Abbott 1001
Abstract method, Development of 729
Abstract nature of m., Reason for 638
Abstract reasoning, Objection to 1941
Abstractness, math., Compared with logical 1304
Adams, Henry, M. and history 1699
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 1632
Alexander 901 902
Algebra Chapter XVII
Algebra, Advantages of 1701 1703 1705
Algebra, and geometry 525—527 1610 1707
Algebra, As an art 1711
Algebra, Burlesque on modern 1741
Algebra, Definitions of 110 1714 1715
Algebra, Designations of 1717
Algebra, Hume on 1863
Algebra, laws of 1708—1710
Algebra, Of use to grown men 425
Algebra, Origin of 1736
Algebra, Problems in 320 530 1738
Algebra, Review of 1713
Algebraic notation, value of 1213 1214
Algebraic treatises, How to read 601
Amusements in m. 904 905
Anagrams, On De Morgan 947
Anagrams, On Domus Lescinia 2155
Anagrams, On Flamsteed 968
Anagrams, On Macaulay 996
Anagrams, On Nelson 2153
Anagrams, On Newton 1028
Anagrams, On Voltaire 2154
Analysis, Invigorates the faculty of resolution 416
Analysis, Relation of geometry to 1931
Analytical geometry 1889 1890 1893
Analytical geometry, Burlesque on 2040
Analytical geometry, Importance of 949
Analytical geometry, Method of 310
Ancient geometry, Characteristics of 712 714
Ancient geometry, Compared with modem 1711— 1716
Ancient geometry, Method of 1425 1873—1875
Ancients, M. among the 321
And Plato 1427
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
Anglo-Saxons, Newton as representative of 1014
Anonymous, Song of the screw 1894
Applied m. 1312
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
Arago, M. the enemy of scientific romances, Euler as a computer 962
Arago, M. the enemy of scientific romances, Euler, “analysis incarnate” 961
Arago, M. the enemy of scientific romances, Geometry as an instrument 1868
Arago, M. the enemy of scientific romances, Newton’s efforts superhuman 1006
Arago, M. the enemy of scientific romances, On Kepler’s discovery 982
Arago, M. the enemy of scientific romances, On probabilities 1591
Arbuthnot, M. compared to music 1112
Arbuthnot, M. frees from prejudice, credulity and superstition 449
Arbuthnot, M. the friend of religion 468
Arbuthnot, On math, reasoning 1603
Archimedes, And engineering 908
Archimedes, Character of his work 912 913
Archimedes, Compared with Newton 911
Archimedes, Death of 909
Archimedes, Estimate of math, appliances 904—906 908
Archimedes, His machines 903 904
Archimedes, His tomb 910
Archimedes, Schiller on 907
Archimedes, Wordsworth on 906
Architecture and m. 276
Archytas 904
Aristippus the Cyrenaic 845
Aristotle 914
Aristotle, On relation of m. to esthetics 318
Arithmetic Chapter XVI
Arithmetic, A master-key 1571
Arithmetic, As logic 1624 1625
Arithmetic, Based on concept of time 1613
Arithmetic, Definitions of 106 110 1611 1612 1714
Arithmetic, Emerson on advantage of study of 408
Arithmetic, Higher 1755
Arithmetic, Hume on 1863
Arithmetic, Method of teaching 1618
Arithmetic, Problems in 528
Arithmetic, Purpose of teaching 454 1624
Arithmetic, The queen of m. 1642
Arithmetical theorems 1639
Art, M. as a fine Chapter XI
Arts, M. and the 1568—1570 1573
Astronomy and m. 1554 1559 1562—1567
Authority in science 1528
Axioms 518 2015
Axioms, And the idea of space 2004
Axioms, Def. in disguise 2005
Axioms, Euclid’s 2007—2010 2014
Axioms, In geometry 1812 2004 2006
Axioms, Nature of 2012
Axioms, Proofs of 2013
Babbage 923
Bacon, Lord, Classification of m. 106
Bacon, Lord, Growth of m. 1611
Bacon, Lord, His knowledge of m. 917 918
Bacon, Lord, His view of m. 916 916
Bacon, Lord, M. and logic 1310
Bacon, Lord, M. cures distraction of mind 412
Bacon, Lord, M. develops concentration of mind 411
Bacon, Lord, M. essential to study of nature 436
Bacon, Lord, M. held in high esteem by ancients 321
Bacon, Lord, M. makes men subtile 248
Bacon, Lord, On the generalizing power of m. 327
Bacon, Lord, On the value of math, studies 410
Bacon, Lord, View of m. 316 915 916
Bacon, Roger, Neglect of m. works injury to all science 310
Bacon, Roger, On the value of m. 1647
Bain, Importance of m. in education 442
Bain, M. and science teaching 622
Bain, On the charm of the study of m. 463
Bain, Teaching of arithmetic 1618
Ball, R. S. 2010
Ball, W. W. R., Advance in physics 1630
Ball, W. W. R., De Morgan and the actuary 946
Ball, W. W. R., Gauss as astronomer 971
Ball, W. W. R., Gauss’s estimate of Newton 1029
Ball, W. W. R., Lagrange, Laplace and Gauss contrasted 993
Ball, W. W. R., Laplace’s “It is easy to see” 986
Ball, W. W. R., M. and philosophy 1417
Ball, W. W. R., Newton’s interest in chemistry and theology 1016
Ball, W. W. R., Notation of the calculus 1904
Ball, W. W. R., On Babbage 923
Ball, W. W. R., On Demoivre’s death 944
Ball, W. W. R., On Newton’s discovery of the calculus 1027
Ball, W. W. R., On Newton’s method of work 1026
Ball, W. W. R., Plato on geometry 1804
Barnett, M. the type of perfect reasoning 307
Barrow, Euclid’s definition of proportion 1836
Barrow, Eulogy of m. 330
Barrow, M. and eloquence 830
Barrow, M. as a discipline of the mind 402
Barrow, On surd numbers 1728
Barrow, On the method of m. 213 227
| Barrow, Philosophy and m. 1430
Barrow, Uses of m. 1672
Beattie 1431
Beauty of m. 453 824 1208
Beauty of m., And truth 1114
Beauty of m., Consists in simplicity 242 315
Beauty of m., Kummer on 1111
Beauty of m., Russell on 1104
Beauty of m., Sylvester on 1101
Beauty of m., White on 1119
Beauty of m., Young on 1110
Beltrami, On reading of the masters 614
Berkeley, On fluxions 1916 1942—1944
Berkeley, On geometry as logic 428
Berkeley, On infinite divisibility 1946
Berkeley, On math, symbols 1214
Bernoulli, Daniel 919
Bernoulli, James, Computation of sum of tenth powers of numbers 921
Bernoulli, James, Discussion of logarithmic spiral 922
Bernoulli, James, Legend for his tomb 920 922
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
Bocher, Geometry as a natural science 1866
Bocher, Interrelation of m. and logic 1313
Bocher, M. likened to painting 1103
Boeme, On Pythagoras 1866
Bois-Reymond, Natural selection and the calculus 1921
Bois-Reymond, On the analytic method 1893
Boltzmann on 1116
Boltzmann, On beauty in m. 1116
Bolyai, Janos, Duel with officers 924
Bolyai, Janos, Science absolute of space 926
Bolyai, Janos, Universal language 925
Bolyai, Wolfgang 927
Bolyai, Wolfgang, On Gauss 972
Bolzano 928
Bolzano, Cured by Euclid 929
Bolzano, 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. 1406
Boswell 981
Bowditch, On Laplace’s “Thus it plainly appears” 986
Boyle, Advantages of algebra 1703
Boyle, Ignorance of m. 1677
Boyle, M. and physiology 1582
Boyle, M. and science 1613 1633
Boyle, Usefulness of m. to physics 437
Boyle, Wings of m. 1626
Brahmagupta, Estimate of m. 320
Brewster, On Euler as a computer 963
Brewster, On Euler’s knowledge of the Aeneid 959
Brewster, 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
Burkhardt, On universal symbolism 1221
Butler, N. M., Geometry before algebra 1871
Butler, N. M., M. demonstrates the supremacy of the human reason 309
Butler, N. M., M. the most astounding intellectual creation 707
Butler, Samuel 2118
Byerly, On hyperbolic functions 1929
Cajori, On Bolyai 927
Cajori, On the value of the history of m. 616
Calculating machines 1641
Calculation, Importance of 602
Calculation, Not the sole object of m. 268
Calculus Chapter XIX
Calculus, As a method 309
Calculus, Foundation of 253
Calculus, May be taught at an early age 519 1917 1918
Cambridge m. 836 1210
Cantor, On freedom in m. 205 207
Cantor, On the character of Gauss’s writing 976
Cantor, On the infinite 1962
Cantor, Zeno’s problem 1938
Carlisle life tables 946
Carnot, On limiting ratios 1908
Carnot, On the infinitesimal method 1907
Carson, Value of geometrical training 1841
Cartesian method 1889 1890
Carus, Estimate of m. 326
Carus, M. reveals supernatural God 460
Carus, Non-euclidean geometry 2016
Carus, Number and nature 1603
Carus, Zero and infinity 1948
Cathedral, “Petrified mathematics” 1110
Causation in m. 251 254
Cayley, Advantage of modem geometry over ancient 711
Cayley, Compared with Euler 934
Cayley, Forsyth on 932—934
Cayley, Hermite on 935
Cayley, His estimate of quaternions 937
Cayley, His method 933
Cayley, His style 932
Cayley, His view of Euclid 936
Cayley, M. and philosophy 1420
Cayley, Noether on 931
Cayley, On the imaginary 722
Cayley, Sylvester on 930
Cayley’s view of Euclid 936
Cayley’s view of Euclid, On Euler’s math, power 964
Cayley’s view of Euclid, On Indian m. 1737
Cayley’s view of Euclid, On modem calculation 1614
Cayley’s view of Euclid, On music and m. among the Pythagoreans 1130
Cayley’s view of Euclid, On Napier’s rule 1888
Cayley’s view of Euclid, On review in arithmetic 1713
Cayley’s view of Euclid, On Sylvester’s first class at Johns Hopkins 1031
Cayley’s view of Euclid, On the characteristics of ancient geometry 1873
Cayley’s view of Euclid, On the Darmstaetter prize 967
Cayley’s view of Euclid, On the extent of Euler’s work 960
Cayley’s view of Euclid, On the greatest achievement of the Hindoos 1615
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. 266
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
Chrystal, Definition of quantity 116
Chrystal, His algebra 635
Chrystal, How to read m. 607
Chrystal, On Bernoulli’s numbers 921
Chrystal, On Horner’s method 1744
Chrystal, On math, versus logical abstractness 1304
Chrystal, On modem text-books 633
Chrystal, On probabilities 1967
Chrystal, On problem solving 631
Chrystal, On universal arithmetic 1717
Chrystal, Rules of algebra 1710
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 662
Colburn 967
Coleridge, M. the quintessence of truth 2019
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