teaching of geometry 629
Wallace, On m. and natural selection 833 834
Wallace, On the frequency of the math, faculty 832
Wallace, Parallel growth of m. and music 1136
Walton, Aagling like m. 739
Weber, On m. and physics 1649
Webster, Estimate of m. 331
Weierstrass, And Sylvester 1050
Weierstrass, Anecdote concerning 1049
Weierstrass, Math'ns are poets 802
Weierstrass, Problem of infinitesimals 1938
Weismann, On the origin of the math, faculty 1136
Wells, On m. as a world language 1201
Whately, On geometrical demonstrations 1839
Whately, On m. and navigation 1644
Whately, On m. as an exercise 427
Whately, On Swift’s ignorance of m. 2124
Whetham, On symbolic logic 1319
Whewell, Fame of math'ns 826
Whewell, Geometry and experience 1814
Whewell, Geometry not an inductive science 1830
Whewell, M. not an inductive science 223
Whewell, Math'ns men of talent 826
Whewell, Nature of m. 224
Whewell, On limits 1909
Whewell, On m. ana science 1634
Whewell, On m. and applications 1641
Whewell, On mixed and pure math. 107
Whewell, On Newton's theory 1006
Whewell, On Newton’s greatness 1004
Whewell, On Newton’s humility 1026
Whewell, On philosophy and m. 1429
Whewell, On Plato and the regular solids 2133 2135
Whewell, On symbols 1212
Whewell, On the idea of space 2004
Whewell, On theoretical investigations 660 662
Whewell, Quotationfrom R. Bacon 1647
Whewell, Value of geometry 445
Whewell’s definition of 107
White, H. S., On the growth of m. 211
White, W. F., Definition of m. 131 1203
White, W. F., M. as a prerequisite for public speaking 420
White, W. F., On beauty in m. 1119
White, W. F., On m. and social science 1586
White, W. F., The cost of Manhattan island 2130
White, W. F., The place of the math’n 1529
Whitehead, Archimedes compared with Newton 911
Whitehead, Characteristics of ancient geometry 713
Whitehead, Definition of m. 122
Whitehead, Difficulty of math, notation 1218
Whitehead, On + and — signs 1727
Whitehead, On obscurity in m. and philosophy 1407
Whitehead, On philosophy and m. 1403
Whitehead, On practical applications 655
Whitehead, On Swift’s ignorance of m. 2125
Whitehead, On symbolic logic 1320
Whitehead, On the Arabic notation 1217
Whitehead, On the Cartesian method 1890
Whitehead, On the extent of m. 737
Whitehead, On the ideal of m. 119
Whitehead, On the laws of algebra 1708
Whitehead, On the nature of m. 233
Whitehead, On the scope of m. 126
Whitehead, On theoretical investigations 659
Whitehead, On universal algebra 1753
Whitehead, Precision necessary in m. 639
Whitehead, Principia Mathematica 1326
Whitworth, On the solution of problems 611
Williamson, Infinitesimals and limits 1905
Williamson, On infinitesimals 1946
Williamson, On the value of m 1676
Wilson, E. B., On m. and economics 1593
Wilson, E. B., On the nature of axioms 2012
Wilson, E. B., On the social value of m. 1588
Wilson, John, Newton and Linnaeus 1013
Wilson, John, On Newton and Shakespeare 1012
Woodward, On probabilities 1689
Woodward, On the theory of errors 1973 1974
Wordsworth, W., M. and solitude 1859
Wordsworth, W., On Archimedes 906
Wordsworth, W., On geometric rules 1418
Wordsworth, W., On geometry 1840 1848
Wordsworth, W., On poetry and geometric truth 1117
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., Beauty in m. 1110
Young, J. W. A., Development of abstract methods 729
Young, J. W. A., M. as preparation for science study 421
Young, J. W. A., M. essential to comprehension of nature 435
Young, J. W. A., On Euclid’s axiom 2014
Young, J. W. A., On m. as type a of thought 404
Zeno, His problems 1938
Zero 1948 1954
“Auge et impera” 631
“Divide et impera” 631
“Divinez avant de demontrer” 630
“Eadem mutata resurgo” 920 922
“It is easy to see” 985 986 1045
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